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

My crude code, can be polished up much more:
____________________________________

struct ct_directions
{ glm::vec2 m_normals[2];
};

glm::vec2
ct_draw_directions(
ct::plot::cairo::plot_2d& scene,
unsigned long& frame_i,
glm::vec2 current,
ct_directions const& dirs,
float unit,
ct::plot::cairo::pixel color,
unsigned long n
) {
char frame_name[256] = { '\0' };

for (unsigned long i = 0; i < n; ++i)
{
glm::vec2 next = current + dirs.m_normals[i % 2] * unit;
plot_arrow_line(scene, current, next, color, 3);
//std::sprintf(frame_name, "./frames/ct_frame_%lu.png", frame_i++);
//scene.save(frame_name);
current = next;
}

return current;
}

void
ct_test_algo_for_dj_james(
ct::plot::cairo::plot_2d& scene,
float unit,
bool plot,
unsigned long yn
) {
float max_dis = 0;

glm::vec2 origin = { 0, 0 };
glm::vec2 current = origin;

unsigned long n = 1;
unsigned long origin_n = n;

unsigned long frame_i = 0;

scene.circle(current, unit, CT_RGBF(1, 0, 0), 2);

// first cell...
current = ct_draw_directions(scene, frame_i, current, { { { 1, 0 },
{ 0, 1 } } }, unit, CT_RGBF(1, 0, 0), 2);
current = ct_draw_directions(scene, frame_i, current, { { { -1, 0
}, { 0, -1 } } }, unit, CT_RGBF(1, 0, 0), 2);
current = ct_draw_directions(scene, frame_i, current, { { { -1, 0 }
} }, unit, CT_RGBF(1, 1, 1), 1);

// Going out...
for (unsigned long i = 0; i < yn; ++i)
{
current = ct_draw_directions(scene, frame_i, current, { { { 0,
-1 }, { 1, 0 } } }, unit, CT_RGBF(1, 0, 0), n + 3);
current = ct_draw_directions(scene, frame_i, current, { { { 0,
1 }, { 1, 0 } } }, unit, CT_RGBF(1, 0, 0), n + 3);
current = ct_draw_directions(scene, frame_i, current, { { { 0,
1 }, { -1, 0 } } }, unit, CT_RGBF(1, 0, 0), n + 5);
if (i == yn - 1) n -= 1;
current = ct_draw_directions(scene, frame_i, current, { { { 0,
-1 }, { -1, 0 } } }, unit, CT_RGBF(1, 0, 0), n + 5);
n += 4;
std::cout << "going out: " << i << " of " << yn << std::endl;
}

scene.circle(current, unit, CT_RGBF(1, 1, 0), 2);

// Going in...
for (unsigned long i = 0; i < yn; ++i)
{
current = ct_draw_directions(scene, frame_i, current, { { { 1,
0 }, { 0, 1 } } }, unit, CT_RGBF(1, 1, 0), n);
current = ct_draw_directions(scene, frame_i, current, { { { 1,
0 }, { 0, -1 } } }, unit, CT_RGBF(1, 1, 0), n);
current = ct_draw_directions(scene, frame_i, current, { { { -1,
0 }, { 0, -1 } } }, unit, CT_RGBF(1, 1, 0), n - 2);
current = ct_draw_directions(scene, frame_i, current, { { { -1,
0 }, { 0, 1 } } }, unit, CT_RGBF(1, 1, 0), n - 2);
n -= 4;
std::cout << "going in: " << i << " of " << yn << std::endl;
}

scene.circle(current, unit / 2, CT_RGBF(1, 0, 1), 2);
}

____________________________________

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:
[...]

Check this out Dan:

https://i.ibb.co/GWwZky9/image.png

What do you think?

On Tuesday, June 13, 2023 at 10:21:06 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:
> [...]
>
> Check this out Dan:
>
> https://i.ibb.co/GWwZky9/image.png
>
> What do you think?
No way diching anything. but this new one looks really interesting
No pathway needed just build all connecting squares in a certain manner
without raising the pencil. I just sent another larger one and just as I suspected
the odd numbers up and down increase by 2 as you build this lattice.
The first one had 1,3,5,7,7,5,3,2,1 in each vertical row, this larger one has 1,3,5,7,9,9,7,5,3,1
all drawn not lifting a pencil. I am using inkey$ U,R,D,L, to draw the lines. If tI happen to hit any
other key it wipes out the image.
Now I have to track my key storks that will give me the correct order of the 4 directions.
A little tricky but I think it can be done. I did receive your rendering and yes all these cells
are formed right at the start. Done a certain way I believe each succeeding larger and larger
one having that odd vertical pattern are possible without lifting the pencil.
Just something we can work together on in the future.

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

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.

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.
..

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.

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.
Do it in slow-motion and you will really appreciate
the pencil not leaving the page.
This rendering is a rectangular lattice with ---
1,3,5,7,7,5,3,1 vertical cells.
The next one will have--
1,3,5,7,9,9,7,5,3,1 vertical cells.
Next
1,3,5,7,9,11,11,9,7,5,3,1 and so on --->oo

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 way to build these is go first clockwise until
you reach a point about 270 degrees from start and
then go back counter clockwise because you can't go
any further without creating a path.
Do the same counter clockwise because you can't go
any further because if you do you will make the same
path that you encountered moving clockwise.
Do this as many times as to what size you want this
thing and always end up going clockwise to fill in
the final cells on the bottom.
You will get how to do larger lattice's if you do it slow-motion.
Remarkable if I do say so myself.

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.
> Do it in slow-motion and you will really appreciate
> the pencil not leaving the page.
> This rendering is a rectangular lattice with ---
> 1,3,5,7,7,5,3,1 vertical cells.
> The next one will have--
> 1,3,5,7,9,9,7,5,3,1 vertical cells.
> Next
> 1,3,5,7,9,11,11,9,7,5,3,1 and so on --->oo
>
> 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 way to build these is go first clockwise until
> you reach a point about 270 degrees from start and

It is not 270 degrees it is more like 150 degrees.

> then go back counter clockwise because you can't go
> any further without creating a path.
> Do the same counter clockwise because you can't go
> any further because if you do you will make the same
> path that you encountered moving clockwise.
> Do this as many times as to what size you want this
> thing and always end up going clockwise to fill in
> the final cells on the bottom.
> You will get how to do larger lattice's if you do it slow-motion.
> Remarkable if I do say so myself.

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
[...]

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.

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?

On Wednesday, June 14, 2023 at 7:33:06 PM UTC-4, 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.
I can't detect a pattern yet. I will change the directions from letters to numbers like R=1,D=2,L=3 and U=4

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.

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 (...)
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 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 (...)

:^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 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

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.

On 6/15/2023 12:53 AM, 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.

From the end point in the yellow circle.

On Thursday, June 15, 2023 at 3:51:36 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 (...)
> [...]
>
> 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
Chris,
First I want to apologize to James. In our early part of discussions about any of this being
possible, the argument was about a square lattice. This is not a square lattice so now this
new method I don't believe it can be done for a square lattice only a rectangular lattice.
I just wanted to clear that up. Only the outward path method I believe will work for a square
lattice.
Now the rendering you are showing, You can terminate it with the last arrow going up to
complete the lattice, which the rest of the directions in the original list will do.
But if you want to go for a larger lattice that last arrow should go down and then to the
right then back around counterclockwise to either terminate there or even get a bigger
lattice coming back clockwise again and so forth. So you can make this lattice as large
as you want but the final hole to fill gets slowly larger at termination point. This is roughly
located at the lower left of the structure
That is why if you truncate the few terminating directions to add another rotation for a
larger lattice is another way to go.
I hope that is clear, if not please ask anything you like.
Whatever, it is interesting.

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.

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

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.
Look at the 8th post in this thread (June 14) that is the original list.

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

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.