On 6/7/2023 9:41 PM, Chris M. Thomasson wrote:
> On 6/4/2023 10:18 AM, Dan joyce wrote:
>> I know this sounds rediculus but, drawing an --->oo lattice
>> because to draw this you have to come back in from --->oo
>> to the origin or the center of this --->oo lattice.
> [...]
>
> This is ported up to line 160 in your GWBASIC code:
>
> https://i.ibb.co/mDLYbg0/image.png
>
> Looking good? Any mistakes?
>

Here is what I got porting up to line 260:

https://i.ibb.co/JjXHnjB/image.png

Looking good to you?

On 6/7/2023 9:58 PM, Chris M. Thomasson wrote:
> On 6/7/2023 9:41 PM, Chris M. Thomasson wrote:
>> On 6/4/2023 10:18 AM, Dan joyce wrote:
>>> I know this sounds rediculus but, drawing an --->oo lattice
>>> because to draw this you have to come back in from --->oo
>>> to the origin or the center of this --->oo lattice.
>> [...]
>>
>> This is ported up to line 160 in your GWBASIC code:
>>
>> https://i.ibb.co/mDLYbg0/image.png
>>
>> Looking good? Any mistakes?
>>
>
> Here is what I got porting up to line 260:
>
> https://i.ibb.co/JjXHnjB/image.png
>
> Looking good to you?

Now this is interesting to me. I should be able to create a much more
compact algorithm to get me to this stage at line 260. Humm... I need to
do something else right now, but will get back on it.

On 6/7/2023 9:45 PM, Archimedes Plutonium wrote:
> Chris Thomasson the mosquito prick of math, when all his posts belong in --- art.talk. Help get Chris out of sci.math and into a more insane newsgroup where he can thrive.

When is the last you used BASIC? Its been decades for me.

;^o

>
> On Wednesday, June 7, 2023 at 11:41:23 PM UTC-5, Chris M. Thomasson wrote:
>> On 6/4/2023 10:18 AM, Dan joyce wrote:
>>> I know this sounds rediculus but, drawing an --->oo lattice
>>> because to draw this you have to come back in from --->oo
>>> to the origin or the center of this --->oo lattice.
>> [...]
>>
>> This is ported up to line 160 in your GWBASIC code:
>>
>> https://i.ibb.co/mDLYbg0/image.png
>>
>> Looking good? Any mistakes?

On 6/7/2023 9:59 PM, Chris M. Thomasson wrote:
> On 6/7/2023 9:58 PM, Chris M. Thomasson wrote:
>> On 6/7/2023 9:41 PM, Chris M. Thomasson wrote:
>>> On 6/4/2023 10:18 AM, Dan joyce wrote:
>>>> I know this sounds rediculus but, drawing an --->oo lattice
>>>> because to draw this you have to come back in from --->oo
>>>> to the origin or the center of this --->oo lattice.
>>> [...]
>>>
>>> This is ported up to line 160 in your GWBASIC code:
>>>
>>> https://i.ibb.co/mDLYbg0/image.png
>>>
>>> Looking good? Any mistakes?
>>>
>>
>> Here is what I got porting up to line 260:
>>
>> https://i.ibb.co/JjXHnjB/image.png
>>
>> Looking good to you?
>
> Now this is interesting to me. I should be able to create a much more
> compact algorithm to get me to this stage at line 260. Humm... I need to
> do something else right now, but will get back on it.

Humm... It seems to be increasing by adding two to the ladders. 1, 3, 5,
7, 9, counting the green arrows going up in the spiral progression. So I
wonder if a level might be able to be defined as:

i[0] = 1
i[1] = i[0] + 2 = 3
i[2] = i[1] + 2 = 5
i[3] = i[2] + 2 = 7
i[4] = i[3] + 2 = 9
....

Or: i[n] = 2 * n + 1

?

Need to try it out.

On Thursday, June 8, 2023 at 12:41:23 AM UTC-4, Chris M. Thomasson wrote:
> On 6/4/2023 10:18 AM, Dan joyce wrote:
> > I know this sounds rediculus but, drawing an --->oo lattice
> > because to draw this you have to come back in from --->oo
> > to the origin or the center of this --->oo lattice.
> [...]
>
> This is ported up to line 160 in your GWBASIC code:
>
> https://i.ibb.co/mDLYbg0/image.png
>
> Looking good? Any mistakes?

What the final presentation should have is a nice background color then one contrasting colored line
in the going out spiral and another color on the ingoing spiral lines. In other words 3 colors.
You have a better control of colors then I do. Looks good.

On Thursday, June 8, 2023 at 12:58:23 AM UTC-4, Chris M. Thomasson wrote:
> On 6/7/2023 9:41 PM, Chris M. Thomasson wrote:
> > On 6/4/2023 10:18 AM, Dan joyce wrote:
> >> I know this sounds rediculus but, drawing an --->oo lattice
> >> because to draw this you have to come back in from --->oo
> >> to the origin or the center of this --->oo lattice.
> > [...]
> >
> > This is ported up to line 160 in your GWBASIC code:
> >
> > https://i.ibb.co/mDLYbg0/image.png
> >
> > Looking good? Any mistakes?
> >
> Here is what I got porting up to line 260:
>
> https://i.ibb.co/JjXHnjB/image.png
>
> Looking good to you?
You must be a west coast guy. I am just getting caught up with all your posts here on the east coast.
This looks good. The last instruction on top of the square can now start the second sequence of numbers
for the return path to complete the square lattice.

On Thursday, June 8, 2023 at 1:00:35 AM UTC-4, Chris M. Thomasson wrote:
> On 6/7/2023 9:45 PM, Archimedes Plutonium wrote:
> > Chris Thomasson the mosquito prick of math, when all his posts belong in --- art.talk. Help get Chris out of sci.math and into a more insane newsgroup where he can thrive.
> When is the last you used BASIC? Its been decades for me.
>
> ;^o
I use Python but not falmiliar with the java graphics libraries connected with Python
when doing graphics so I just refered back to my old basic for this project..
Yes, it has been a long time. That was the first language for personal pc's back in the late 70's,
That along with Apple. In the bisness world I was involved with Cobal for the main frames.
Its been a long journey.
> >
> > On Wednesday, June 7, 2023 at 11:41:23 PM UTC-5, Chris M. Thomasson wrote:
> >> On 6/4/2023 10:18 AM, Dan joyce wrote:
> >>> I know this sounds rediculus but, drawing an --->oo lattice
> >>> because to draw this you have to come back in from --->oo
> >>> to the origin or the center of this --->oo lattice.
> >> [...]
> >>
> >> This is ported up to line 160 in your GWBASIC code:
> >>
> >> https://i.ibb.co/mDLYbg0/image.png
> >>
> >> Looking good? Any mistakes?

Dan joyce <danj4084@gmail.com> wrote:
....
>>>>>> Draw an infinite square lattice without lifting the pencil. ...
>>>>>> A much harder, and likely impossible drawing is where you make
>>>>>> the grid without lifting the pencil and without retracing where
>>>>>> you already been before.
....
> So Chris how is it going.
> You have seen the videos so what is your assessment?
> The pencil never leaves the paper. Bogus or real?
> I definitely believe it is real. The videos prove it.
> It is surprising that some that are questioning it have run complex
> algorithms that left me in the dust where I had no clue on how they
> did it. I will send the largest square lattice ever produced where
> it runs off the top and bottom of the screen. In which the old
> algorithm would have used thousands of these directions R,U,D,L
> where now it just uses a handful but in multiple times for
> completing a large square lattice. Watch for the new video.

Of course it's easy to make an indefinitely large drawing which "runs
off the top and bottom of the screen" while enclosing lots and lots of
squares. No question. However, the phrase "Draw an infinite square
lattice" ought to imply a drawing, without lift or retrace, such that
for any distance from the origin all the segments within that distance
eventually get filled in. I proved (and Mike Terry also proved, in a
simpler way) that's not possible in a one-way drawing that starts at
the origin. As Mike also noted, if you allow adding lines at both
ends of the trace it's easy to do. But a space-filling (without
missing segments) single-ended trace without lift or retrace is not
possible.

On Thursday, June 8, 2023 at 12:40:26 PM UTC-4, James Waldby wrote:
> Dan joyce <danj...@gmail.com> wrote:
> ...
> >>>>>> Draw an infinite square lattice without lifting the pencil. ...
> >>>>>> A much harder, and likely impossible drawing is where you make
> >>>>>> the grid without lifting the pencil and without retracing where
> >>>>>> you already been before.
> ...
> > So Chris how is it going.
> > You have seen the videos so what is your assessment?
> > The pencil never leaves the paper. Bogus or real?
> > I definitely believe it is real. The videos prove it.
> > It is surprising that some that are questioning it have run complex
> > algorithms that left me in the dust where I had no clue on how they
> > did it. I will send the largest square lattice ever produced where
> > it runs off the top and bottom of the screen. In which the old
> > algorithm would have used thousands of these directions R,U,D,L
> > where now it just uses a handful but in multiple times for
> > completing a large square lattice. Watch for the new video.
>
> Of course it's easy to make an indefinitely large drawing which "runs
> off the top and bottom of the screen" while enclosing lots and lots of
> squares. No question. However, the phrase "Draw an infinite square
> lattice" ought to imply a drawing, without lift or retrace, such that
> for any distance from the origin all the segments within that distance
> eventually get filled in. I proved (and Mike Terry also proved, in a
> simpler way) that's not possible in a one-way drawing that starts at
> the origin. As Mike also noted, if you allow adding lines at both
> ends of the trace it's easy to do. But a space-filling (without
> missing segments) single-ended trace without lift or retrace is not
> possible.
I never implied that. It was going out in certain steps ---->oo LEAVING A PATH that
later gets filled has always been what I have been saying. I have mentioned that many
times about going out and leaving a path. Then on the return to the center ot the square
lattice or the origin all gets filled in without crossing any lines or retraces.

On 6/8/2023 4:58 AM, Dan joyce wrote:
> On Thursday, June 8, 2023 at 12:58:23 AM UTC-4, Chris M. Thomasson wrote:
>> On 6/7/2023 9:41 PM, Chris M. Thomasson wrote:
>>> On 6/4/2023 10:18 AM, Dan joyce wrote:
>>>> I know this sounds rediculus but, drawing an --->oo lattice
>>>> because to draw this you have to come back in from --->oo
>>>> to the origin or the center of this --->oo lattice.
>>> [...]
>>>
>>> This is ported up to line 160 in your GWBASIC code:
>>>
>>> https://i.ibb.co/mDLYbg0/image.png
>>>
>>> Looking good? Any mistakes?
>>>
>> Here is what I got porting up to line 260:
>>
>> https://i.ibb.co/JjXHnjB/image.png
>>
>> Looking good to you?
> You must be a west coast guy.

Indeed, I am. :^)

Found some free time to work on your work, last night. :^)

> I am just getting caught up with all your posts here on the east coast.
> This looks good. The last instruction on top of the square can now start the second sequence of numbers
> for the return path to complete the square lattice.

Cool!

On Thursday, June 8, 2023 at 3:07:59 PM UTC-4, Chris M. Thomasson wrote:
> On 6/8/2023 4:58 AM, Dan joyce wrote:
> > On Thursday, June 8, 2023 at 12:58:23 AM UTC-4, Chris M. Thomasson wrote:
> >> On 6/7/2023 9:41 PM, Chris M. Thomasson wrote:
> >>> On 6/4/2023 10:18 AM, Dan joyce wrote:
> >>>> I know this sounds rediculus but, drawing an --->oo lattice
> >>>> because to draw this you have to come back in from --->oo
> >>>> to the origin or the center of this --->oo lattice.
> >>> [...]
> >>>
> >>> This is ported up to line 160 in your GWBASIC code:
> >>>
> >>> https://i.ibb.co/mDLYbg0/image.png
> >>>
> >>> Looking good? Any mistakes?
> >>>
> >> Here is what I got porting up to line 260:
> >>
> >> https://i.ibb.co/JjXHnjB/image.png
> >>
> >> Looking good to you?
> > You must be a west coast guy.
> Indeed, I am. :^)
>
> Found some free time to work on your work, last night. :^)
> > I am just getting caught up with all your posts here on the east coast.
> > This looks good. The last instruction on top of the square can now start the second sequence of numbers
> > for the return path to complete the square lattice.
> Cool!
A question for you. Where is this documented as know and simple fact?

On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
> On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
>> I know this sounds rediculus but, drawing an --->oo lattice
>
> Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will. But in new true blue Math, that slipshod old math is no longer acceptable.
>
> So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.

Huh? Humm....

On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
> > On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
> >> I know this sounds rediculus but, drawing an --->oo lattice
> >
> > Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will.. But in new true blue Math, that slipshod old math is no longer acceptable..
> >
> > So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
> Huh? Humm....
I would like to ask Archi, if someone gave you a picture of a large square lattice with many cells and said,
can you draw this lattice without retracing or crossing another line and not lift the pencil from the
paper? Would your answer be, Yeah, sure or no it is impossible.
So I don't care how large this lattice is because whether the size is finite or --->oo the answer is ,Yeah sure.
And another thing, If this square lattice is well known and easy, where is it documented?

On Thursday, June 8, 2023 at 4:16:56 PM UTC-4, Dan joyce wrote:
> On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
> > > On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
> > >> I know this sounds rediculus but, drawing an --->oo lattice
> > >
> > > Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will. But in new true blue Math, that slipshod old math is no longer acceptable.
> > >
> > > So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
> > Huh? Humm....
> I would like to ask Archi, if someone gave you a picture of a large square lattice with many cells and said,
> can you draw this lattice without retracing or crossing another line and not lift the pencil from the
> paper? Would your answer be, Yeah, sure or no it is impossible.
> So I don't care how large this lattice is because whether the size is finite or --->oo the answer is ,Yeah sure.
> And another thing, If this square lattice is well known and easy, where is it documented?
Of cource, just hypothetical because it is not possible to draw this --->oo lattice.
Just trying to make a point.

On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
> > On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
> >> I know this sounds rediculus but, drawing an --->oo lattice
> >
> > Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will.. But in new true blue Math, that slipshod old math is no longer acceptable..
> >
> > So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
> Huh? Humm....
So Chris, even though some think this is trivial the idea of two different colors for the lattice where
one color for going out and a different color for going back in to the origin (center of the lattice) is a good
idea?
Whst do you think?

On 6/8/2023 1:40 PM, Dan joyce wrote:
> On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
>> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
>>> On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
>>>> I know this sounds rediculus but, drawing an --->oo lattice
>>>
>>> Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will. But in new true blue Math, that slipshod old math is no longer acceptable.
>>>
>>> So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
>> Huh? Humm....
> So Chris, even though some think this is trivial the idea of two different colors for the lattice where
> one color for going out and a different color for going back in to the origin (center of the lattice) is a good
> idea?
> Whst do you think?

It makes me think of an older vector field of mine that has a spiral,
then the field gets sucked back into itself. Can you run it on your end?
I have my code there:

https://www.shadertoy.com/view/3dffDX

:^)

I just need to inverse my spiral plot to find the way back home... So to
speak. ;^)

On 6/8/2023 1:44 PM, Chris M. Thomasson wrote:
> On 6/8/2023 1:40 PM, Dan joyce wrote:
>> On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
>>> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
>>>> On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
>>>>> I know this sounds rediculus but, drawing an --->oo lattice
>>>>
>>>> Dan needs a little advice here in mathematics. Of course in the old
>>>> days, in math you could whip out the word "infinity and infinite" at
>>>> free will. But in new true blue Math, that slipshod old math is no
>>>> longer acceptable.
>>>>
>>>> So Dan Joyce needs to say-- what his infinite borderline is exactly
>>>> , and not pretend it is "never ending". This slipshod attitude got
>>>> Cantor and Godel and most everyone in Old Math, got them on the
>>>> wrong side of the track.
>>> Huh? Humm....
>> So Chris, even though some think this is trivial the idea of two
>> different colors for the lattice where
>> one color for going out and a different color for going back in to the
>> origin (center of the lattice) is a good
>> idea?
>> Whst do you think?
>
> It makes me think of an older vector field of mine that has a spiral,
> then the field gets sucked back into itself. Can you run it on your end?
> I have my code there:
>
> https://www.shadertoy.com/view/3dffDX
>
> :^)
>
> I just need to inverse my spiral plot to find the way back home... So to
> speak. ;^)

A screenshot with line 13, CT_N at 42

https://i.ibb.co/Ht5kSk4/image.png

:^)

On Thursday, June 8, 2023 at 4:45:24 PM UTC-4, Chris M. Thomasson wrote:
> On 6/8/2023 1:40 PM, Dan joyce wrote:
> > On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
> >> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
> >>> On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
> >>>> I know this sounds rediculus but, drawing an --->oo lattice
> >>>
> >>> Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will. But in new true blue Math, that slipshod old math is no longer acceptable.
> >>>
> >>> So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
> >> Huh? Humm....
> > So Chris, even though some think this is trivial the idea of two different colors for the lattice where
> > one color for going out and a different color for going back in to the origin (center of the lattice) is a good
> > idea?
> > Whst do you think?
> It makes me think of an older vector field of mine that has a spiral,
> then the field gets sucked back into itself. Can you run it on your end?
> I have my code there:
Don't have up to date basic on my PC but that is neat.
> https://www.shadertoy.com/view/3dffDX
>
> :^)
>
> I just need to inverse my spiral plot to find the way back home... So to
> speak. ;^)
It is all in the second module just a reverse of the first module.
The last command in the first module which you show is L=1 D=1 setting
up the next module for RD= the first largest number in the second sequence.
The rest is just a piece of cake back to the spiraling back to the origin.

On 6/8/2023 2:10 PM, Dan joyce wrote:
> On Thursday, June 8, 2023 at 4:45:24 PM UTC-4, Chris M. Thomasson wrote:
>> On 6/8/2023 1:40 PM, Dan joyce wrote:
>>> On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
>>>> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
>>>>> On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
>>>>>> I know this sounds rediculus but, drawing an --->oo lattice
>>>>>
>>>>> Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will. But in new true blue Math, that slipshod old math is no longer acceptable.
>>>>>
>>>>> So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
>>>> Huh? Humm....
>>> So Chris, even though some think this is trivial the idea of two different colors for the lattice where
>>> one color for going out and a different color for going back in to the origin (center of the lattice) is a good
>>> idea?
>>> Whst do you think?
>> It makes me think of an older vector field of mine that has a spiral,
>> then the field gets sucked back into itself. Can you run it on your end?
>> I have my code there:
> Don't have up to date basic on my PC but that is neat.
>> https://www.shadertoy.com/view/3dffDX

This is in the OpenGL shader language GLSL.

>>
>> :^)
>>
>> I just need to inverse my spiral plot to find the way back home... So to
>> speak. ;^)
> It is all in the second module just a reverse of the first module.
> The last command in the first module which you show is L=1 D=1 setting
> up the next module for RD= the first largest number in the second sequence.
> The rest is just a piece of cake back to the spiraling back to the origin.

Have not tried it yet, but inverting my direction mods might work.
Basically reverse my loop. Have some ideas.

On Thursday, June 8, 2023 at 5:20:19 PM UTC-4, Chris M. Thomasson wrote:
> On 6/8/2023 2:10 PM, Dan joyce wrote:
> > On Thursday, June 8, 2023 at 4:45:24 PM UTC-4, Chris M. Thomasson wrote:
> >> On 6/8/2023 1:40 PM, Dan joyce wrote:
> >>> On Thursday, June 8, 2023 at 3:50:19 PM UTC-4, Chris M. Thomasson wrote:
> >>>> On 6/7/2023 9:43 PM, Archimedes Plutonium wrote:
> >>>>> On Sunday, June 4, 2023 at 12:18:14 PM UTC-5, Dan joyce wrote:
> >>>>>> I know this sounds rediculus but, drawing an --->oo lattice
> >>>>>
> >>>>> Dan needs a little advice here in mathematics. Of course in the old days, in math you could whip out the word "infinity and infinite" at free will. But in new true blue Math, that slipshod old math is no longer acceptable.
> >>>>>
> >>>>> So Dan Joyce needs to say-- what his infinite borderline is exactly , and not pretend it is "never ending". This slipshod attitude got Cantor and Godel and most everyone in Old Math, got them on the wrong side of the track.
> >>>> Huh? Humm....
> >>> So Chris, even though some think this is trivial the idea of two different colors for the lattice where
> >>> one color for going out and a different color for going back in to the origin (center of the lattice) is a good
> >>> idea?
> >>> Whst do you think?
> >> It makes me think of an older vector field of mine that has a spiral,
> >> then the field gets sucked back into itself. Can you run it on your end?
> >> I have my code there:
> > Don't have up to date basic on my PC but that is neat.
> >> https://www.shadertoy.com/view/3dffDX
> This is in the OpenGL shader language GLSL.
> >>
> >> :^)
> >>
> >> I just need to inverse my spiral plot to find the way back home... So to
> >> speak. ;^)
> > It is all in the second module just a reverse of the first module.
> > The last command in the first module which you show is L=1 D=1 setting
> > up the next module for RD= the first largest number in the second sequence.
> > The rest is just a piece of cake back to the spiraling back to the origin.
> Have not tried it yet, but inverting my direction mods might work.
> Basically reverse my loop. Have some ideas.
The key is in the second coming back in sequence where the patterns of each
4 integers matter (1 revolution each). It is interesting because they are related
to the out going pattern of 4 that created the path for the second sequence..

Dan joyce <danj4084@gmail.com> wrote:
> On Thursday, June 8, 2023 at 12:40:26???PM UTC-4, James Waldby wrote:
>> Dan joyce <danj...@gmail.com> wrote:
>> ...
>> >>>>>> Draw an infinite square lattice without lifting the pencil. ...
>> >>>>>> A much harder, and likely impossible drawing is where you make
>> >>>>>> the grid without lifting the pencil and without retracing where
>> >>>>>> you already been before.
>> ...
>> > So Chris how is it going.
>> > You have seen the videos so what is your assessment?
>> > The pencil never leaves the paper. Bogus or real?
>> > I definitely believe it is real. The videos prove it.
>> > It is surprising that some that are questioning it have run complex
>> > algorithms that left me in the dust where I had no clue on how they
>> > did it. I will send the largest square lattice ever produced where
>> > it runs off the top and bottom of the screen. In which the old
>> > algorithm would have used thousands of these directions R,U,D,L
>> > where now it just uses a handful but in multiple times for
>> > completing a large square lattice. Watch for the new video.
>>
>> Of course it's easy to make an indefinitely large drawing which "runs
>> off the top and bottom of the screen" while enclosing lots and lots of
>> squares. No question. However, the phrase "Draw an infinite square
>> lattice" ought to imply a drawing, without lift or retrace, such that
>> for any distance from the origin all the segments within that distance
>> eventually get filled in. I proved (and Mike Terry also proved, in a
>> simpler way) that's not possible in a one-way drawing that starts at
>> the origin. As Mike also noted, if you allow adding lines at both
>> ends of the trace it's easy to do. But a space-filling (without
>> missing segments) single-ended trace without lift or retrace is not
>> possible.

> I never implied that. It was going out in certain steps ---->oo
> LEAVING A PATH that later gets filled has always been what I have
> been saying. I have mentioned that many times about going out and
> leaving a path. Then on the return to the center of the square
> lattice or the origin all gets filled in without crossing any lines
> or retraces.

Yes, I agree your method draws arbitrarily large square lattices of
fixed sizes ok. But by no means does it do an "infinite lattice".

On Thursday, June 8, 2023 at 8:20:35 PM UTC-4, James Waldby wrote:
> Dan joyce <danj...@gmail.com> wrote:
> > On Thursday, June 8, 2023 at 12:40:26???PM UTC-4, James Waldby wrote:
> >> Dan joyce <danj...@gmail.com> wrote:
> >> ...
> >> >>>>>> Draw an infinite square lattice without lifting the pencil. ...
> >> >>>>>> A much harder, and likely impossible drawing is where you make
> >> >>>>>> the grid without lifting the pencil and without retracing where
> >> >>>>>> you already been before.
> >> ...
> >> > So Chris how is it going.
> >> > You have seen the videos so what is your assessment?
> >> > The pencil never leaves the paper. Bogus or real?
> >> > I definitely believe it is real. The videos prove it.
> >> > It is surprising that some that are questioning it have run complex
> >> > algorithms that left me in the dust where I had no clue on how they
> >> > did it. I will send the largest square lattice ever produced where
> >> > it runs off the top and bottom of the screen. In which the old
> >> > algorithm would have used thousands of these directions R,U,D,L
> >> > where now it just uses a handful but in multiple times for
> >> > completing a large square lattice. Watch for the new video.
> >>
> >> Of course it's easy to make an indefinitely large drawing which "runs
> >> off the top and bottom of the screen" while enclosing lots and lots of
> >> squares. No question. However, the phrase "Draw an infinite square
> >> lattice" ought to imply a drawing, without lift or retrace, such that
> >> for any distance from the origin all the segments within that distance
> >> eventually get filled in. I proved (and Mike Terry also proved, in a
> >> simpler way) that's not possible in a one-way drawing that starts at
> >> the origin. As Mike also noted, if you allow adding lines at both
> >> ends of the trace it's easy to do. But a space-filling (without
> >> missing segments) single-ended trace without lift or retrace is not
> >> possible.
>
> > I never implied that. It was going out in certain steps ---->oo
> > LEAVING A PATH that later gets filled has always been what I have
> > been saying. I have mentioned that many times about going out and
> > leaving a path. Then on the return to the center of the square
> > lattice or the origin all gets filled in without crossing any lines
> > or retraces.
> Yes, I agree your method draws arbitrarily large square lattices of
> fixed sizes ok. But by no means does it do an "infinite lattice".

James, I agree. It just sounded more sexy as the infinite lattice
instead of a lattice that can --->oo.
I have always approched infinity, no pun intended, that way.

On Friday, June 9, 2023 at 8:28:16 AM UTC-4, Dan joyce wrote:
> On Thursday, June 8, 2023 at 8:20:35 PM UTC-4, James Waldby wrote:
> > Dan joyce <danj...@gmail.com> wrote:
> > > On Thursday, June 8, 2023 at 12:40:26???PM UTC-4, James Waldby wrote:
> > >> Dan joyce <danj...@gmail.com> wrote:
> > >> ...
> > >> >>>>>> Draw an infinite square lattice without lifting the pencil. ....
> > >> >>>>>> A much harder, and likely impossible drawing is where you make
> > >> >>>>>> the grid without lifting the pencil and without retracing where
> > >> >>>>>> you already been before.
> > >> ...
> > >> > So Chris how is it going.
> > >> > You have seen the videos so what is your assessment?
> > >> > The pencil never leaves the paper. Bogus or real?
> > >> > I definitely believe it is real. The videos prove it.
> > >> > It is surprising that some that are questioning it have run complex
> > >> > algorithms that left me in the dust where I had no clue on how they
> > >> > did it. I will send the largest square lattice ever produced where
> > >> > it runs off the top and bottom of the screen. In which the old
> > >> > algorithm would have used thousands of these directions R,U,D,L
> > >> > where now it just uses a handful but in multiple times for
> > >> > completing a large square lattice. Watch for the new video.
> > >>
> > >> Of course it's easy to make an indefinitely large drawing which "runs
> > >> off the top and bottom of the screen" while enclosing lots and lots of
> > >> squares. No question. However, the phrase "Draw an infinite square
> > >> lattice" ought to imply a drawing, without lift or retrace, such that
> > >> for any distance from the origin all the segments within that distance
> > >> eventually get filled in. I proved (and Mike Terry also proved, in a
> > >> simpler way) that's not possible in a one-way drawing that starts at
> > >> the origin. As Mike also noted, if you allow adding lines at both
> > >> ends of the trace it's easy to do. But a space-filling (without
> > >> missing segments) single-ended trace without lift or retrace is not
> > >> possible.
> >
> > > I never implied that. It was going out in certain steps ---->oo
> > > LEAVING A PATH that later gets filled has always been what I have
> > > been saying. I have mentioned that many times about going out and
> > > leaving a path. Then on the return to the center of the square
> > > lattice or the origin all gets filled in without crossing any lines
> > > or retraces.
> > Yes, I agree your method draws arbitrarily large square lattices of
> > fixed sizes ok. But by no means does it do an "infinite lattice".
> James, I agree. It just sounded more sexy as the infinite lattice
> instead of a lattice that can --->oo.
> I have always approched infinity, no pun intended, that way.

I even stated in one of my post on this subject, not the exact wording, that
suppose you wanted a huge square lattice --->oo and lets say in this case
a square lattice with one hundread quaudrillion (10^17) cells on just one of its 4 sides
that it is possible to draw that without lifting a pencil.
I know it is wrong to put a number on --->oo but just saying how much bigger
than one hundred quaudrillion cells on just one of its 4 sides of a square lattice
could be. Even a square lattice with 10^303 (Centillion) cells on one of its sides.
So I guess the name for this lattice, not as the infinite lattice, but (a square lattice--->oo)
would be more appropriate.

On Friday, June 9, 2023 at 9:18:00 AM UTC-4, Dan joyce wrote:
> On Friday, June 9, 2023 at 8:28:16 AM UTC-4, Dan joyce wrote:
> > On Thursday, June 8, 2023 at 8:20:35 PM UTC-4, James Waldby wrote:
> > > Dan joyce <danj...@gmail.com> wrote:
> > > > On Thursday, June 8, 2023 at 12:40:26???PM UTC-4, James Waldby wrote:
> > > >> Dan joyce <danj...@gmail.com> wrote:
> > > >> ...
> > > >> >>>>>> Draw an infinite square lattice without lifting the pencil. ...
> > > >> >>>>>> A much harder, and likely impossible drawing is where you make
> > > >> >>>>>> the grid without lifting the pencil and without retracing where
> > > >> >>>>>> you already been before.
> > > >> ...
> > > >> > So Chris how is it going.
> > > >> > You have seen the videos so what is your assessment?
> > > >> > The pencil never leaves the paper. Bogus or real?
> > > >> > I definitely believe it is real. The videos prove it.
> > > >> > It is surprising that some that are questioning it have run complex
> > > >> > algorithms that left me in the dust where I had no clue on how they
> > > >> > did it. I will send the largest square lattice ever produced where
> > > >> > it runs off the top and bottom of the screen. In which the old
> > > >> > algorithm would have used thousands of these directions R,U,D,L
> > > >> > where now it just uses a handful but in multiple times for
> > > >> > completing a large square lattice. Watch for the new video.
> > > >>
> > > >> Of course it's easy to make an indefinitely large drawing which "runs
> > > >> off the top and bottom of the screen" while enclosing lots and lots of
> > > >> squares. No question. However, the phrase "Draw an infinite square
> > > >> lattice" ought to imply a drawing, without lift or retrace, such that
> > > >> for any distance from the origin all the segments within that distance
> > > >> eventually get filled in. I proved (and Mike Terry also proved, in a
> > > >> simpler way) that's not possible in a one-way drawing that starts at
> > > >> the origin. As Mike also noted, if you allow adding lines at both
> > > >> ends of the trace it's easy to do. But a space-filling (without
> > > >> missing segments) single-ended trace without lift or retrace is not
> > > >> possible.
> > >
> > > > I never implied that. It was going out in certain steps ---->oo
> > > > LEAVING A PATH that later gets filled has always been what I have
> > > > been saying. I have mentioned that many times about going out and
> > > > leaving a path. Then on the return to the center of the square
> > > > lattice or the origin all gets filled in without crossing any lines
> > > > or retraces.
> > > Yes, I agree your method draws arbitrarily large square lattices of
> > > fixed sizes ok. But by no means does it do an "infinite lattice".
> > James, I agree. It just sounded more sexy as the infinite lattice
> > instead of a lattice that can --->oo.
> > I have always approched infinity, no pun intended, that way.
> I even stated in one of my post on this subject, not the exact wording, that
> suppose you wanted a huge square lattice --->oo and lets say in this case
> a square lattice with one hundread quaudrillion (10^17) cells on just one of its 4 sides
> that it is possible to draw that without lifting a pencil.
> I know it is wrong to put a number on --->oo but just saying how much bigger
> than one hundred quaudrillion cells on just one of its 4 sides of a square lattice
> could be. Even a square lattice with 10^303 (Centillion) cells on one of its sides.
> So I guess the name for this lattice, not as the infinite lattice, but (a square lattice--->oo)
> would be more appropriate.

Another thing I want to straigten out is, it is not really a square lattice more of a rectangle
but the closest to a square that you can possibly get. The top portion where it reverses and
comes back down the path does not need to protrude (stick above the border of the rectangle
drawn around the lattice.) I just need to shorten the last 2 lines going out to U-1 and L-1.
Then just adjust the return path length for that one side to D-1 and R-1.
Just by changing the last integer (n) in the first sequance to n-1.
Then change the first integer (n) in the second sequence to n-1.

On Friday, June 9, 2023 at 12:55:26 PM UTC-4, Dan joyce wrote:
> On Friday, June 9, 2023 at 9:18:00 AM UTC-4, Dan joyce wrote:
> > On Friday, June 9, 2023 at 8:28:16 AM UTC-4, Dan joyce wrote:
> > > On Thursday, June 8, 2023 at 8:20:35 PM UTC-4, James Waldby wrote:
> > > > Dan joyce <danj...@gmail.com> wrote:
> > > > > On Thursday, June 8, 2023 at 12:40:26???PM UTC-4, James Waldby wrote:
> > > > >> Dan joyce <danj...@gmail.com> wrote:
> > > > >> ...
> > > > >> >>>>>> Draw an infinite square lattice without lifting the pencil. ...
> > > > >> >>>>>> A much harder, and likely impossible drawing is where you make
> > > > >> >>>>>> the grid without lifting the pencil and without retracing where
> > > > >> >>>>>> you already been before.
> > > > >> ...
> > > > >> > So Chris how is it going.
> > > > >> > You have seen the videos so what is your assessment?
> > > > >> > The pencil never leaves the paper. Bogus or real?
> > > > >> > I definitely believe it is real. The videos prove it.
> > > > >> > It is surprising that some that are questioning it have run complex
> > > > >> > algorithms that left me in the dust where I had no clue on how they
> > > > >> > did it. I will send the largest square lattice ever produced where
> > > > >> > it runs off the top and bottom of the screen. In which the old
> > > > >> > algorithm would have used thousands of these directions R,U,D,L
> > > > >> > where now it just uses a handful but in multiple times for
> > > > >> > completing a large square lattice. Watch for the new video.
> > > > >>
> > > > >> Of course it's easy to make an indefinitely large drawing which "runs
> > > > >> off the top and bottom of the screen" while enclosing lots and lots of
> > > > >> squares. No question. However, the phrase "Draw an infinite square
> > > > >> lattice" ought to imply a drawing, without lift or retrace, such that
> > > > >> for any distance from the origin all the segments within that distance
> > > > >> eventually get filled in. I proved (and Mike Terry also proved, in a
> > > > >> simpler way) that's not possible in a one-way drawing that starts at
> > > > >> the origin. As Mike also noted, if you allow adding lines at both
> > > > >> ends of the trace it's easy to do. But a space-filling (without
> > > > >> missing segments) single-ended trace without lift or retrace is not
> > > > >> possible.
> > > >
> > > > > I never implied that. It was going out in certain steps ---->oo
> > > > > LEAVING A PATH that later gets filled has always been what I have
> > > > > been saying. I have mentioned that many times about going out and
> > > > > leaving a path. Then on the return to the center of the square
> > > > > lattice or the origin all gets filled in without crossing any lines
> > > > > or retraces.
> > > > Yes, I agree your method draws arbitrarily large square lattices of
> > > > fixed sizes ok. But by no means does it do an "infinite lattice".
> > > James, I agree. It just sounded more sexy as the infinite lattice
> > > instead of a lattice that can --->oo.
> > > I have always approched infinity, no pun intended, that way.
> > I even stated in one of my post on this subject, not the exact wording, that
> > suppose you wanted a huge square lattice --->oo and lets say in this case
> > a square lattice with one hundread quaudrillion (10^17) cells on just one of its 4 sides
> > that it is possible to draw that without lifting a pencil.
> > I know it is wrong to put a number on --->oo but just saying how much bigger
> > than one hundred quaudrillion cells on just one of its 4 sides of a square lattice
> > could be. Even a square lattice with 10^303 (Centillion) cells on one of its sides.
> > So I guess the name for this lattice, not as the infinite lattice, but (a square lattice--->oo)
> > would be more appropriate.
> Another thing I want to straigten out is, it is not really a square lattice more of a rectangle
> but the closest to a square that you can possibly get. The top portion where it reverses and
> comes back down the path does not need to protrude (stick above the border of the rectangle
> drawn around the lattice.) I just need to shorten the last 2 lines going out to U-1 and L-1.
> Then just adjust the return path length for that one side to D-1 and R-1.
> Just by changing the last integer (n) in the first sequance to n-1.
> Then change the first integer (n) in the second sequence to n-1.
Then if you sdd another set of 4 pattern integers at the end of the first sequence then put the n-1 back to n+1 before you add the new set that actually breaks the pattern with the n-1 for the last number. The same for the second sequence adding 1 back to the starting number in that sequence before
you add the new set of 3 unique pattern integers for that sequence + n-1as the first number.