On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/15/2023 4:15 AM, Dan joyce wrote:
> > > On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> > >> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M. Thomasson wrote:
> > >>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> > >>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> > >>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce wrote:
> > >>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.. Thomasson
> > >>>>>> wrote:
> > >>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> > >>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M. Thomasson
> > >>>>>>>> wrote:
> > >>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> > >>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan joyce wrote:
> > >>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan joyce wrote:
> > >>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan joyce wrote:
> > >>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan joyce wrote:
> > >>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4, Chris M.
> > >>>>>>>>>>>>>> Thomasson wrote:
> > >>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> > >>>>>>>>>>>>>>>> I got the square lattice down, using a different algorithm
> > >>>>>>>>>>>>>>>> than James'
> > >>>>>>>>>>>>>>>> version. However, Dan has a new version out, is that right?
> > >>>>>>>>>>>>>>>> Can you post
> > >>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid without
> > >>>>>>>>>>>>>>>> using a path
> > >>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current version of
> > >>>>>>>>>>>>>>>> the lattice:
> > >>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> > >>>>>>>>>>>>>>> [...]
> > >>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>> Here is another one built using a completely different
> > >>>>>>>>>>>>>>> algorithm:
> > >>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> > >>>>>>>>>>>>>> Nice!
> > >>>>>>>>>>>>>> I like the two color idea, one for going right and the other
> > >>>>>>>>>>>>>> one going up and left.
> > >>>>>>>>>>>>>> Has this actually been done before? A lattice that is finite
> > >>>>>>>>>>>>>> in width but --->oo in length.
> > >>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> > >>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path before
> > >>>>>>>>>>>>> their 90 degree turn at the top
> > >>>>>>>>>>>>> of their line.
> > >>>>>>>>>>>>> .
> > >>>>>>>>>>>> Chris, did you receive my photo of the lattice that creates the
> > >>>>>>>>>>>> cells as it goes.
> > >>>>>>>>>>>> No pathways present. Also it will --->oo in all directions..
> > >>>>>>>>>>>> Even very small fractional
> > >>>>>>>>>>>> directions --->oo.
> > >>>>>>>>>>>>
> > >>>>>>>>>>>> I believe this is significant over my original pathway lattice.
> > >>>>>>>>>>>> The reason being that had to follow a pathway back to origin to
> > >>>>>>>>>>>> complete all the cells in
> > >>>>>>>>>>>> any size square lattice --->oo.
> > >>>>>>>>>>>> Even the new one that you propose has finite width and --->oo
> > >>>>>>>>>>>> length.
> > >>>>>>>>>>>> That is a nice one also along with my original but this new one
> > >>>>>>>>>>>> is something else that
> > >>>>>>>>>>>> i am sure some will say not possible.
> > >>>>>>>>>>>> I am going to start to build the sequence of directions R,D,LU
> > >>>>>>>>>>>> to prove it is possible to start a lattice
> > >>>>>>>>>>>> filling cells as you go without lifting the pencil. All the
> > >>>>>>>>>>>> while making 90 degree turns right or left or
> > >>>>>>>>>>>> up or down at the end of each line.
> > >>>>>>>>>>>> What do you think?
> > >>>>>>>>>>>> If this is true, it would be more significant then my original
> > >>>>>>>>>>>> and the new lattice you propose.
> > >>>>>>>>>>> It is true Chris,
> > >>>>>>>>>>>
> > >>>>>>>>>>> A simple straight forward list of directions that
> > >>>>>>>>>>> represents the first rendering I sent you.
> > >>>>>>>>> This one?
> > >>>>>>>>>
> > >>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> > >>>>>>>>> [...]
> > >>>>>>>> Yes!
> > >>>>>>>> That is the list of directions for building it.
> > >>>>>>>> Do it in slow-motion and you will really appreciate the pencil not
> > >>>>>>>> lifting off the page
> > >>>>>>>> or in this case when I enter each direction via keyboard it end up
> > >>>>>>>> as that image
> > >>>>>>>> I sent you.
> > >>>>>>>> I have made the next one but need to capture the directions and
> > >>>>>>>> when I do I will send it along.
> > >>>>>>> Okay. Well, basically, I think a proper animation simply must show all
> > >>>>>>> the different ways this can be constructed. From your originals and my
> > >>>>>>> and James' work, up to your new work. Fair enough?
> > >>>>>> Sounds great!
> > >>>>>> This last one, if you read some of James's remarks that what I just
> > >>>>>> did in this one was not possible.
> > >>>>>> I think James will be surprised when he runs the direction list I
> > >>>>>> just sent. Also more larger ones can be built.
> > >>>>>> It is good to have you guys on board with this. It adds to the effort
> > >>>>>> of perfecting all of this for presentation.
> > >>>>>> Thanks to both you guys.
> > >>>>>
> > >>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > >>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > >>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > >>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> > >>>> [...]
> > >>>>
> > >>>> Looking good. The start circle in red, the origin, is nice and tangent
> > >>>> with the end point, the center of the circle in yellow.
> > >>>>
> > >>>> https://i.ibb.co/zhjM4KY/image.png
> > >>>>
> > >>>> :^D
> > >>>>
> > >>> Actually, not exactly sure where to go from here. I get into dead ends
> > >>> when I want to continue it. Do I go left? If I got right, then I have to
> > >>> go up and have to go left. So, the initial size might be an issue?
> > >>> Humm... Not sure yet.
> > >> Use the original list.
> > >> (L,U,R,D,R,U,L,U) is truncated from the original list only if you want
> > >> a larger lattice.
> > > My smart phone is screwed up. I couldn't open up the animation you sent 2 days ago.
> > > Send to my other e-mail address. Thanks
> > Sorry about the FB link. However, can you go to it and see the content?
> > This one has a path back home:
> >
> > https://www.facebook.com/100034470228086/videos/791843519283462/
> >
> >
> > The following link goes to the one that is the "infinite" builder...
> > Very tall, infinitely tall... ;^D
> >
> > https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> >
> > Many rooms... ;^)
> >
> > lol. ;^)
> Nice presentation on both.
> I like the one color going out and the different color coming back in.
> Thanks.
> You left out the last 8 directions on the original post to complete my new lattice.
> (L,U,R,D,R,U,L,U)
> It probably confused you because just to continue to the next larger lattice the above
> had to be truncated and then I showed the added directions to get the next larger lattice.
> I won't do that again because it is confusing.
> I will just send each larger and larger set of directions for each lattice.
These have to be done in slow motion to really appreciate the pencil not leaving the paper.

On 6/15/2023 4:18 PM, Dan joyce wrote:
> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson wrote:
>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M. Thomasson wrote:
>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce wrote:
>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M. Thomasson
>>>>>>>>> wrote:
>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M. Thomasson
>>>>>>>>>>> wrote:
>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4, Chris M.
>>>>>>>>>>>>>>>>> Thomasson wrote:
>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different algorithm
>>>>>>>>>>>>>>>>>>> than James'
>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is that right?
>>>>>>>>>>>>>>>>>>> Can you post
>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid without
>>>>>>>>>>>>>>>>>>> using a path
>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current version of
>>>>>>>>>>>>>>>>>>> the lattice:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
>>>>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
>>>>>>>>>>>>>>>>>> algorithm:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
>>>>>>>>>>>>>>>>> Nice!
>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and the other
>>>>>>>>>>>>>>>>> one going up and left.
>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that is finite
>>>>>>>>>>>>>>>>> in width but --->oo in length.
>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path before
>>>>>>>>>>>>>>>> their 90 degree turn at the top
>>>>>>>>>>>>>>>> of their line.
>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that creates the
>>>>>>>>>>>>>>> cells as it goes.
>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all directions.
>>>>>>>>>>>>>>> Even very small fractional
>>>>>>>>>>>>>>> directions --->oo.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I believe this is significant over my original pathway lattice.
>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to origin to
>>>>>>>>>>>>>>> complete all the cells in
>>>>>>>>>>>>>>> any size square lattice --->oo.
>>>>>>>>>>>>>>> Even the new one that you propose has finite width and --->oo
>>>>>>>>>>>>>>> length.
>>>>>>>>>>>>>>> That is a nice one also along with my original but this new one
>>>>>>>>>>>>>>> is something else that
>>>>>>>>>>>>>>> i am sure some will say not possible.
>>>>>>>>>>>>>>> I am going to start to build the sequence of directions R,D,LU
>>>>>>>>>>>>>>> to prove it is possible to start a lattice
>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil. All the
>>>>>>>>>>>>>>> while making 90 degree turns right or left or
>>>>>>>>>>>>>>> up or down at the end of each line.
>>>>>>>>>>>>>>> What do you think?
>>>>>>>>>>>>>>> If this is true, it would be more significant then my original
>>>>>>>>>>>>>>> and the new lattice you propose.
>>>>>>>>>>>>>> It is true Chris,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A simple straight forward list of directions that
>>>>>>>>>>>>>> represents the first rendering I sent you.
>>>>>>>>>>>> This one?
>>>>>>>>>>>>
>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
>>>>>>>>>>>> [...]
>>>>>>>>>>> Yes!
>>>>>>>>>>> That is the list of directions for building it.
>>>>>>>>>>> Do it in slow-motion and you will really appreciate the pencil not
>>>>>>>>>>> lifting off the page
>>>>>>>>>>> or in this case when I enter each direction via keyboard it end up
>>>>>>>>>>> as that image
>>>>>>>>>>> I sent you.
>>>>>>>>>>> I have made the next one but need to capture the directions and
>>>>>>>>>>> when I do I will send it along.
>>>>>>>>>> Okay. Well, basically, I think a proper animation simply must show all
>>>>>>>>>> the different ways this can be constructed. From your originals and my
>>>>>>>>>> and James' work, up to your new work. Fair enough?
>>>>>>>>> Sounds great!
>>>>>>>>> This last one, if you read some of James's remarks that what I just
>>>>>>>>> did in this one was not possible.
>>>>>>>>> I think James will be surprised when he runs the direction list I
>>>>>>>>> just sent. Also more larger ones can be built.
>>>>>>>>> It is good to have you guys on board with this. It adds to the effort
>>>>>>>>> of perfecting all of this for presentation.
>>>>>>>>> Thanks to both you guys.
>>>>>>>>
>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
>>>>>>> [...]
>>>>>>>
>>>>>>> Looking good. The start circle in red, the origin, is nice and tangent
>>>>>>> with the end point, the center of the circle in yellow.
>>>>>>>
>>>>>>> https://i.ibb.co/zhjM4KY/image.png
>>>>>>>
>>>>>>> :^D
>>>>>>>
>>>>>> Actually, not exactly sure where to go from here. I get into dead ends
>>>>>> when I want to continue it. Do I go left? If I got right, then I have to
>>>>>> go up and have to go left. So, the initial size might be an issue?
>>>>>> Humm... Not sure yet.
>>>>> Use the original list.
>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if you want
>>>>> a larger lattice.
>>>> My smart phone is screwed up. I couldn't open up the animation you sent 2 days ago.
>>>> Send to my other e-mail address. Thanks
>>> Sorry about the FB link. However, can you go to it and see the content?
>>> This one has a path back home:
>>>
>>> https://www.facebook.com/100034470228086/videos/791843519283462/
>>>
>>>
>>> The following link goes to the one that is the "infinite" builder...
>>> Very tall, infinitely tall... ;^D
>>>
>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
>>>
>>> Many rooms... ;^)
>>>
>>> lol. ;^)
>> Nice presentation on both.
>> I like the one color going out and the different color coming back in.
>> Thanks.
>> You left out the last 8 directions on the original post to complete my new lattice.
>> (L,U,R,D,R,U,L,U)
>> It probably confused you because just to continue to the next larger lattice the above
>> had to be truncated and then I showed the added directions to get the next larger lattice.
>> I won't do that again because it is confusing.
>> I will just send each larger and larger set of directions for each lattice.
> These have to be done in slow motion to really appreciate the pencil not leaving the paper.

On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
> On 6/15/2023 4:18 PM, Dan joyce wrote:
> > On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> >> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson wrote:
> >>> On 6/15/2023 4:15 AM, Dan joyce wrote:
> >>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> >>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M. Thomasson wrote:
> >>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> >>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> >>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce wrote:
> >>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M. Thomasson
> >>>>>>>>> wrote:
> >>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> >>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M. Thomasson
> >>>>>>>>>>> wrote:
> >>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> >>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan joyce wrote:
> >>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan joyce wrote:
> >>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan joyce wrote:
> >>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan joyce wrote:
> >>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4, Chris M.
> >>>>>>>>>>>>>>>>> Thomasson wrote:
> >>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different algorithm
> >>>>>>>>>>>>>>>>>>> than James'
> >>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is that right?
> >>>>>>>>>>>>>>>>>>> Can you post
> >>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid without
> >>>>>>>>>>>>>>>>>>> using a path
> >>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current version of
> >>>>>>>>>>>>>>>>>>> the lattice:
> >>>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> >>>>>>>>>>>>>>>>>> [...]
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> Here is another one built using a completely different
> >>>>>>>>>>>>>>>>>> algorithm:
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> >>>>>>>>>>>>>>>>> Nice!
> >>>>>>>>>>>>>>>>> I like the two color idea, one for going right and the other
> >>>>>>>>>>>>>>>>> one going up and left.
> >>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that is finite
> >>>>>>>>>>>>>>>>> in width but --->oo in length.
> >>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> >>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path before
> >>>>>>>>>>>>>>>> their 90 degree turn at the top
> >>>>>>>>>>>>>>>> of their line.
> >>>>>>>>>>>>>>>> .
> >>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that creates the
> >>>>>>>>>>>>>>> cells as it goes.
> >>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all directions.
> >>>>>>>>>>>>>>> Even very small fractional
> >>>>>>>>>>>>>>> directions --->oo.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> I believe this is significant over my original pathway lattice.
> >>>>>>>>>>>>>>> The reason being that had to follow a pathway back to origin to
> >>>>>>>>>>>>>>> complete all the cells in
> >>>>>>>>>>>>>>> any size square lattice --->oo.
> >>>>>>>>>>>>>>> Even the new one that you propose has finite width and --->oo
> >>>>>>>>>>>>>>> length.
> >>>>>>>>>>>>>>> That is a nice one also along with my original but this new one
> >>>>>>>>>>>>>>> is something else that
> >>>>>>>>>>>>>>> i am sure some will say not possible.
> >>>>>>>>>>>>>>> I am going to start to build the sequence of directions R,D,LU
> >>>>>>>>>>>>>>> to prove it is possible to start a lattice
> >>>>>>>>>>>>>>> filling cells as you go without lifting the pencil. All the
> >>>>>>>>>>>>>>> while making 90 degree turns right or left or
> >>>>>>>>>>>>>>> up or down at the end of each line.
> >>>>>>>>>>>>>>> What do you think?
> >>>>>>>>>>>>>>> If this is true, it would be more significant then my original
> >>>>>>>>>>>>>>> and the new lattice you propose.
> >>>>>>>>>>>>>> It is true Chris,
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> A simple straight forward list of directions that
> >>>>>>>>>>>>>> represents the first rendering I sent you.
> >>>>>>>>>>>> This one?
> >>>>>>>>>>>>
> >>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> >>>>>>>>>>>> [...]
> >>>>>>>>>>> Yes!
> >>>>>>>>>>> That is the list of directions for building it.
> >>>>>>>>>>> Do it in slow-motion and you will really appreciate the pencil not
> >>>>>>>>>>> lifting off the page
> >>>>>>>>>>> or in this case when I enter each direction via keyboard it end up
> >>>>>>>>>>> as that image
> >>>>>>>>>>> I sent you.
> >>>>>>>>>>> I have made the next one but need to capture the directions and
> >>>>>>>>>>> when I do I will send it along.
> >>>>>>>>>> Okay. Well, basically, I think a proper animation simply must show all
> >>>>>>>>>> the different ways this can be constructed. From your originals and my
> >>>>>>>>>> and James' work, up to your new work. Fair enough?
> >>>>>>>>> Sounds great!
> >>>>>>>>> This last one, if you read some of James's remarks that what I just
> >>>>>>>>> did in this one was not possible.
> >>>>>>>>> I think James will be surprised when he runs the direction list I
> >>>>>>>>> just sent. Also more larger ones can be built.
> >>>>>>>>> It is good to have you guys on board with this. It adds to the effort
> >>>>>>>>> of perfecting all of this for presentation.
> >>>>>>>>> Thanks to both you guys.
> >>>>>>>>
> >>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> >>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> >>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> >>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> >>>>>>> [...]
> >>>>>>>
> >>>>>>> Looking good. The start circle in red, the origin, is nice and tangent
> >>>>>>> with the end point, the center of the circle in yellow.
> >>>>>>>
> >>>>>>> https://i.ibb.co/zhjM4KY/image.png
> >>>>>>>
> >>>>>>> :^D
> >>>>>>>
> >>>>>> Actually, not exactly sure where to go from here. I get into dead ends
> >>>>>> when I want to continue it. Do I go left? If I got right, then I have to
> >>>>>> go up and have to go left. So, the initial size might be an issue?
> >>>>>> Humm... Not sure yet.
> >>>>> Use the original list.
> >>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if you want
> >>>>> a larger lattice.
> >>>> My smart phone is screwed up. I couldn't open up the animation you sent 2 days ago.
> >>>> Send to my other e-mail address. Thanks
> >>> Sorry about the FB link. However, can you go to it and see the content?
> >>> This one has a path back home:
> >>>
> >>> https://www.facebook.com/100034470228086/videos/791843519283462/
> >>>
> >>>
> >>> The following link goes to the one that is the "infinite" builder...
> >>> Very tall, infinitely tall... ;^D
> >>>
> >>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> >>>
> >>> Many rooms... ;^)
> >>>
> >>> lol. ;^)
> >> Nice presentation on both.
> >> I like the one color going out and the different color coming back in.
> >> Thanks.
> >> You left out the last 8 directions on the original post to complete my new lattice.
> >> (L,U,R,D,R,U,L,U)
> >> It probably confused you because just to continue to the next larger lattice the above
> >> had to be truncated and then I showed the added directions to get the next larger lattice.
> >> I won't do that again because it is confusing.
> >> I will just send each larger and larger set of directions for each lattice.
> > These have to be done in slow motion to really appreciate the pencil not leaving the paper.
> How many frames per second? 24, 60, 120? I can time and orchestrate
> things using the fps.

On 6/15/2023 5:48 PM, Dan joyce wrote:
> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
>> On 6/15/2023 4:18 PM, Dan joyce wrote:
>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson wrote:
>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M. Thomasson wrote:
>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M. Thomasson
>>>>>>>>>>> wrote:
>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M. Thomasson
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4, Chris M.
>>>>>>>>>>>>>>>>>>> Thomasson wrote:
>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different algorithm
>>>>>>>>>>>>>>>>>>>>> than James'
>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is that right?
>>>>>>>>>>>>>>>>>>>>> Can you post
>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid without
>>>>>>>>>>>>>>>>>>>>> using a path
>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current version of
>>>>>>>>>>>>>>>>>>>>> the lattice:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
>>>>>>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
>>>>>>>>>>>>>>>>>>>> algorithm:
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
>>>>>>>>>>>>>>>>>>> Nice!
>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and the other
>>>>>>>>>>>>>>>>>>> one going up and left.
>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that is finite
>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path before
>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
>>>>>>>>>>>>>>>>>> of their line.
>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that creates the
>>>>>>>>>>>>>>>>> cells as it goes.
>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all directions.
>>>>>>>>>>>>>>>>> Even very small fractional
>>>>>>>>>>>>>>>>> directions --->oo.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway lattice.
>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to origin to
>>>>>>>>>>>>>>>>> complete all the cells in
>>>>>>>>>>>>>>>>> any size square lattice --->oo.
>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and --->oo
>>>>>>>>>>>>>>>>> length.
>>>>>>>>>>>>>>>>> That is a nice one also along with my original but this new one
>>>>>>>>>>>>>>>>> is something else that
>>>>>>>>>>>>>>>>> i am sure some will say not possible.
>>>>>>>>>>>>>>>>> I am going to start to build the sequence of directions R,D,LU
>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil. All the
>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
>>>>>>>>>>>>>>>>> up or down at the end of each line.
>>>>>>>>>>>>>>>>> What do you think?
>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my original
>>>>>>>>>>>>>>>>> and the new lattice you propose.
>>>>>>>>>>>>>>>> It is true Chris,
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> A simple straight forward list of directions that
>>>>>>>>>>>>>>>> represents the first rendering I sent you.
>>>>>>>>>>>>>> This one?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>> Yes!
>>>>>>>>>>>>> That is the list of directions for building it.
>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the pencil not
>>>>>>>>>>>>> lifting off the page
>>>>>>>>>>>>> or in this case when I enter each direction via keyboard it end up
>>>>>>>>>>>>> as that image
>>>>>>>>>>>>> I sent you.
>>>>>>>>>>>>> I have made the next one but need to capture the directions and
>>>>>>>>>>>>> when I do I will send it along.
>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply must show all
>>>>>>>>>>>> the different ways this can be constructed. From your originals and my
>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
>>>>>>>>>>> Sounds great!
>>>>>>>>>>> This last one, if you read some of James's remarks that what I just
>>>>>>>>>>> did in this one was not possible.
>>>>>>>>>>> I think James will be surprised when he runs the direction list I
>>>>>>>>>>> just sent. Also more larger ones can be built.
>>>>>>>>>>> It is good to have you guys on board with this. It adds to the effort
>>>>>>>>>>> of perfecting all of this for presentation.
>>>>>>>>>>> Thanks to both you guys.
>>>>>>>>>>
>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
>>>>>>>>> [...]
>>>>>>>>>
>>>>>>>>> Looking good. The start circle in red, the origin, is nice and tangent
>>>>>>>>> with the end point, the center of the circle in yellow.
>>>>>>>>>
>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
>>>>>>>>>
>>>>>>>>> :^D
>>>>>>>>>
>>>>>>>> Actually, not exactly sure where to go from here. I get into dead ends
>>>>>>>> when I want to continue it. Do I go left? If I got right, then I have to
>>>>>>>> go up and have to go left. So, the initial size might be an issue?
>>>>>>>> Humm... Not sure yet.
>>>>>>> Use the original list.
>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if you want
>>>>>>> a larger lattice.
>>>>>> My smart phone is screwed up. I couldn't open up the animation you sent 2 days ago.
>>>>>> Send to my other e-mail address. Thanks
>>>>> Sorry about the FB link. However, can you go to it and see the content?
>>>>> This one has a path back home:
>>>>>
>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
>>>>>
>>>>>
>>>>> The following link goes to the one that is the "infinite" builder...
>>>>> Very tall, infinitely tall... ;^D
>>>>>
>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
>>>>>
>>>>> Many rooms... ;^)
>>>>>
>>>>> lol. ;^)
>>>> Nice presentation on both.
>>>> I like the one color going out and the different color coming back in.
>>>> Thanks.
>>>> You left out the last 8 directions on the original post to complete my new lattice.
>>>> (L,U,R,D,R,U,L,U)
>>>> It probably confused you because just to continue to the next larger lattice the above
>>>> had to be truncated and then I showed the added directions to get the next larger lattice.
>>>> I won't do that again because it is confusing.
>>>> I will just send each larger and larger set of directions for each lattice.
>>> These have to be done in slow motion to really appreciate the pencil not leaving the paper.
>> How many frames per second? 24, 60, 120? I can time and orchestrate
>> things using the fps.
>
> If it can be done like 4 fps, like a pencil drawing it fast.
> I will send you all 4 lattice directions.
> The first has 1,3,5,7,7,5,3,1 vertical cells.
> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
> I still have to capture more data for the last one.
> A nice way to present this is show the full lattice with a question.
> Can you draw this lattice without retracing or crossing a line and not lifting the pencil
> from the paper in the process?

On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> On 6/15/2023 5:48 PM, Dan joyce wrote:
>> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
>>> On 6/15/2023 4:18 PM, Dan joyce wrote:
>>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
>>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson
>>>>> wrote:
>>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
>>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
>>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
>>>>>>>> Thomasson wrote:
>>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
>>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
>>>>>>>>>>> wrote:
>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
>>>>>>>>>>>> Thomasson
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
>>>>>>>>>>>>>> Thomasson
>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
>>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
>>>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
>>>>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
>>>>>>>>>>>>>>>>>>>> Chris M.
>>>>>>>>>>>>>>>>>>>> Thomasson wrote:
>>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
>>>>>>>>>>>>>>>>>>>>>> algorithm
>>>>>>>>>>>>>>>>>>>>>> than James'
>>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
>>>>>>>>>>>>>>>>>>>>>> that right?
>>>>>>>>>>>>>>>>>>>>>> Can you post
>>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
>>>>>>>>>>>>>>>>>>>>>> without
>>>>>>>>>>>>>>>>>>>>>> using a path
>>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
>>>>>>>>>>>>>>>>>>>>>> version of
>>>>>>>>>>>>>>>>>>>>>> the lattice:
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
>>>>>>>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
>>>>>>>>>>>>>>>>>>>>> algorithm:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
>>>>>>>>>>>>>>>>>>>> Nice!
>>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
>>>>>>>>>>>>>>>>>>>> the other
>>>>>>>>>>>>>>>>>>>> one going up and left.
>>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
>>>>>>>>>>>>>>>>>>>> is finite
>>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
>>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
>>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
>>>>>>>>>>>>>>>>>>> before
>>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
>>>>>>>>>>>>>>>>>>> of their line.
>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
>>>>>>>>>>>>>>>>>> creates the
>>>>>>>>>>>>>>>>>> cells as it goes.
>>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
>>>>>>>>>>>>>>>>>> directions.
>>>>>>>>>>>>>>>>>> Even very small fractional
>>>>>>>>>>>>>>>>>> directions --->oo.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
>>>>>>>>>>>>>>>>>> lattice.
>>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
>>>>>>>>>>>>>>>>>> origin to
>>>>>>>>>>>>>>>>>> complete all the cells in
>>>>>>>>>>>>>>>>>> any size square lattice --->oo.
>>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
>>>>>>>>>>>>>>>>>> --->oo
>>>>>>>>>>>>>>>>>> length.
>>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
>>>>>>>>>>>>>>>>>> this new one
>>>>>>>>>>>>>>>>>> is something else that
>>>>>>>>>>>>>>>>>> i am sure some will say not possible.
>>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
>>>>>>>>>>>>>>>>>> directions R,D,LU
>>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
>>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil.
>>>>>>>>>>>>>>>>>> All the
>>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
>>>>>>>>>>>>>>>>>> up or down at the end of each line.
>>>>>>>>>>>>>>>>>> What do you think?
>>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
>>>>>>>>>>>>>>>>>> original
>>>>>>>>>>>>>>>>>> and the new lattice you propose.
>>>>>>>>>>>>>>>>> It is true Chris,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> A simple straight forward list of directions that
>>>>>>>>>>>>>>>>> represents the first rendering I sent you.
>>>>>>>>>>>>>>> This one?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>> Yes!
>>>>>>>>>>>>>> That is the list of directions for building it.
>>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
>>>>>>>>>>>>>> pencil not
>>>>>>>>>>>>>> lifting off the page
>>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
>>>>>>>>>>>>>> it end up
>>>>>>>>>>>>>> as that image
>>>>>>>>>>>>>> I sent you.
>>>>>>>>>>>>>> I have made the next one but need to capture the
>>>>>>>>>>>>>> directions and
>>>>>>>>>>>>>> when I do I will send it along.
>>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
>>>>>>>>>>>>> must show all
>>>>>>>>>>>>> the different ways this can be constructed. From your
>>>>>>>>>>>>> originals and my
>>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
>>>>>>>>>>>> Sounds great!
>>>>>>>>>>>> This last one, if you read some of James's remarks that what
>>>>>>>>>>>> I just
>>>>>>>>>>>> did in this one was not possible.
>>>>>>>>>>>> I think James will be surprised when he runs the direction
>>>>>>>>>>>> list I
>>>>>>>>>>>> just sent. Also more larger ones can be built.
>>>>>>>>>>>> It is good to have you guys on board with this. It adds to
>>>>>>>>>>>> the effort
>>>>>>>>>>>> of perfecting all of this for presentation.
>>>>>>>>>>>> Thanks to both you guys.
>>>>>>>>>>>
>>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
>>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
>>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
>>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
>>>>>>>>>> [...]
>>>>>>>>>>
>>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
>>>>>>>>>> tangent
>>>>>>>>>> with the end point, the center of the circle in yellow.
>>>>>>>>>>
>>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
>>>>>>>>>>
>>>>>>>>>> :^D
>>>>>>>>>>
>>>>>>>>> Actually, not exactly sure where to go from here. I get into
>>>>>>>>> dead ends
>>>>>>>>> when I want to continue it. Do I go left? If I got right, then
>>>>>>>>> I have to
>>>>>>>>> go up and have to go left. So, the initial size might be an issue?
>>>>>>>>> Humm... Not sure yet.
>>>>>>>> Use the original list.
>>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
>>>>>>>> you want
>>>>>>>> a larger lattice.
>>>>>>> My smart phone is screwed up. I couldn't open up the animation
>>>>>>> you sent 2 days ago.
>>>>>>> Send to my other e-mail address. Thanks
>>>>>> Sorry about the FB link. However, can you go to it and see the
>>>>>> content?
>>>>>> This one has a path back home:
>>>>>>
>>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
>>>>>>
>>>>>>
>>>>>> The following link goes to the one that is the "infinite" builder...
>>>>>> Very tall, infinitely tall... ;^D
>>>>>>
>>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
>>>>>>
>>>>>> Many rooms... ;^)
>>>>>>
>>>>>> lol. ;^)
>>>>> Nice presentation on both.
>>>>> I like the one color going out and the different color coming back in.
>>>>> Thanks.
>>>>> You left out the last 8 directions on the original post to complete
>>>>> my new lattice.
>>>>> (L,U,R,D,R,U,L,U)
>>>>> It probably confused you because just to continue to the next
>>>>> larger lattice the above
>>>>> had to be truncated and then I showed the added directions to get
>>>>> the next larger lattice.
>>>>> I won't do that again because it is confusing.
>>>>> I will just send each larger and larger set of directions for each
>>>>> lattice.
>>>> These have to be done in slow motion to really appreciate the pencil
>>>> not leaving the paper.
>>> How many frames per second? 24, 60, 120? I can time and orchestrate
>>> things using the fps.
>>
>> If it can be done like 4 fps, like a pencil drawing it fast.

On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> On 6/15/2023 5:48 PM, Dan joyce wrote:
>> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
>>> On 6/15/2023 4:18 PM, Dan joyce wrote:
>>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
>>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson
>>>>> wrote:
>>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
>>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
>>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
>>>>>>>> Thomasson wrote:
>>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
>>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
>>>>>>>>>>> wrote:
>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
>>>>>>>>>>>> Thomasson
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
>>>>>>>>>>>>>> Thomasson
>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
>>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
>>>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
>>>>>>>>>>>>>>>>>>> joyce wrote:
>>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
>>>>>>>>>>>>>>>>>>>> Chris M.
>>>>>>>>>>>>>>>>>>>> Thomasson wrote:
>>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
>>>>>>>>>>>>>>>>>>>>>> algorithm
>>>>>>>>>>>>>>>>>>>>>> than James'
>>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
>>>>>>>>>>>>>>>>>>>>>> that right?
>>>>>>>>>>>>>>>>>>>>>> Can you post
>>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
>>>>>>>>>>>>>>>>>>>>>> without
>>>>>>>>>>>>>>>>>>>>>> using a path
>>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
>>>>>>>>>>>>>>>>>>>>>> version of
>>>>>>>>>>>>>>>>>>>>>> the lattice:
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
>>>>>>>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
>>>>>>>>>>>>>>>>>>>>> algorithm:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
>>>>>>>>>>>>>>>>>>>> Nice!
>>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
>>>>>>>>>>>>>>>>>>>> the other
>>>>>>>>>>>>>>>>>>>> one going up and left.
>>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
>>>>>>>>>>>>>>>>>>>> is finite
>>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
>>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
>>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
>>>>>>>>>>>>>>>>>>> before
>>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
>>>>>>>>>>>>>>>>>>> of their line.
>>>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
>>>>>>>>>>>>>>>>>> creates the
>>>>>>>>>>>>>>>>>> cells as it goes.
>>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
>>>>>>>>>>>>>>>>>> directions.
>>>>>>>>>>>>>>>>>> Even very small fractional
>>>>>>>>>>>>>>>>>> directions --->oo.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
>>>>>>>>>>>>>>>>>> lattice.
>>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
>>>>>>>>>>>>>>>>>> origin to
>>>>>>>>>>>>>>>>>> complete all the cells in
>>>>>>>>>>>>>>>>>> any size square lattice --->oo.
>>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
>>>>>>>>>>>>>>>>>> --->oo
>>>>>>>>>>>>>>>>>> length.
>>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
>>>>>>>>>>>>>>>>>> this new one
>>>>>>>>>>>>>>>>>> is something else that
>>>>>>>>>>>>>>>>>> i am sure some will say not possible.
>>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
>>>>>>>>>>>>>>>>>> directions R,D,LU
>>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
>>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil.
>>>>>>>>>>>>>>>>>> All the
>>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
>>>>>>>>>>>>>>>>>> up or down at the end of each line.
>>>>>>>>>>>>>>>>>> What do you think?
>>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
>>>>>>>>>>>>>>>>>> original
>>>>>>>>>>>>>>>>>> and the new lattice you propose.
>>>>>>>>>>>>>>>>> It is true Chris,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> A simple straight forward list of directions that
>>>>>>>>>>>>>>>>> represents the first rendering I sent you.
>>>>>>>>>>>>>>> This one?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
>>>>>>>>>>>>>>> [...]
>>>>>>>>>>>>>> Yes!
>>>>>>>>>>>>>> That is the list of directions for building it.
>>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
>>>>>>>>>>>>>> pencil not
>>>>>>>>>>>>>> lifting off the page
>>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
>>>>>>>>>>>>>> it end up
>>>>>>>>>>>>>> as that image
>>>>>>>>>>>>>> I sent you.
>>>>>>>>>>>>>> I have made the next one but need to capture the
>>>>>>>>>>>>>> directions and
>>>>>>>>>>>>>> when I do I will send it along.
>>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
>>>>>>>>>>>>> must show all
>>>>>>>>>>>>> the different ways this can be constructed. From your
>>>>>>>>>>>>> originals and my
>>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
>>>>>>>>>>>> Sounds great!
>>>>>>>>>>>> This last one, if you read some of James's remarks that what
>>>>>>>>>>>> I just
>>>>>>>>>>>> did in this one was not possible.
>>>>>>>>>>>> I think James will be surprised when he runs the direction
>>>>>>>>>>>> list I
>>>>>>>>>>>> just sent. Also more larger ones can be built.
>>>>>>>>>>>> It is good to have you guys on board with this. It adds to
>>>>>>>>>>>> the effort
>>>>>>>>>>>> of perfecting all of this for presentation.
>>>>>>>>>>>> Thanks to both you guys.
>>>>>>>>>>>
>>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
>>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
>>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
>>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
>>>>>>>>>> [...]
>>>>>>>>>>
>>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
>>>>>>>>>> tangent
>>>>>>>>>> with the end point, the center of the circle in yellow.
>>>>>>>>>>
>>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
>>>>>>>>>>
>>>>>>>>>> :^D
>>>>>>>>>>
>>>>>>>>> Actually, not exactly sure where to go from here. I get into
>>>>>>>>> dead ends
>>>>>>>>> when I want to continue it. Do I go left? If I got right, then
>>>>>>>>> I have to
>>>>>>>>> go up and have to go left. So, the initial size might be an issue?
>>>>>>>>> Humm... Not sure yet.
>>>>>>>> Use the original list.
>>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
>>>>>>>> you want
>>>>>>>> a larger lattice.
>>>>>>> My smart phone is screwed up. I couldn't open up the animation
>>>>>>> you sent 2 days ago.
>>>>>>> Send to my other e-mail address. Thanks
>>>>>> Sorry about the FB link. However, can you go to it and see the
>>>>>> content?
>>>>>> This one has a path back home:
>>>>>>
>>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
>>>>>>
>>>>>>
>>>>>> The following link goes to the one that is the "infinite" builder...
>>>>>> Very tall, infinitely tall... ;^D
>>>>>>
>>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
>>>>>>
>>>>>> Many rooms... ;^)
>>>>>>
>>>>>> lol. ;^)
>>>>> Nice presentation on both.
>>>>> I like the one color going out and the different color coming back in.
>>>>> Thanks.
>>>>> You left out the last 8 directions on the original post to complete
>>>>> my new lattice.
>>>>> (L,U,R,D,R,U,L,U)
>>>>> It probably confused you because just to continue to the next
>>>>> larger lattice the above
>>>>> had to be truncated and then I showed the added directions to get
>>>>> the next larger lattice.
>>>>> I won't do that again because it is confusing.
>>>>> I will just send each larger and larger set of directions for each
>>>>> lattice.
>>>> These have to be done in slow motion to really appreciate the pencil
>>>> not leaving the paper.
>>> How many frames per second? 24, 60, 120? I can time and orchestrate
>>> things using the fps.
>>
>> If it can be done like 4 fps, like a pencil drawing it fast.
>> I will send you all 4 lattice directions.
>> The first has 1,3,5,7,7,5,3,1 vertical cells.
>> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
>> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
>> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
>> I still have to capture more data for the last one.
>> A nice way to present this is show the full lattice with a question.
>> Can you draw this lattice without retracing or crossing a line and not
>> lifting the pencil
>> from the paper in the process?
>
> Basically, how many frames to draw a single line with an arrow on it... ?

On Thursday, June 15, 2023 at 10:42:28 PM UTC-4, Chris M. Thomasson wrote:
> On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> > On 6/15/2023 5:48 PM, Dan joyce wrote:
> >> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
> >>> On 6/15/2023 4:18 PM, Dan joyce wrote:
> >>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> >>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson
> >>>>> wrote:
> >>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
> >>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> >>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
> >>>>>>>> Thomasson wrote:
> >>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> >>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> >>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
> >>>>>>>>>>> wrote:
> >>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
> >>>>>>>>>>>> Thomasson
> >>>>>>>>>>>> wrote:
> >>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> >>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
> >>>>>>>>>>>>>> Thomasson
> >>>>>>>>>>>>>> wrote:
> >>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> >>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
> >>>>>>>>>>>>>>>> joyce wrote:
> >>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
> >>>>>>>>>>>>>>>>> joyce wrote:
> >>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
> >>>>>>>>>>>>>>>>>> joyce wrote:
> >>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
> >>>>>>>>>>>>>>>>>>> joyce wrote:
> >>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
> >>>>>>>>>>>>>>>>>>>> Chris M.
> >>>>>>>>>>>>>>>>>>>> Thomasson wrote:
> >>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
> >>>>>>>>>>>>>>>>>>>>>> algorithm
> >>>>>>>>>>>>>>>>>>>>>> than James'
> >>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
> >>>>>>>>>>>>>>>>>>>>>> that right?
> >>>>>>>>>>>>>>>>>>>>>> Can you post
> >>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
> >>>>>>>>>>>>>>>>>>>>>> without
> >>>>>>>>>>>>>>>>>>>>>> using a path
> >>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
> >>>>>>>>>>>>>>>>>>>>>> version of
> >>>>>>>>>>>>>>>>>>>>>> the lattice:
> >>>>>>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> >>>>>>>>>>>>>>>>>>>>> [...]
> >>>>>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
> >>>>>>>>>>>>>>>>>>>>> algorithm:
> >>>>>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> >>>>>>>>>>>>>>>>>>>> Nice!
> >>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
> >>>>>>>>>>>>>>>>>>>> the other
> >>>>>>>>>>>>>>>>>>>> one going up and left.
> >>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
> >>>>>>>>>>>>>>>>>>>> is finite
> >>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
> >>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate..
> >>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
> >>>>>>>>>>>>>>>>>>> before
> >>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
> >>>>>>>>>>>>>>>>>>> of their line.
> >>>>>>>>>>>>>>>>>>> .
> >>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
> >>>>>>>>>>>>>>>>>> creates the
> >>>>>>>>>>>>>>>>>> cells as it goes.
> >>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
> >>>>>>>>>>>>>>>>>> directions.
> >>>>>>>>>>>>>>>>>> Even very small fractional
> >>>>>>>>>>>>>>>>>> directions --->oo.
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
> >>>>>>>>>>>>>>>>>> lattice.
> >>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
> >>>>>>>>>>>>>>>>>> origin to
> >>>>>>>>>>>>>>>>>> complete all the cells in
> >>>>>>>>>>>>>>>>>> any size square lattice --->oo.
> >>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
> >>>>>>>>>>>>>>>>>> --->oo
> >>>>>>>>>>>>>>>>>> length.
> >>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
> >>>>>>>>>>>>>>>>>> this new one
> >>>>>>>>>>>>>>>>>> is something else that
> >>>>>>>>>>>>>>>>>> i am sure some will say not possible.
> >>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
> >>>>>>>>>>>>>>>>>> directions R,D,LU
> >>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
> >>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil.
> >>>>>>>>>>>>>>>>>> All the
> >>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
> >>>>>>>>>>>>>>>>>> up or down at the end of each line.
> >>>>>>>>>>>>>>>>>> What do you think?
> >>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
> >>>>>>>>>>>>>>>>>> original
> >>>>>>>>>>>>>>>>>> and the new lattice you propose.
> >>>>>>>>>>>>>>>>> It is true Chris,
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> A simple straight forward list of directions that
> >>>>>>>>>>>>>>>>> represents the first rendering I sent you.
> >>>>>>>>>>>>>>> This one?
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> >>>>>>>>>>>>>>> [...]
> >>>>>>>>>>>>>> Yes!
> >>>>>>>>>>>>>> That is the list of directions for building it.
> >>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
> >>>>>>>>>>>>>> pencil not
> >>>>>>>>>>>>>> lifting off the page
> >>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
> >>>>>>>>>>>>>> it end up
> >>>>>>>>>>>>>> as that image
> >>>>>>>>>>>>>> I sent you.
> >>>>>>>>>>>>>> I have made the next one but need to capture the
> >>>>>>>>>>>>>> directions and
> >>>>>>>>>>>>>> when I do I will send it along.
> >>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
> >>>>>>>>>>>>> must show all
> >>>>>>>>>>>>> the different ways this can be constructed. From your
> >>>>>>>>>>>>> originals and my
> >>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
> >>>>>>>>>>>> Sounds great!
> >>>>>>>>>>>> This last one, if you read some of James's remarks that what
> >>>>>>>>>>>> I just
> >>>>>>>>>>>> did in this one was not possible.
> >>>>>>>>>>>> I think James will be surprised when he runs the direction
> >>>>>>>>>>>> list I
> >>>>>>>>>>>> just sent. Also more larger ones can be built.
> >>>>>>>>>>>> It is good to have you guys on board with this. It adds to
> >>>>>>>>>>>> the effort
> >>>>>>>>>>>> of perfecting all of this for presentation.
> >>>>>>>>>>>> Thanks to both you guys.
> >>>>>>>>>>>
> >>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> >>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> >>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> >>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> >>>>>>>>>> [...]
> >>>>>>>>>>
> >>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
> >>>>>>>>>> tangent
> >>>>>>>>>> with the end point, the center of the circle in yellow.
> >>>>>>>>>>
> >>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
> >>>>>>>>>>
> >>>>>>>>>> :^D
> >>>>>>>>>>
> >>>>>>>>> Actually, not exactly sure where to go from here. I get into
> >>>>>>>>> dead ends
> >>>>>>>>> when I want to continue it. Do I go left? If I got right, then
> >>>>>>>>> I have to
> >>>>>>>>> go up and have to go left. So, the initial size might be an issue?
> >>>>>>>>> Humm... Not sure yet.
> >>>>>>>> Use the original list.
> >>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
> >>>>>>>> you want
> >>>>>>>> a larger lattice.
> >>>>>>> My smart phone is screwed up. I couldn't open up the animation
> >>>>>>> you sent 2 days ago.
> >>>>>>> Send to my other e-mail address. Thanks
> >>>>>> Sorry about the FB link. However, can you go to it and see the
> >>>>>> content?
> >>>>>> This one has a path back home:
> >>>>>>
> >>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
> >>>>>>
> >>>>>>
> >>>>>> The following link goes to the one that is the "infinite" builder....
> >>>>>> Very tall, infinitely tall... ;^D
> >>>>>>
> >>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> >>>>>>
> >>>>>> Many rooms... ;^)
> >>>>>>
> >>>>>> lol. ;^)
> >>>>> Nice presentation on both.
> >>>>> I like the one color going out and the different color coming back in.
> >>>>> Thanks.
> >>>>> You left out the last 8 directions on the original post to complete
> >>>>> my new lattice.
> >>>>> (L,U,R,D,R,U,L,U)
> >>>>> It probably confused you because just to continue to the next
> >>>>> larger lattice the above
> >>>>> had to be truncated and then I showed the added directions to get
> >>>>> the next larger lattice.
> >>>>> I won't do that again because it is confusing.
> >>>>> I will just send each larger and larger set of directions for each
> >>>>> lattice.
> >>>> These have to be done in slow motion to really appreciate the pencil
> >>>> not leaving the paper.
> >>> How many frames per second? 24, 60, 120? I can time and orchestrate
> >>> things using the fps.
> >>
> >> If it can be done like 4 fps, like a pencil drawing it fast.
> >> I will send you all 4 lattice directions.
> >> The first has 1,3,5,7,7,5,3,1 vertical cells.
> >> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
> >> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
> >> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
> >> I still have to capture more data for the last one.
> >> A nice way to present this is show the full lattice with a question.
> >> Can you draw this lattice without retracing or crossing a line and not
> >> lifting the pencil
> >> from the paper in the process?
> >
> > Basically, how many frames to draw a single line with an arrow on it... ?
> One second per line with animation in the per second frame interval. So,
> say 60fps, 60 frames for a growing line animation per second.

On Thursday, June 15, 2023 at 3:08:36 AM UTC-4, Chris M. Thomasson wrote:
> On 6/14/2023 7:36 PM, Dan joyce wrote:
> > On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce wrote:
> >> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M. Thomasson wrote:
> >>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> >>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M. Thomasson wrote:
> >>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> >>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan joyce wrote:
> >>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan joyce wrote:
> >>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan joyce wrote:
> >>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan joyce wrote:
> >>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4, Chris M. Thomasson wrote:
> >>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>>> I got the square lattice down, using a different algorithm than James'
> >>>>>>>>>>>> version. However, Dan has a new version out, is that right? Can you post
> >>>>>>>>>>>> it in this fresh thread? It builds out the grid without using a path
> >>>>>>>>>>>> back home? Fwiw, here is a result of my current version of the lattice:
> >>>>>>>>>>>>
> >>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> >>>>>>>>>>> [...]
> >>>>>>>>>>>
> >>>>>>>>>>> Here is another one built using a completely different algorithm:
> >>>>>>>>>>>
> >>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> >>>>>>>>>> Nice!
> >>>>>>>>>> I like the two color idea, one for going right and the other one going up and left.
> >>>>>>>>>> Has this actually been done before? A lattice that is finite in width but --->oo in length.
> >>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> >>>>>>>>> I have that wrong. (Both) colors have an upward path before their 90 degree turn at the top
> >>>>>>>>> of their line.
> >>>>>>>>> .
> >>>>>>>> Chris, did you receive my photo of the lattice that creates the cells as it goes.
> >>>>>>>> No pathways present. Also it will --->oo in all directions. Even very small fractional
> >>>>>>>> directions --->oo.
> >>>>>>>>
> >>>>>>>> I believe this is significant over my original pathway lattice.
> >>>>>>>> The reason being that had to follow a pathway back to origin to complete all the cells in
> >>>>>>>> any size square lattice --->oo.
> >>>>>>>> Even the new one that you propose has finite width and --->oo length.
> >>>>>>>> That is a nice one also along with my original but this new one is something else that
> >>>>>>>> i am sure some will say not possible.
> >>>>>>>> I am going to start to build the sequence of directions R,D,LU to prove it is possible to start a lattice
> >>>>>>>> filling cells as you go without lifting the pencil. All the while making 90 degree turns right or left or
> >>>>>>>> up or down at the end of each line.
> >>>>>>>> What do you think?
> >>>>>>>> If this is true, it would be more significant then my original and the new lattice you propose.
> >>>>>>> It is true Chris,
> >>>>>>>
> >>>>>>> A simple straight forward list of directions that
> >>>>>>> represents the first rendering I sent you.
> >>>>> This one?
> >>>>>
> >>>>> https://i.ibb.co/D1LQrFZ/image.png
> >>>>> [...]
> >>>> Yes!
> >>>> That is the list of directions for building it.
> >>>> Do it in slow-motion and you will really appreciate the pencil not lifting off the page
> >>>> or in this case when I enter each direction via keyboard it end up as that image
> >>>> I sent you.
> >>>> I have made the next one but need to capture the directions and when I do I will send it along.
> >>> Okay. Well, basically, I think a proper animation simply must show all
> >>> the different ways this can be constructed. From your originals and my
> >>> and James' work, up to your new work. Fair enough?
> >> Sounds great!
> >> This last one, if you read some of James's remarks that what I just did in this one was not possible.
> >> I think James will be surprised when he runs the direction list I just sent. Also more larger ones can be built.
> >> It is good to have you guys on board with this. It adds to the effort of perfecting all of this for presentation.
> >> Thanks to both you guys.
> >
> > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> Ahhh! Nice one, Dan! I plugged in your commands up to here in my
> program, and got this:
>
> https://i.ibb.co/cCjgCSm/image.png
>
> Okay. I will try to create an algorithm that generates it based on a
> single number, n. No predefined commands. Might work into the night,
> need to finish up some other work on a project right now, but that
> should be done in about an hour. Some GLSL rather tedious shader work.
> Anyway, I have to compute your new work in a finite step-by-step basis
> first to get on the same page, oh wait, I already did that... but I
> wonder about letting it run wild and zoom out to accommodate it as it
> automatically grows? Thinking of zooming out as it builds itself?
>
> Perhaps set to this song? lol. ;^D
>
> https://youtu.be/wgBgwd0ekIk?t=176
>
> ;^D Listen to the lyrics. lol!
>
> By the way, I did not plot the commands that should not be plotted (...)

The only reason to leave them out is to add more directions for a bigger
lattice. Leave them in to finish the current lattice.

> :^D
> > from the end of the last completed lattice but
> > continue from here to make a bigger lattice then
> > the last one where this one has 1,3,5,7,9,9,7,5,3,1
> > vertical cells where the first one above had --
> > 1,3,5,7,7,5,3,1 so a bigger lattice that will complete
> > in a counter clockwise fashion where the first one
> > completed in a clockwise fashion. As these get larger
> > and larger it will keep switching back and forth
> > where the outward finished cells will either finish
> > in a clockwise or counter clockwise fashion. Always
> > switching direction to the next larger lattice.
> > Here are the rest of the directions to finish this
> > lager lattice.---
> > L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U,L,U,L,U,L,U
> > L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D,R,D,R,U,R,D
> > R,U,L,U
> > Just add this before (...)to the above larger
> > sequence of directions. This completed one will
> > have 1,3,5,7,9,9,7,5,3,1 vertical cells.
> > The next larger one 1,3,5,7,9,11,11,9,7,5,3,2,1
> > vertical cells the same thing happens. A 1/2
> > dozen or so will be truncated from the end of
> > the above shorter sequence and another short
> > sequence is added to that. All the while adding
> > more and more to the sequence as a whole and
> > truncating a small number at the end of the last
> > completed lattice..
> > This creates a lattice --->oo in all directions
> > where the pencil never leaves the paper.
> >
> >

On Thursday, June 15, 2023 at 10:49:08 PM UTC-4, Dan joyce wrote:
> On Thursday, June 15, 2023 at 10:42:28 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> > > On 6/15/2023 5:48 PM, Dan joyce wrote:
> > >> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
> > >>> On 6/15/2023 4:18 PM, Dan joyce wrote:
> > >>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> > >>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson
> > >>>>> wrote:
> > >>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
> > >>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> > >>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
> > >>>>>>>> Thomasson wrote:
> > >>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> > >>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> > >>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
> > >>>>>>>>>>> wrote:
> > >>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
> > >>>>>>>>>>>> Thomasson
> > >>>>>>>>>>>> wrote:
> > >>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> > >>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
> > >>>>>>>>>>>>>> Thomasson
> > >>>>>>>>>>>>>> wrote:
> > >>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> > >>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
> > >>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
> > >>>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
> > >>>>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
> > >>>>>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
> > >>>>>>>>>>>>>>>>>>>> Chris M.
> > >>>>>>>>>>>>>>>>>>>> Thomasson wrote:
> > >>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> > >>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
> > >>>>>>>>>>>>>>>>>>>>>> algorithm
> > >>>>>>>>>>>>>>>>>>>>>> than James'
> > >>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
> > >>>>>>>>>>>>>>>>>>>>>> that right?
> > >>>>>>>>>>>>>>>>>>>>>> Can you post
> > >>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
> > >>>>>>>>>>>>>>>>>>>>>> without
> > >>>>>>>>>>>>>>>>>>>>>> using a path
> > >>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
> > >>>>>>>>>>>>>>>>>>>>>> version of
> > >>>>>>>>>>>>>>>>>>>>>> the lattice:
> > >>>>>>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> > >>>>>>>>>>>>>>>>>>>>> [...]
> > >>>>>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
> > >>>>>>>>>>>>>>>>>>>>> algorithm:
> > >>>>>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> > >>>>>>>>>>>>>>>>>>>> Nice!
> > >>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
> > >>>>>>>>>>>>>>>>>>>> the other
> > >>>>>>>>>>>>>>>>>>>> one going up and left.
> > >>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
> > >>>>>>>>>>>>>>>>>>>> is finite
> > >>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
> > >>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> > >>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
> > >>>>>>>>>>>>>>>>>>> before
> > >>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
> > >>>>>>>>>>>>>>>>>>> of their line.
> > >>>>>>>>>>>>>>>>>>> .
> > >>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
> > >>>>>>>>>>>>>>>>>> creates the
> > >>>>>>>>>>>>>>>>>> cells as it goes.
> > >>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
> > >>>>>>>>>>>>>>>>>> directions.
> > >>>>>>>>>>>>>>>>>> Even very small fractional
> > >>>>>>>>>>>>>>>>>> directions --->oo.
> > >>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
> > >>>>>>>>>>>>>>>>>> lattice.
> > >>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
> > >>>>>>>>>>>>>>>>>> origin to
> > >>>>>>>>>>>>>>>>>> complete all the cells in
> > >>>>>>>>>>>>>>>>>> any size square lattice --->oo.
> > >>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
> > >>>>>>>>>>>>>>>>>> --->oo
> > >>>>>>>>>>>>>>>>>> length.
> > >>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
> > >>>>>>>>>>>>>>>>>> this new one
> > >>>>>>>>>>>>>>>>>> is something else that
> > >>>>>>>>>>>>>>>>>> i am sure some will say not possible.
> > >>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
> > >>>>>>>>>>>>>>>>>> directions R,D,LU
> > >>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
> > >>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil.
> > >>>>>>>>>>>>>>>>>> All the
> > >>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
> > >>>>>>>>>>>>>>>>>> up or down at the end of each line.
> > >>>>>>>>>>>>>>>>>> What do you think?
> > >>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
> > >>>>>>>>>>>>>>>>>> original
> > >>>>>>>>>>>>>>>>>> and the new lattice you propose.
> > >>>>>>>>>>>>>>>>> It is true Chris,
> > >>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>> A simple straight forward list of directions that
> > >>>>>>>>>>>>>>>>> represents the first rendering I sent you.
> > >>>>>>>>>>>>>>> This one?
> > >>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> > >>>>>>>>>>>>>>> [...]
> > >>>>>>>>>>>>>> Yes!
> > >>>>>>>>>>>>>> That is the list of directions for building it.
> > >>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
> > >>>>>>>>>>>>>> pencil not
> > >>>>>>>>>>>>>> lifting off the page
> > >>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
> > >>>>>>>>>>>>>> it end up
> > >>>>>>>>>>>>>> as that image
> > >>>>>>>>>>>>>> I sent you.
> > >>>>>>>>>>>>>> I have made the next one but need to capture the
> > >>>>>>>>>>>>>> directions and
> > >>>>>>>>>>>>>> when I do I will send it along.
> > >>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
> > >>>>>>>>>>>>> must show all
> > >>>>>>>>>>>>> the different ways this can be constructed. From your
> > >>>>>>>>>>>>> originals and my
> > >>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
> > >>>>>>>>>>>> Sounds great!
> > >>>>>>>>>>>> This last one, if you read some of James's remarks that what
> > >>>>>>>>>>>> I just
> > >>>>>>>>>>>> did in this one was not possible.
> > >>>>>>>>>>>> I think James will be surprised when he runs the direction
> > >>>>>>>>>>>> list I
> > >>>>>>>>>>>> just sent. Also more larger ones can be built.
> > >>>>>>>>>>>> It is good to have you guys on board with this. It adds to
> > >>>>>>>>>>>> the effort
> > >>>>>>>>>>>> of perfecting all of this for presentation.
> > >>>>>>>>>>>> Thanks to both you guys.
> > >>>>>>>>>>>
> > >>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > >>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > >>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > >>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> > >>>>>>>>>> [...]
> > >>>>>>>>>>
> > >>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
> > >>>>>>>>>> tangent
> > >>>>>>>>>> with the end point, the center of the circle in yellow.
> > >>>>>>>>>>
> > >>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
> > >>>>>>>>>>
> > >>>>>>>>>> :^D
> > >>>>>>>>>>
> > >>>>>>>>> Actually, not exactly sure where to go from here. I get into
> > >>>>>>>>> dead ends
> > >>>>>>>>> when I want to continue it. Do I go left? If I got right, then
> > >>>>>>>>> I have to
> > >>>>>>>>> go up and have to go left. So, the initial size might be an issue?
> > >>>>>>>>> Humm... Not sure yet.
> > >>>>>>>> Use the original list.
> > >>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
> > >>>>>>>> you want
> > >>>>>>>> a larger lattice.
> > >>>>>>> My smart phone is screwed up. I couldn't open up the animation
> > >>>>>>> you sent 2 days ago.
> > >>>>>>> Send to my other e-mail address. Thanks
> > >>>>>> Sorry about the FB link. However, can you go to it and see the
> > >>>>>> content?
> > >>>>>> This one has a path back home:
> > >>>>>>
> > >>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
> > >>>>>>
> > >>>>>>
> > >>>>>> The following link goes to the one that is the "infinite" builder...
> > >>>>>> Very tall, infinitely tall... ;^D
> > >>>>>>
> > >>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> > >>>>>>
> > >>>>>> Many rooms... ;^)
> > >>>>>>
> > >>>>>> lol. ;^)
> > >>>>> Nice presentation on both.
> > >>>>> I like the one color going out and the different color coming back in.
> > >>>>> Thanks.
> > >>>>> You left out the last 8 directions on the original post to complete
> > >>>>> my new lattice.
> > >>>>> (L,U,R,D,R,U,L,U)
> > >>>>> It probably confused you because just to continue to the next
> > >>>>> larger lattice the above
> > >>>>> had to be truncated and then I showed the added directions to get
> > >>>>> the next larger lattice.
> > >>>>> I won't do that again because it is confusing.
> > >>>>> I will just send each larger and larger set of directions for each
> > >>>>> lattice.
> > >>>> These have to be done in slow motion to really appreciate the pencil
> > >>>> not leaving the paper.
> > >>> How many frames per second? 24, 60, 120? I can time and orchestrate
> > >>> things using the fps.
> > >>
> > >> If it can be done like 4 fps, like a pencil drawing it fast.
> > >> I will send you all 4 lattice directions.
> > >> The first has 1,3,5,7,7,5,3,1 vertical cells.
> > >> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
> > >> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
> > >> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
> > >> I still have to capture more data for the last one.
> > >> A nice way to present this is show the full lattice with a question.
> > >> Can you draw this lattice without retracing or crossing a line and not
> > >> lifting the pencil
> > >> from the paper in the process?
> > >
> > > Basically, how many frames to draw a single line with an arrow on it.... ?
> > One second per line with animation in the per second frame interval. So,
> > say 60fps, 60 frames for a growing line animation per second.
> Sounds good.
> I am posting 3 completed lattices. I and am still gathering data on the 4th one.
> The first lattice below where the pencil
> never leaves the paper.
> (1,3,5,7,7,5,3,1) vertical cells
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,U,R,D,R,U,L,U
>
> The second lattice.
> (1,3,5,7,9,9,7,5,3,1) vertical cells.
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> R,D,R,U,R,D,R,U,L,U
>
> The third lattice
> (1,3,5,7,9,11,11,9,7,5,3,1) vertical cells.
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> R,D,L,U,L,U,L,U,R,U,R,U,R,U,R,U,R,U,R,U,R,D
> R,D,R,D,R,D,R,D,R,D,L,D,L,D,L,D,L,D,L,D,L,D
> L,U,L,U,L,U,R,D,R,U,L,U
> I hope these are correct.

On Friday, June 16, 2023 at 9:44:55 AM UTC-4, Dan joyce wrote:
> On Thursday, June 15, 2023 at 10:49:08 PM UTC-4, Dan joyce wrote:
> > On Thursday, June 15, 2023 at 10:42:28 PM UTC-4, Chris M. Thomasson wrote:
> > > On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> > > > On 6/15/2023 5:48 PM, Dan joyce wrote:
> > > >> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
> > > >>> On 6/15/2023 4:18 PM, Dan joyce wrote:
> > > >>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> > > >>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M.. Thomasson
> > > >>>>> wrote:
> > > >>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
> > > >>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> > > >>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
> > > >>>>>>>> Thomasson wrote:
> > > >>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> > > >>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> > > >>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
> > > >>>>>>>>>>> wrote:
> > > >>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
> > > >>>>>>>>>>>> Thomasson
> > > >>>>>>>>>>>> wrote:
> > > >>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> > > >>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
> > > >>>>>>>>>>>>>> Thomasson
> > > >>>>>>>>>>>>>> wrote:
> > > >>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> > > >>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
> > > >>>>>>>>>>>>>>>> joyce wrote:
> > > >>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
> > > >>>>>>>>>>>>>>>>> joyce wrote:
> > > >>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
> > > >>>>>>>>>>>>>>>>>> joyce wrote:
> > > >>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
> > > >>>>>>>>>>>>>>>>>>> joyce wrote:
> > > >>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
> > > >>>>>>>>>>>>>>>>>>>> Chris M.
> > > >>>>>>>>>>>>>>>>>>>> Thomasson wrote:
> > > >>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> > > >>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
> > > >>>>>>>>>>>>>>>>>>>>>> algorithm
> > > >>>>>>>>>>>>>>>>>>>>>> than James'
> > > >>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
> > > >>>>>>>>>>>>>>>>>>>>>> that right?
> > > >>>>>>>>>>>>>>>>>>>>>> Can you post
> > > >>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
> > > >>>>>>>>>>>>>>>>>>>>>> without
> > > >>>>>>>>>>>>>>>>>>>>>> using a path
> > > >>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
> > > >>>>>>>>>>>>>>>>>>>>>> version of
> > > >>>>>>>>>>>>>>>>>>>>>> the lattice:
> > > >>>>>>>>>>>>>>>>>>>>>>
> > > >>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> > > >>>>>>>>>>>>>>>>>>>>> [...]
> > > >>>>>>>>>>>>>>>>>>>>>
> > > >>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
> > > >>>>>>>>>>>>>>>>>>>>> algorithm:
> > > >>>>>>>>>>>>>>>>>>>>>
> > > >>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> > > >>>>>>>>>>>>>>>>>>>> Nice!
> > > >>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
> > > >>>>>>>>>>>>>>>>>>>> the other
> > > >>>>>>>>>>>>>>>>>>>> one going up and left.
> > > >>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
> > > >>>>>>>>>>>>>>>>>>>> is finite
> > > >>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
> > > >>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> > > >>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
> > > >>>>>>>>>>>>>>>>>>> before
> > > >>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
> > > >>>>>>>>>>>>>>>>>>> of their line.
> > > >>>>>>>>>>>>>>>>>>> .
> > > >>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
> > > >>>>>>>>>>>>>>>>>> creates the
> > > >>>>>>>>>>>>>>>>>> cells as it goes.
> > > >>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
> > > >>>>>>>>>>>>>>>>>> directions.
> > > >>>>>>>>>>>>>>>>>> Even very small fractional
> > > >>>>>>>>>>>>>>>>>> directions --->oo.
> > > >>>>>>>>>>>>>>>>>>
> > > >>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
> > > >>>>>>>>>>>>>>>>>> lattice.
> > > >>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
> > > >>>>>>>>>>>>>>>>>> origin to
> > > >>>>>>>>>>>>>>>>>> complete all the cells in
> > > >>>>>>>>>>>>>>>>>> any size square lattice --->oo.
> > > >>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
> > > >>>>>>>>>>>>>>>>>> --->oo
> > > >>>>>>>>>>>>>>>>>> length.
> > > >>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
> > > >>>>>>>>>>>>>>>>>> this new one
> > > >>>>>>>>>>>>>>>>>> is something else that
> > > >>>>>>>>>>>>>>>>>> i am sure some will say not possible.
> > > >>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
> > > >>>>>>>>>>>>>>>>>> directions R,D,LU
> > > >>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
> > > >>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil..
> > > >>>>>>>>>>>>>>>>>> All the
> > > >>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
> > > >>>>>>>>>>>>>>>>>> up or down at the end of each line.
> > > >>>>>>>>>>>>>>>>>> What do you think?
> > > >>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
> > > >>>>>>>>>>>>>>>>>> original
> > > >>>>>>>>>>>>>>>>>> and the new lattice you propose.
> > > >>>>>>>>>>>>>>>>> It is true Chris,
> > > >>>>>>>>>>>>>>>>>
> > > >>>>>>>>>>>>>>>>> A simple straight forward list of directions that
> > > >>>>>>>>>>>>>>>>> represents the first rendering I sent you.
> > > >>>>>>>>>>>>>>> This one?
> > > >>>>>>>>>>>>>>>
> > > >>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> > > >>>>>>>>>>>>>>> [...]
> > > >>>>>>>>>>>>>> Yes!
> > > >>>>>>>>>>>>>> That is the list of directions for building it.
> > > >>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
> > > >>>>>>>>>>>>>> pencil not
> > > >>>>>>>>>>>>>> lifting off the page
> > > >>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
> > > >>>>>>>>>>>>>> it end up
> > > >>>>>>>>>>>>>> as that image
> > > >>>>>>>>>>>>>> I sent you.
> > > >>>>>>>>>>>>>> I have made the next one but need to capture the
> > > >>>>>>>>>>>>>> directions and
> > > >>>>>>>>>>>>>> when I do I will send it along.
> > > >>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
> > > >>>>>>>>>>>>> must show all
> > > >>>>>>>>>>>>> the different ways this can be constructed. From your
> > > >>>>>>>>>>>>> originals and my
> > > >>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
> > > >>>>>>>>>>>> Sounds great!
> > > >>>>>>>>>>>> This last one, if you read some of James's remarks that what
> > > >>>>>>>>>>>> I just
> > > >>>>>>>>>>>> did in this one was not possible.
> > > >>>>>>>>>>>> I think James will be surprised when he runs the direction
> > > >>>>>>>>>>>> list I
> > > >>>>>>>>>>>> just sent. Also more larger ones can be built.
> > > >>>>>>>>>>>> It is good to have you guys on board with this. It adds to
> > > >>>>>>>>>>>> the effort
> > > >>>>>>>>>>>> of perfecting all of this for presentation.
> > > >>>>>>>>>>>> Thanks to both you guys.
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > >>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > >>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > >>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> > > >>>>>>>>>> [...]
> > > >>>>>>>>>>
> > > >>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
> > > >>>>>>>>>> tangent
> > > >>>>>>>>>> with the end point, the center of the circle in yellow.
> > > >>>>>>>>>>
> > > >>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
> > > >>>>>>>>>>
> > > >>>>>>>>>> :^D
> > > >>>>>>>>>>
> > > >>>>>>>>> Actually, not exactly sure where to go from here. I get into
> > > >>>>>>>>> dead ends
> > > >>>>>>>>> when I want to continue it. Do I go left? If I got right, then
> > > >>>>>>>>> I have to
> > > >>>>>>>>> go up and have to go left. So, the initial size might be an issue?
> > > >>>>>>>>> Humm... Not sure yet.
> > > >>>>>>>> Use the original list.
> > > >>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
> > > >>>>>>>> you want
> > > >>>>>>>> a larger lattice.
> > > >>>>>>> My smart phone is screwed up. I couldn't open up the animation
> > > >>>>>>> you sent 2 days ago.
> > > >>>>>>> Send to my other e-mail address. Thanks
> > > >>>>>> Sorry about the FB link. However, can you go to it and see the
> > > >>>>>> content?
> > > >>>>>> This one has a path back home:
> > > >>>>>>
> > > >>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
> > > >>>>>>
> > > >>>>>>
> > > >>>>>> The following link goes to the one that is the "infinite" builder...
> > > >>>>>> Very tall, infinitely tall... ;^D
> > > >>>>>>
> > > >>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> > > >>>>>>
> > > >>>>>> Many rooms... ;^)
> > > >>>>>>
> > > >>>>>> lol. ;^)
> > > >>>>> Nice presentation on both.
> > > >>>>> I like the one color going out and the different color coming back in.
> > > >>>>> Thanks.
> > > >>>>> You left out the last 8 directions on the original post to complete
> > > >>>>> my new lattice.
> > > >>>>> (L,U,R,D,R,U,L,U)
> > > >>>>> It probably confused you because just to continue to the next
> > > >>>>> larger lattice the above
> > > >>>>> had to be truncated and then I showed the added directions to get
> > > >>>>> the next larger lattice.
> > > >>>>> I won't do that again because it is confusing.
> > > >>>>> I will just send each larger and larger set of directions for each
> > > >>>>> lattice.
> > > >>>> These have to be done in slow motion to really appreciate the pencil
> > > >>>> not leaving the paper.
> > > >>> How many frames per second? 24, 60, 120? I can time and orchestrate
> > > >>> things using the fps.
> > > >>
> > > >> If it can be done like 4 fps, like a pencil drawing it fast.
> > > >> I will send you all 4 lattice directions.
> > > >> The first has 1,3,5,7,7,5,3,1 vertical cells.
> > > >> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
> > > >> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
> > > >> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
> > > >> I still have to capture more data for the last one.
> > > >> A nice way to present this is show the full lattice with a question.
> > > >> Can you draw this lattice without retracing or crossing a line and not
> > > >> lifting the pencil
> > > >> from the paper in the process?
> > > >
> > > > Basically, how many frames to draw a single line with an arrow on it... ?
> > > One second per line with animation in the per second frame interval. So,
> > > say 60fps, 60 frames for a growing line animation per second.
> > Sounds good.
> > I am posting 3 completed lattices. I and am still gathering data on the 4th one.
> > The first lattice below where the pencil
> > never leaves the paper.
> > (1,3,5,7,7,5,3,1) vertical cells
> > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > L,D,L,D,L,U,L,U,R,D,R,U,L,U
> >
> > The second lattice.
> > (1,3,5,7,9,9,7,5,3,1) vertical cells.
> > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> > L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> > R,D,R,U,R,D,R,U,L,U
> >
> > The third lattice
> > (1,3,5,7,9,11,11,9,7,5,3,1) vertical cells.
> > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> > L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> > R,D,L,U,L,U,L,U,R,U,R,U,R,U,R,U,R,U,R,U,R,D
> > R,D,R,D,R,D,R,D,R,D,L,D,L,D,L,D,L,D,L,D,L,D
> > L,U,L,U,L,U,R,D,R,U,L,U
> > I hope these are correct.
> Chris,
> Once you display these in slow motion, the question I have to anyone is, what other paths are
> possible in the given lattice ruling out the one mirror image or reversing the path or applying
> my --->oo and back algorithm? Also the other restriction is, the cell you start on has to be an
> internal cell of the lattice and not a border cell.
I just discovered another one for a lattice with vertical cells of 1,3,5,7,7,5,3,1 with the above
restrictions. So there could be more for that one lattice!

On Friday, June 16, 2023 at 1:03:58 PM UTC-4, Dan joyce wrote:
> On Friday, June 16, 2023 at 9:44:55 AM UTC-4, Dan joyce wrote:
> > On Thursday, June 15, 2023 at 10:49:08 PM UTC-4, Dan joyce wrote:
> > > On Thursday, June 15, 2023 at 10:42:28 PM UTC-4, Chris M. Thomasson wrote:
> > > > On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> > > > > On 6/15/2023 5:48 PM, Dan joyce wrote:
> > > > >> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
> > > > >>> On 6/15/2023 4:18 PM, Dan joyce wrote:
> > > > >>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> > > > >>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson
> > > > >>>>> wrote:
> > > > >>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
> > > > >>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> > > > >>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
> > > > >>>>>>>> Thomasson wrote:
> > > > >>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> > > > >>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> > > > >>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
> > > > >>>>>>>>>>> wrote:
> > > > >>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
> > > > >>>>>>>>>>>> Thomasson
> > > > >>>>>>>>>>>> wrote:
> > > > >>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> > > > >>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
> > > > >>>>>>>>>>>>>> Thomasson
> > > > >>>>>>>>>>>>>> wrote:
> > > > >>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> > > > >>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
> > > > >>>>>>>>>>>>>>>> joyce wrote:
> > > > >>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
> > > > >>>>>>>>>>>>>>>>> joyce wrote:
> > > > >>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
> > > > >>>>>>>>>>>>>>>>>> joyce wrote:
> > > > >>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
> > > > >>>>>>>>>>>>>>>>>>> joyce wrote:
> > > > >>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
> > > > >>>>>>>>>>>>>>>>>>>> Chris M.
> > > > >>>>>>>>>>>>>>>>>>>> Thomasson wrote:
> > > > >>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> > > > >>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
> > > > >>>>>>>>>>>>>>>>>>>>>> algorithm
> > > > >>>>>>>>>>>>>>>>>>>>>> than James'
> > > > >>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
> > > > >>>>>>>>>>>>>>>>>>>>>> that right?
> > > > >>>>>>>>>>>>>>>>>>>>>> Can you post
> > > > >>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
> > > > >>>>>>>>>>>>>>>>>>>>>> without
> > > > >>>>>>>>>>>>>>>>>>>>>> using a path
> > > > >>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
> > > > >>>>>>>>>>>>>>>>>>>>>> version of
> > > > >>>>>>>>>>>>>>>>>>>>>> the lattice:
> > > > >>>>>>>>>>>>>>>>>>>>>>
> > > > >>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> > > > >>>>>>>>>>>>>>>>>>>>> [...]
> > > > >>>>>>>>>>>>>>>>>>>>>
> > > > >>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
> > > > >>>>>>>>>>>>>>>>>>>>> algorithm:
> > > > >>>>>>>>>>>>>>>>>>>>>
> > > > >>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> > > > >>>>>>>>>>>>>>>>>>>> Nice!
> > > > >>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
> > > > >>>>>>>>>>>>>>>>>>>> the other
> > > > >>>>>>>>>>>>>>>>>>>> one going up and left.
> > > > >>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
> > > > >>>>>>>>>>>>>>>>>>>> is finite
> > > > >>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
> > > > >>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> > > > >>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
> > > > >>>>>>>>>>>>>>>>>>> before
> > > > >>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
> > > > >>>>>>>>>>>>>>>>>>> of their line.
> > > > >>>>>>>>>>>>>>>>>>> .
> > > > >>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
> > > > >>>>>>>>>>>>>>>>>> creates the
> > > > >>>>>>>>>>>>>>>>>> cells as it goes.
> > > > >>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
> > > > >>>>>>>>>>>>>>>>>> directions.
> > > > >>>>>>>>>>>>>>>>>> Even very small fractional
> > > > >>>>>>>>>>>>>>>>>> directions --->oo.
> > > > >>>>>>>>>>>>>>>>>>
> > > > >>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
> > > > >>>>>>>>>>>>>>>>>> lattice.
> > > > >>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
> > > > >>>>>>>>>>>>>>>>>> origin to
> > > > >>>>>>>>>>>>>>>>>> complete all the cells in
> > > > >>>>>>>>>>>>>>>>>> any size square lattice --->oo.
> > > > >>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
> > > > >>>>>>>>>>>>>>>>>> --->oo
> > > > >>>>>>>>>>>>>>>>>> length.
> > > > >>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
> > > > >>>>>>>>>>>>>>>>>> this new one
> > > > >>>>>>>>>>>>>>>>>> is something else that
> > > > >>>>>>>>>>>>>>>>>> i am sure some will say not possible.
> > > > >>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
> > > > >>>>>>>>>>>>>>>>>> directions R,D,LU
> > > > >>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
> > > > >>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil.
> > > > >>>>>>>>>>>>>>>>>> All the
> > > > >>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
> > > > >>>>>>>>>>>>>>>>>> up or down at the end of each line.
> > > > >>>>>>>>>>>>>>>>>> What do you think?
> > > > >>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
> > > > >>>>>>>>>>>>>>>>>> original
> > > > >>>>>>>>>>>>>>>>>> and the new lattice you propose.
> > > > >>>>>>>>>>>>>>>>> It is true Chris,
> > > > >>>>>>>>>>>>>>>>>
> > > > >>>>>>>>>>>>>>>>> A simple straight forward list of directions that
> > > > >>>>>>>>>>>>>>>>> represents the first rendering I sent you.
> > > > >>>>>>>>>>>>>>> This one?
> > > > >>>>>>>>>>>>>>>
> > > > >>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> > > > >>>>>>>>>>>>>>> [...]
> > > > >>>>>>>>>>>>>> Yes!
> > > > >>>>>>>>>>>>>> That is the list of directions for building it.
> > > > >>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
> > > > >>>>>>>>>>>>>> pencil not
> > > > >>>>>>>>>>>>>> lifting off the page
> > > > >>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
> > > > >>>>>>>>>>>>>> it end up
> > > > >>>>>>>>>>>>>> as that image
> > > > >>>>>>>>>>>>>> I sent you.
> > > > >>>>>>>>>>>>>> I have made the next one but need to capture the
> > > > >>>>>>>>>>>>>> directions and
> > > > >>>>>>>>>>>>>> when I do I will send it along.
> > > > >>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
> > > > >>>>>>>>>>>>> must show all
> > > > >>>>>>>>>>>>> the different ways this can be constructed. From your
> > > > >>>>>>>>>>>>> originals and my
> > > > >>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
> > > > >>>>>>>>>>>> Sounds great!
> > > > >>>>>>>>>>>> This last one, if you read some of James's remarks that what
> > > > >>>>>>>>>>>> I just
> > > > >>>>>>>>>>>> did in this one was not possible.
> > > > >>>>>>>>>>>> I think James will be surprised when he runs the direction
> > > > >>>>>>>>>>>> list I
> > > > >>>>>>>>>>>> just sent. Also more larger ones can be built.
> > > > >>>>>>>>>>>> It is good to have you guys on board with this. It adds to
> > > > >>>>>>>>>>>> the effort
> > > > >>>>>>>>>>>> of perfecting all of this for presentation.
> > > > >>>>>>>>>>>> Thanks to both you guys.
> > > > >>>>>>>>>>>
> > > > >>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > > >>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > > >>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > > >>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> > > > >>>>>>>>>> [...]
> > > > >>>>>>>>>>
> > > > >>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
> > > > >>>>>>>>>> tangent
> > > > >>>>>>>>>> with the end point, the center of the circle in yellow.
> > > > >>>>>>>>>>
> > > > >>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
> > > > >>>>>>>>>>
> > > > >>>>>>>>>> :^D
> > > > >>>>>>>>>>
> > > > >>>>>>>>> Actually, not exactly sure where to go from here. I get into
> > > > >>>>>>>>> dead ends
> > > > >>>>>>>>> when I want to continue it. Do I go left? If I got right, then
> > > > >>>>>>>>> I have to
> > > > >>>>>>>>> go up and have to go left. So, the initial size might be an issue?
> > > > >>>>>>>>> Humm... Not sure yet.
> > > > >>>>>>>> Use the original list.
> > > > >>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
> > > > >>>>>>>> you want
> > > > >>>>>>>> a larger lattice.
> > > > >>>>>>> My smart phone is screwed up. I couldn't open up the animation
> > > > >>>>>>> you sent 2 days ago.
> > > > >>>>>>> Send to my other e-mail address. Thanks
> > > > >>>>>> Sorry about the FB link. However, can you go to it and see the
> > > > >>>>>> content?
> > > > >>>>>> This one has a path back home:
> > > > >>>>>>
> > > > >>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
> > > > >>>>>>
> > > > >>>>>>
> > > > >>>>>> The following link goes to the one that is the "infinite" builder...
> > > > >>>>>> Very tall, infinitely tall... ;^D
> > > > >>>>>>
> > > > >>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> > > > >>>>>>
> > > > >>>>>> Many rooms... ;^)
> > > > >>>>>>
> > > > >>>>>> lol. ;^)
> > > > >>>>> Nice presentation on both.
> > > > >>>>> I like the one color going out and the different color coming back in.
> > > > >>>>> Thanks.
> > > > >>>>> You left out the last 8 directions on the original post to complete
> > > > >>>>> my new lattice.
> > > > >>>>> (L,U,R,D,R,U,L,U)
> > > > >>>>> It probably confused you because just to continue to the next
> > > > >>>>> larger lattice the above
> > > > >>>>> had to be truncated and then I showed the added directions to get
> > > > >>>>> the next larger lattice.
> > > > >>>>> I won't do that again because it is confusing.
> > > > >>>>> I will just send each larger and larger set of directions for each
> > > > >>>>> lattice.
> > > > >>>> These have to be done in slow motion to really appreciate the pencil
> > > > >>>> not leaving the paper.
> > > > >>> How many frames per second? 24, 60, 120? I can time and orchestrate
> > > > >>> things using the fps.
> > > > >>
> > > > >> If it can be done like 4 fps, like a pencil drawing it fast.
> > > > >> I will send you all 4 lattice directions.
> > > > >> The first has 1,3,5,7,7,5,3,1 vertical cells.
> > > > >> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
> > > > >> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
> > > > >> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
> > > > >> I still have to capture more data for the last one.
> > > > >> A nice way to present this is show the full lattice with a question.
> > > > >> Can you draw this lattice without retracing or crossing a line and not
> > > > >> lifting the pencil
> > > > >> from the paper in the process?
> > > > >
> > > > > Basically, how many frames to draw a single line with an arrow on it... ?
> > > > One second per line with animation in the per second frame interval.. So,
> > > > say 60fps, 60 frames for a growing line animation per second.
> > > Sounds good.
> > > I am posting 3 completed lattices. I and am still gathering data on the 4th one.
> > > The first lattice below where the pencil
> > > never leaves the paper.
> > > (1,3,5,7,7,5,3,1) vertical cells
> > > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > L,D,L,D,L,U,L,U,R,D,R,U,L,U
> > >
> > > The second lattice.
> > > (1,3,5,7,9,9,7,5,3,1) vertical cells.
> > > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> > > L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> > > R,D,R,U,R,D,R,U,L,U
> > >
> > > The third lattice
> > > (1,3,5,7,9,11,11,9,7,5,3,1) vertical cells.
> > > R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> > > L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> > > R,D,L,U,L,U,L,U,R,U,R,U,R,U,R,U,R,U,R,U,R,D
> > > R,D,R,D,R,D,R,D,R,D,L,D,L,D,L,D,L,D,L,D,L,D
> > > L,U,L,U,L,U,R,D,R,U,L,U
> > > I hope these are correct.
> > Chris,
> > Once you display these in slow motion, the question I have to anyone is, what other paths are
> > possible in the given lattice ruling out the one mirror image or reversing the path or applying
> > my --->oo and back algorithm? Also the other restriction is, the cell you start on has to be an
> > internal cell of the lattice and not a border cell.
> I just discovered another one for a lattice with vertical cells of 1,3,5,7,7,5,3,1 with the above
> restrictions. So there could be more for that one lattice!
I just looked up Lattice order in Wikipedia and my brain hurts. Lattice theory does deal with sets
as I thought. Not knowing anything about set theory I opened up my own can of worms so to speak.

On Thursday, June 15, 2023 at 10:49:08 PM UTC-4, Dan joyce wrote:
> On Thursday, June 15, 2023 at 10:42:28 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/15/2023 6:47 PM, Chris M. Thomasson wrote:
> > > On 6/15/2023 5:48 PM, Dan joyce wrote:
> > >> On Thursday, June 15, 2023 at 7:25:39 PM UTC-4, Chris M. Thomasson wrote:
> > >>> On 6/15/2023 4:18 PM, Dan joyce wrote:
> > >>>> On Thursday, June 15, 2023 at 5:10:38 PM UTC-4, Dan joyce wrote:
> > >>>>> On Thursday, June 15, 2023 at 4:27:50 PM UTC-4, Chris M. Thomasson
> > >>>>> wrote:
> > >>>>>> On 6/15/2023 4:15 AM, Dan joyce wrote:
> > >>>>>>> On Thursday, June 15, 2023 at 6:55:17 AM UTC-4, Dan joyce wrote:
> > >>>>>>>> On Thursday, June 15, 2023 at 3:53:59 AM UTC-4, Chris M.
> > >>>>>>>> Thomasson wrote:
> > >>>>>>>>> On 6/15/2023 12:51 AM, Chris M. Thomasson wrote:
> > >>>>>>>>>> On 6/14/2023 7:36 PM, Dan joyce wrote:
> > >>>>>>>>>>> On Wednesday, June 14, 2023 at 7:47:41 PM UTC-4, Dan joyce
> > >>>>>>>>>>> wrote:
> > >>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:35:45 PM UTC-4, Chris M.
> > >>>>>>>>>>>> Thomasson
> > >>>>>>>>>>>> wrote:
> > >>>>>>>>>>>>> On 6/14/2023 4:33 PM, Dan joyce wrote:
> > >>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 7:07:33 PM UTC-4, Chris M.
> > >>>>>>>>>>>>>> Thomasson
> > >>>>>>>>>>>>>> wrote:
> > >>>>>>>>>>>>>>> On 6/14/2023 3:26 PM, Dan joyce wrote:
> > >>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 6:23:33 PM UTC-4, Dan
> > >>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 3:33:54 PM UTC-4, Dan
> > >>>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:59:27 AM UTC-4, Dan
> > >>>>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>>>> On Wednesday, June 14, 2023 at 8:54:12 AM UTC-4, Dan
> > >>>>>>>>>>>>>>>>>>> joyce wrote:
> > >>>>>>>>>>>>>>>>>>>> On Tuesday, June 13, 2023 at 10:49:01 PM UTC-4,
> > >>>>>>>>>>>>>>>>>>>> Chris M.
> > >>>>>>>>>>>>>>>>>>>> Thomasson wrote:
> > >>>>>>>>>>>>>>>>>>>>> On 6/13/2023 6:42 PM, Chris M. Thomasson wrote:
> > >>>>>>>>>>>>>>>>>>>>>> I got the square lattice down, using a different
> > >>>>>>>>>>>>>>>>>>>>>> algorithm
> > >>>>>>>>>>>>>>>>>>>>>> than James'
> > >>>>>>>>>>>>>>>>>>>>>> version. However, Dan has a new version out, is
> > >>>>>>>>>>>>>>>>>>>>>> that right?
> > >>>>>>>>>>>>>>>>>>>>>> Can you post
> > >>>>>>>>>>>>>>>>>>>>>> it in this fresh thread? It builds out the grid
> > >>>>>>>>>>>>>>>>>>>>>> without
> > >>>>>>>>>>>>>>>>>>>>>> using a path
> > >>>>>>>>>>>>>>>>>>>>>> back home? Fwiw, here is a result of my current
> > >>>>>>>>>>>>>>>>>>>>>> version of
> > >>>>>>>>>>>>>>>>>>>>>> the lattice:
> > >>>>>>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C802QKf/image.png
> > >>>>>>>>>>>>>>>>>>>>> [...]
> > >>>>>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>>>>> Here is another one built using a completely different
> > >>>>>>>>>>>>>>>>>>>>> algorithm:
> > >>>>>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>>>>> https://i.ibb.co/C14qksJ/image.png
> > >>>>>>>>>>>>>>>>>>>> Nice!
> > >>>>>>>>>>>>>>>>>>>> I like the two color idea, one for going right and
> > >>>>>>>>>>>>>>>>>>>> the other
> > >>>>>>>>>>>>>>>>>>>> one going up and left.
> > >>>>>>>>>>>>>>>>>>>> Has this actually been done before? A lattice that
> > >>>>>>>>>>>>>>>>>>>> is finite
> > >>>>>>>>>>>>>>>>>>>> in width but --->oo in length.
> > >>>>>>>>>>>>>>>>>>>> Talk about a rectangular shape, this is the ultimate.
> > >>>>>>>>>>>>>>>>>>> I have that wrong. (Both) colors have an upward path
> > >>>>>>>>>>>>>>>>>>> before
> > >>>>>>>>>>>>>>>>>>> their 90 degree turn at the top
> > >>>>>>>>>>>>>>>>>>> of their line.
> > >>>>>>>>>>>>>>>>>>> .
> > >>>>>>>>>>>>>>>>>> Chris, did you receive my photo of the lattice that
> > >>>>>>>>>>>>>>>>>> creates the
> > >>>>>>>>>>>>>>>>>> cells as it goes.
> > >>>>>>>>>>>>>>>>>> No pathways present. Also it will --->oo in all
> > >>>>>>>>>>>>>>>>>> directions.
> > >>>>>>>>>>>>>>>>>> Even very small fractional
> > >>>>>>>>>>>>>>>>>> directions --->oo.
> > >>>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>>> I believe this is significant over my original pathway
> > >>>>>>>>>>>>>>>>>> lattice.
> > >>>>>>>>>>>>>>>>>> The reason being that had to follow a pathway back to
> > >>>>>>>>>>>>>>>>>> origin to
> > >>>>>>>>>>>>>>>>>> complete all the cells in
> > >>>>>>>>>>>>>>>>>> any size square lattice --->oo.
> > >>>>>>>>>>>>>>>>>> Even the new one that you propose has finite width and
> > >>>>>>>>>>>>>>>>>> --->oo
> > >>>>>>>>>>>>>>>>>> length.
> > >>>>>>>>>>>>>>>>>> That is a nice one also along with my original but
> > >>>>>>>>>>>>>>>>>> this new one
> > >>>>>>>>>>>>>>>>>> is something else that
> > >>>>>>>>>>>>>>>>>> i am sure some will say not possible.
> > >>>>>>>>>>>>>>>>>> I am going to start to build the sequence of
> > >>>>>>>>>>>>>>>>>> directions R,D,LU
> > >>>>>>>>>>>>>>>>>> to prove it is possible to start a lattice
> > >>>>>>>>>>>>>>>>>> filling cells as you go without lifting the pencil.
> > >>>>>>>>>>>>>>>>>> All the
> > >>>>>>>>>>>>>>>>>> while making 90 degree turns right or left or
> > >>>>>>>>>>>>>>>>>> up or down at the end of each line.
> > >>>>>>>>>>>>>>>>>> What do you think?
> > >>>>>>>>>>>>>>>>>> If this is true, it would be more significant then my
> > >>>>>>>>>>>>>>>>>> original
> > >>>>>>>>>>>>>>>>>> and the new lattice you propose.
> > >>>>>>>>>>>>>>>>> It is true Chris,
> > >>>>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>>>> A simple straight forward list of directions that
> > >>>>>>>>>>>>>>>>> represents the first rendering I sent you.
> > >>>>>>>>>>>>>>> This one?
> > >>>>>>>>>>>>>>>
> > >>>>>>>>>>>>>>> https://i.ibb.co/D1LQrFZ/image.png
> > >>>>>>>>>>>>>>> [...]
> > >>>>>>>>>>>>>> Yes!
> > >>>>>>>>>>>>>> That is the list of directions for building it.
> > >>>>>>>>>>>>>> Do it in slow-motion and you will really appreciate the
> > >>>>>>>>>>>>>> pencil not
> > >>>>>>>>>>>>>> lifting off the page
> > >>>>>>>>>>>>>> or in this case when I enter each direction via keyboard
> > >>>>>>>>>>>>>> it end up
> > >>>>>>>>>>>>>> as that image
> > >>>>>>>>>>>>>> I sent you.
> > >>>>>>>>>>>>>> I have made the next one but need to capture the
> > >>>>>>>>>>>>>> directions and
> > >>>>>>>>>>>>>> when I do I will send it along.
> > >>>>>>>>>>>>> Okay. Well, basically, I think a proper animation simply
> > >>>>>>>>>>>>> must show all
> > >>>>>>>>>>>>> the different ways this can be constructed. From your
> > >>>>>>>>>>>>> originals and my
> > >>>>>>>>>>>>> and James' work, up to your new work. Fair enough?
> > >>>>>>>>>>>> Sounds great!
> > >>>>>>>>>>>> This last one, if you read some of James's remarks that what
> > >>>>>>>>>>>> I just
> > >>>>>>>>>>>> did in this one was not possible.
> > >>>>>>>>>>>> I think James will be surprised when he runs the direction
> > >>>>>>>>>>>> list I
> > >>>>>>>>>>>> just sent. Also more larger ones can be built.
> > >>>>>>>>>>>> It is good to have you guys on board with this. It adds to
> > >>>>>>>>>>>> the effort
> > >>>>>>>>>>>> of perfecting all of this for presentation.
> > >>>>>>>>>>>> Thanks to both you guys.
> > >>>>>>>>>>>
> > >>>>>>>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > >>>>>>>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > >>>>>>>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > >>>>>>>>>>> L,D,L,D,L,U,(L,U,R,D,R,U,L,U) Do not run these (...)
> > >>>>>>>>>> [...]
> > >>>>>>>>>>
> > >>>>>>>>>> Looking good. The start circle in red, the origin, is nice and
> > >>>>>>>>>> tangent
> > >>>>>>>>>> with the end point, the center of the circle in yellow.
> > >>>>>>>>>>
> > >>>>>>>>>> https://i.ibb.co/zhjM4KY/image.png
> > >>>>>>>>>>
> > >>>>>>>>>> :^D
> > >>>>>>>>>>
> > >>>>>>>>> Actually, not exactly sure where to go from here. I get into
> > >>>>>>>>> dead ends
> > >>>>>>>>> when I want to continue it. Do I go left? If I got right, then
> > >>>>>>>>> I have to
> > >>>>>>>>> go up and have to go left. So, the initial size might be an issue?
> > >>>>>>>>> Humm... Not sure yet.
> > >>>>>>>> Use the original list.
> > >>>>>>>> (L,U,R,D,R,U,L,U) is truncated from the original list only if
> > >>>>>>>> you want
> > >>>>>>>> a larger lattice.
> > >>>>>>> My smart phone is screwed up. I couldn't open up the animation
> > >>>>>>> you sent 2 days ago.
> > >>>>>>> Send to my other e-mail address. Thanks
> > >>>>>> Sorry about the FB link. However, can you go to it and see the
> > >>>>>> content?
> > >>>>>> This one has a path back home:
> > >>>>>>
> > >>>>>> https://www.facebook.com/100034470228086/videos/791843519283462/
> > >>>>>>
> > >>>>>>
> > >>>>>> The following link goes to the one that is the "infinite" builder...
> > >>>>>> Very tall, infinitely tall... ;^D
> > >>>>>>
> > >>>>>> https://www.facebook.com/100034470228086/videos/pcb.984179659407699/992449118551795
> > >>>>>>
> > >>>>>> Many rooms... ;^)
> > >>>>>>
> > >>>>>> lol. ;^)
> > >>>>> Nice presentation on both.
> > >>>>> I like the one color going out and the different color coming back in.
> > >>>>> Thanks.
> > >>>>> You left out the last 8 directions on the original post to complete
> > >>>>> my new lattice.
> > >>>>> (L,U,R,D,R,U,L,U)
> > >>>>> It probably confused you because just to continue to the next
> > >>>>> larger lattice the above
> > >>>>> had to be truncated and then I showed the added directions to get
> > >>>>> the next larger lattice.
> > >>>>> I won't do that again because it is confusing.
> > >>>>> I will just send each larger and larger set of directions for each
> > >>>>> lattice.
> > >>>> These have to be done in slow motion to really appreciate the pencil
> > >>>> not leaving the paper.
> > >>> How many frames per second? 24, 60, 120? I can time and orchestrate
> > >>> things using the fps.
> > >>
> > >> If it can be done like 4 fps, like a pencil drawing it fast.
> > >> I will send you all 4 lattice directions.
> > >> The first has 1,3,5,7,7,5,3,1 vertical cells.
> > >> The 2nd one has 1,3,5,7,9,9,7,5,3,1 vertical cells.
> > >> The third one has 1,3,5,7,9, 11,11,9,7,5,3,1
> > >> The 4th one has 1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical cells.
> > >> I still have to capture more data for the last one.
> > >> A nice way to present this is show the full lattice with a question.
> > >> Can you draw this lattice without retracing or crossing a line and not
> > >> lifting the pencil
> > >> from the paper in the process?
> > >
> > > Basically, how many frames to draw a single line with an arrow on it.... ?
> > One second per line with animation in the per second frame interval. So,
> > say 60fps, 60 frames for a growing line animation per second.
> Sounds good.
> I am posting 3 completed lattices. I and am still gathering data on the 4th one.
> The first lattice below where the pencil
> never leaves the paper.
> (1,3,5,7,7,5,3,1) vertical cells
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,U,R,D,R,U,L,U
>
> The second lattice.
> (1,3,5,7,9,9,7,5,3,1) vertical cells.
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> R,D,R,U,R,D,R,U,L,U
>
> The third lattice
> (1,3,5,7,9,11,11,9,7,5,3,1) vertical cells.
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
> L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
> R,D,L,U,L,U,L,U,R,U,R,U,R,U,R,U,R,U,R,U,R,D
> R,D,R,D,R,D,R,D,R,D,L,D,L,D,L,D,L,D,L,D,L,D
> L,U,L,U,L,U,R,D,R,U,L,U
> I hope these are correct.
Here is the largest of the 4 lattice's and is probably the one to work on because
it will have the longest path to completion.
The pencil never leaves the paper and never crosses and existing line or does a retrace.
The forth lattice
(1,3,5,7,9,11,13,13,11,9,7,5,3,1) vertical cells.
R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
L,D,L,D,L,U,L,D,R,D,R,U,R,U,R,U,R,U,R,U,R,U
L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D,R,D
R,D,L,U,L,U,L,U,R,U,R,U,R,U,R,U,R,U,R,U,R,D
R,D,R,D,R,D,R,D,R,D,L,D,L,D,L,D,L,D,L,D,L,D
L,D,R,U,R,U,R,U,R,U,R,U,R,U,R,U,R,U,L,U,L,U
L,U,L,U,L,U,L,U,L,U,L,D,L,D,L,D,L,D,L,D,L,D
L,D,L,D,R,D,R,D,R,D.R.D,R,D,R,U,L,U,L,U,R,U
R,D,R,U,L,U

On 6/15/2023 7:49 PM, Dan joyce wrote:
> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> L,D,L,D,L,U,L,U,R,D,R,U,L,U

Produces:

https://i.ibb.co/92DFDM6/image.png

Looking good?

On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> On 6/15/2023 7:49 PM, Dan joyce wrote:
>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
>> L,D,L,D,L,U,L,U,R,D,R,U,L,U
>
> Produces:
>
> https://i.ibb.co/92DFDM6/image.png
>
> Looking good?

I need to break this down with an animation.

On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > On 6/15/2023 7:49 PM, Dan joyce wrote:
> >> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> >> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> >> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> >> L,D,L,D,L,U,L,U,R,D,R,U,L,U
> >
> > Produces:
> >
> > https://i.ibb.co/92DFDM6/image.png
> >
> > Looking good?
> I need to break this down with an animation.
Nice!
That is the smallest lattice of the 4.
Looks good but when completed it is hard to see the actual path with or
without arrows. Just like looking at a plain completed lattice. The animation
will of coerce fix that as you see the path filling in.
That will be interesting to see.
All 4 of these start with the same path but as they grow from one lattice to the next
more revolutions are involved but not completed revolutions. At one point the trace
has to stop and reverse the revolution to the stopping point at the end of that revolution.
Turning around and repeating the process then finally filling the hole at the end of
that revolution. The animation will show this.
Thanks.

Dan

On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > > On 6/15/2023 7:49 PM, Dan joyce wrote:
> > >> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > >> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > >> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > >> L,D,L,D,L,U,L,U,R,D,R,U,L,U
> > >
> > > Produces:
> > >
> > > https://i.ibb.co/92DFDM6/image.png
> > >
> > > Looking good?
> > I need to break this down with an animation.
> Nice!
> That is the smallest lattice of the 4.
> Looks good but when completed it is hard to see the actual path with or
> without arrows. Just like looking at a plain completed lattice. The animation
> will of coerce fix that as you see the path filling in.
> That will be interesting to see.
> All 4 of these start with the same path but as they grow from one lattice to the next
> more revolutions are involved but not completed revolutions. At one point the trace
> has to stop and reverse the revolution to the stopping point at the end of that revolution.
> Turning around and repeating the process then finally filling the hole at the end of
> that revolution. The animation will show this.
> Thanks.
>
> Dan
I believe other paths are possible in just messing around with it but I'm not sure.
Maybe someone else will find a different path. That will be interesting to see.

On Saturday, June 17, 2023 at 1:12:04 AM UTC-4, Dan joyce wrote:
> On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> > On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> > > On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > > > On 6/15/2023 7:49 PM, Dan joyce wrote:
> > > >> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > >> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > >> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > >> L,D,L,D,L,U,L,U,R,D,R,U,L,U
> > > >
> > > > Produces:
> > > >
> > > > https://i.ibb.co/92DFDM6/image.png
> > > >
> > > > Looking good?
> > > I need to break this down with an animation.
> > Nice!
> > That is the smallest lattice of the 4.
> > Looks good but when completed it is hard to see the actual path with or
> > without arrows. Just like looking at a plain completed lattice. The animation
> > will of coerce fix that as you see the path filling in.
> > That will be interesting to see.
> > All 4 of these start with the same path but as they grow from one lattice to the next
> > more revolutions are involved but not completed revolutions. At one point the trace
> > has to stop and reverse the revolution to the stopping point at the end of that revolution.
> > Turning around and repeating the process then finally filling the hole at the end of
> > that revolution. The animation will show this.
> > Thanks.
> >
> > Dan
> I believe other paths are possible in just messing around with it but I'm not sure.
> Maybe someone else will find a different path. That will be interesting to see.
If that is possible, can the two animations run side by side?

On Saturday, June 17, 2023 at 1:14:20 AM UTC-4, Dan joyce wrote:
> On Saturday, June 17, 2023 at 1:12:04 AM UTC-4, Dan joyce wrote:
> > On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> > > On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> > > > On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > > > > On 6/15/2023 7:49 PM, Dan joyce wrote:
> > > > >> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > > > >> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > > > >> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > > > >> L,D,L,D,L,U,L,U,R,D,R,U,L,U
> > > > >
> > > > > Produces:
> > > > >
> > > > > https://i.ibb.co/92DFDM6/image.png
> > > > >
> > > > > Looking good?
> > > > I need to break this down with an animation.
> > > Nice!
> > > That is the smallest lattice of the 4.
> > > Looks good but when completed it is hard to see the actual path with or
> > > without arrows. Just like looking at a plain completed lattice. The animation
> > > will of coerce fix that as you see the path filling in.
> > > That will be interesting to see.
> > > All 4 of these start with the same path but as they grow from one lattice to the next
> > > more revolutions are involved but not completed revolutions. At one point the trace
> > > has to stop and reverse the revolution to the stopping point at the end of that revolution.
> > > Turning around and repeating the process then finally filling the hole at the end of
> > > that revolution. The animation will show this.
> > > Thanks.
> > >
> > I believe other paths are possible in just messing around with it but I'm not sure.
> > Maybe someone else will find a different path. That will be interesting to see.
> If that is possible, can the two animations run side by side?

What's with this joker AP,?
He said what I was doing was impossible, in so many words, but now Chris produced the video's
to prove it and he lashes out again. He doesn't make any sense. AP, you're the baby in the room, not
me. Have a little dignity man and for once admit you were wrong. I do it often.
I see your posts all the time, but I let you do your thing,

On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > > On 6/15/2023 7:49 PM, Dan joyce wrote:
> > >> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> > >> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> > >> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> > >> L,D,L,D,L,U,L,U,R,D,R,U,L,U
> > >
> > > Produces:
> > >
> > > https://i.ibb.co/92DFDM6/image.png
> > >
> > > Looking good?
> > I need to break this down with an animation.
> Nice!
> That is the smallest lattice of the 4.
> Looks good but when completed it is hard to see the actual path with or
> without arrows. Just like looking at a plain completed lattice. The animation
> will of coerce fix that as you see the path filling in.
> That will be interesting to see.
> All 4 of these start with the same path but as they grow from one lattice to the next
> more revolutions are involved but not completed revolutions. At one point the trace
> has to stop and reverse the revolution to the stopping point at the end of that revolution.
> Turning around and repeating the process then finally filling the hole at the end of
> that revolution. The animation will show this.
> Thanks.
>
> Dan
I have come up with another thought, What if after the lattice has completed with the draw
and given a 10 second pause to view the lattice, then reverse the operation by deleting the path
within the lattice with a slow-motion rendering until a blank screen is attained.
Maybe a tough algorithm to initiate because all the direction data has to be reversed.
Starting at the end of the direction list, left becomes right and right becomes left, up
becomes down and down becomes up.

On 6/17/2023 10:54 AM, Dan joyce wrote:
> On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
>> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
>>> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
>>>> On 6/15/2023 7:49 PM, Dan joyce wrote:
>>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
>>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
>>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
>>>>> L,D,L,D,L,U,L,U,R,D,R,U,L,U
>>>>
>>>> Produces:
>>>>
>>>> https://i.ibb.co/92DFDM6/image.png
>>>>
>>>> Looking good?
>>> I need to break this down with an animation.
>> Nice!
>> That is the smallest lattice of the 4.
>> Looks good but when completed it is hard to see the actual path with or
>> without arrows. Just like looking at a plain completed lattice. The animation
>> will of coerce fix that as you see the path filling in.
>> That will be interesting to see.
>> All 4 of these start with the same path but as they grow from one lattice to the next
>> more revolutions are involved but not completed revolutions. At one point the trace
>> has to stop and reverse the revolution to the stopping point at the end of that revolution.
>> Turning around and repeating the process then finally filling the hole at the end of
>> that revolution. The animation will show this.
>> Thanks.
>>
>> Dan
> I have come up with another thought, What if after the lattice has completed with the draw
> and given a 10 second pause to view the lattice, then reverse the operation by deleting the path
> within the lattice with a slow-motion rendering until a blank screen is attained.
> Maybe a tough algorithm to initiate because all the direction data has to be reversed.
> Starting at the end of the direction list, left becomes right and right becomes left, up
> becomes down and down becomes up.

I should have some time, sometime today to do it. Reversing the process
should not be that difficult... I can create some normals that reverses
the directions when multiplied by said normal. First things first, I
need to work for a couple of hours on my own project, then I can work on
yours. These are interesting to me as well. Thanks Dan.

:^)

On Saturday, June 17, 2023 at 4:01:23 PM UTC-4, Chris M. Thomasson wrote:
> On 6/17/2023 10:54 AM, Dan joyce wrote:
> > On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> >> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> >>> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> >>>> On 6/15/2023 7:49 PM, Dan joyce wrote:
> >>>>> R,U,L,D,L,U,R,U,R,D,R,U,L,U,R,D,R,D,L,D,L,D
> >>>>> R,U,R,U,R,U,L,U,L,U,L,D,L,D,L,D,L,D,R,D,L,U
> >>>>> L,U,R,U,R,U,R,U,R,U,R,D,R,D,R,D,R,D,L,D,L,D
> >>>>> L,D,L,D,L,U,L,U,R,D,R,U,L,U
> >>>>
> >>>> Produces:
> >>>>
> >>>> https://i.ibb.co/92DFDM6/image.png
> >>>>
> >>>> Looking good?
> >>> I need to break this down with an animation.
> >> Nice!
> >> That is the smallest lattice of the 4.
> >> Looks good but when completed it is hard to see the actual path with or
> >> without arrows. Just like looking at a plain completed lattice. The animation
> >> will of coerce fix that as you see the path filling in.
> >> That will be interesting to see.
> >> All 4 of these start with the same path but as they grow from one lattice to the next
> >> more revolutions are involved but not completed revolutions. At one point the trace
> >> has to stop and reverse the revolution to the stopping point at the end of that revolution.
> >> Turning around and repeating the process then finally filling the hole at the end of
> >> that revolution. The animation will show this.
> >> Thanks.
> >>
> >> Dan
> > I have come up with another thought, What if after the lattice has completed with the draw
> > and given a 10 second pause to view the lattice, then reverse the operation by deleting the path
> > within the lattice with a slow-motion rendering until a blank screen is attained.
> > Maybe a tough algorithm to initiate because all the direction data has to be reversed.
> > Starting at the end of the direction list, left becomes right and right becomes left, up
> > becomes down and down becomes up.
> I should have some time, sometime today to do it. Reversing the process
> should not be that difficult... I can create some normals that reverses
> the directions when multiplied by said normal. First things first, I
> need to work for a couple of hours on my own project, then I can work on
> yours. These are interesting to me as well. Thanks Dan.
>
> :^)
Two heads are better then one when mulling over ideas.

On 6/17/2023 3:46 PM, Dan joyce wrote:
> On Saturday, June 17, 2023 at 4:01:23 PM UTC-4, Chris M. Thomasson wrote:
>> On 6/17/2023 10:54 AM, Dan joyce wrote:
>>> On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
>>>> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
>>>>> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
>>>>>> On 6/15/2023 7:49 PM, Dan joyce wrote:
[...]
> Two heads are better then one when mulling over ideas.

Did you get my emails? The animation is too fast, but I still have not
hooked up proper FPS to the final animation, yet... ;^)

On Saturday, June 17, 2023 at 10:09:53 PM UTC-4, Chris M. Thomasson wrote:
> On 6/17/2023 3:46 PM, Dan joyce wrote:
> > On Saturday, June 17, 2023 at 4:01:23 PM UTC-4, Chris M. Thomasson wrote:
> >> On 6/17/2023 10:54 AM, Dan joyce wrote:
> >>> On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> >>>> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> >>>>> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> >>>>>> On 6/15/2023 7:49 PM, Dan joyce wrote:
> [...]
> > Two heads are better then one when mulling over ideas.
> Did you get my emails? The animation is too fast, but I still have not
> hooked up proper FPS to the final animation, yet... ;^)

That is fantastic! Double that fantastic slowed down and with a larger lattice.
If you could slow it down a lot more and use the last largest lattice directions with ----
offset by 1----1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical and horizontal cells it would be very impressive.
Each progressive one of these lattices are all connected so to speak.
It is hard to explain but each progressive's sized lattice leaves a hole (unfinished cells) if you add on
the next sized lattice to it leaving out a small increasing number of cells from the previous lattice and
so on to create the tail end of the next draw to complete the latest lattice. It all sounds confusing but
this is the way I can continue theoretically --->oo in the number of lattices that the pencil never leaves the
paper.
Clear as mud I know but very hard to explain.
.

On Sunday, June 18, 2023 at 12:36:04 AM UTC-4, Dan joyce wrote:
> On Saturday, June 17, 2023 at 10:09:53 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/17/2023 3:46 PM, Dan joyce wrote:
> > > On Saturday, June 17, 2023 at 4:01:23 PM UTC-4, Chris M. Thomasson wrote:
> > >> On 6/17/2023 10:54 AM, Dan joyce wrote:
> > >>> On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> > >>>> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> > >>>>> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > >>>>>> On 6/15/2023 7:49 PM, Dan joyce wrote:
> > [...]
> > > Two heads are better then one when mulling over ideas.
> > Did you get my emails? The animation is too fast, but I still have not
> > hooked up proper FPS to the final animation, yet... ;^)
> That is fantastic! Double that fantastic slowed down and with a larger lattice.
> If you could slow it down a lot more and use the last largest lattice directions with ----
> offset by 1----1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical and horizontal cells it would be very impressive.
> Each progressive one of these lattices are all connected so to speak.
> It is hard to explain but each progressive's sized lattice leaves a hole (unfinished cells) if you add on
> the next sized lattice to it leaving out a small increasing number of cells from the previous lattice and
> so on to create the tail end of the next draw to complete the latest lattice. It all sounds confusing but
> this is the way I can continue theoretically --->oo in the number of lattices that the pencil never leaves the
> paper.
> Clear as mud I know but very hard to explain.
> .
I'm going back to view that again before turning in.

On Sunday, June 18, 2023 at 12:40:55 AM UTC-4, Dan joyce wrote:
> On Sunday, June 18, 2023 at 12:36:04 AM UTC-4, Dan joyce wrote:
> > On Saturday, June 17, 2023 at 10:09:53 PM UTC-4, Chris M. Thomasson wrote:
> > > On 6/17/2023 3:46 PM, Dan joyce wrote:
> > > > On Saturday, June 17, 2023 at 4:01:23 PM UTC-4, Chris M. Thomasson wrote:
> > > >> On 6/17/2023 10:54 AM, Dan joyce wrote:
> > > >>> On Saturday, June 17, 2023 at 1:04:24 AM UTC-4, Dan joyce wrote:
> > > >>>> On Friday, June 16, 2023 at 11:36:13 PM UTC-4, Chris M. Thomasson wrote:
> > > >>>>> On 6/16/2023 8:31 PM, Chris M. Thomasson wrote:
> > > >>>>>> On 6/15/2023 7:49 PM, Dan joyce wrote:
> > > [...]
> > > > Two heads are better then one when mulling over ideas.
> > > Did you get my emails? The animation is too fast, but I still have not
> > > hooked up proper FPS to the final animation, yet... ;^)
> > That is fantastic! Double that fantastic slowed down and with a larger lattice.
> > If you could slow it down a lot more and use the last largest lattice directions with ----
> > offset by 1----1,3,5,7,9,11,13,13,11,9,7,5,3,1 vertical and horizontal cells it would be very impressive.
> > Each progressive one of these lattices are all connected so to speak.
> > It is hard to explain but each progressive's sized lattice leaves a hole (unfinished cells) if you add on
> > the next sized lattice to it leaving out a small increasing number of cells from the previous lattice and
> > so on to create the tail end of the next draw to complete the latest lattice. It all sounds confusing but
> > this is the way I can continue theoretically --->oo in the number of lattices that the pencil never leaves the
> > paper.
> > Clear as mud I know but very hard to explain.
> > .
> I'm going back to view that again before turning in.

I slept on this and if the coder fully understands what is going on and how to code it, including
myself on how to code it, this could be continuous frames of larger and larger lattices.
All would start with the smallest lattice in slow-motion and then end. Showing the first lattice until the
user hit the right arrow key (>) in the window. Then the next window would repeat the first lattice all over
again but this time not closing the hole in the last lattice but continuing to now produce the second
lattice and complete that. This would require another hit of the right arrow key (>) by the user to continue
to the next larger lattice showing all previous lattices combined add --->oo.
In the real world there can be no more (>) after a certain sized lattice because the viewing screen has
reached the full capacity of no more discernable shape of this lattice, the borders are now off screen.
That's when the presentation can end or the user can review this whole process again by hitting the
left arrow(<) key to view it all over again.
This would make a fantastic presentation on what is going on.
What do you think Chris?
I will try to explain it more if you have any questions on what I just wrote on how it could be done.
Thanks Chris.