Not sure if this can help you, however, this is what I got with a crude
test algorithm of mine:

https://i.ibb.co/sbv82dd/image.png

_____________________________
void
ct_test_algo_for_dj(
ct::plot::cairo::plot_2d& scene
) {
// DIRECTION DATA
std::array<direction, 4> directions = { {
{ { 1, 0 }, CT_RGBF(1, 0, 0) }, // right, red
{ { 0, 1 }, CT_RGBF(0, 1, 0) }, // up, green
{ { -1, 0 }, CT_RGBF(0, 0, 1) }, // left, blue
{ { 0, -1 }, CT_RGBF(0, 1, 1) }, // down, cyan
} };

float unit = .1;

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

unsigned long n = 1;

// going up to the right? lol... ;^)
{
unsigned long yn = 60;
float normal_color = 1.f / yn;

for (unsigned long y = 0; y < yn; ++y)
{
float color = normal_color * y;

glm::vec2 dir_mod = { 0, 0 };

unsigned long ymod = y % 4;

if (ymod == 0)
{
dir_mod = { 1, 1 };
n += 2;
}

else if (ymod == 1)
{
dir_mod = { -1, 1 };
n -= 1;
}

else if (ymod == 2)
{
dir_mod = { -1, -1 };
n += 2;
}

else if (ymod == 3)
{
dir_mod = { 1, -1 };
n -= 1;
}

for (unsigned long x = 0; x < n * 2; ++x)
{
direction const& dir = directions[x % 2];
glm::vec2 next = current + dir.m_normal * dir_mod * unit;
plot_arrow_line(scene, current, next, CT_RGBF(color, 1
- color, 1), 3);
current = next;
}
}
}
_____________________________

Look okay to you? This is just a crude first try. I can do better. :^)

On 6/7/2023 10:47 PM, Chris M. Thomasson wrote:
> Not sure if this can help you, however, this is what I got with a crude
> test algorithm of mine:
>
> https://i.ibb.co/sbv82dd/image.png
>
> _____________________________
> [...
> Look okay to you? This is just a crude first try. I can do better. :^)

I can get it dense, fitting within any circle:

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

;^)

On 6/7/2023 10:47 PM, Chris M. Thomasson wrote:
> Not sure if this can help you, however, this is what I got with a crude
> test algorithm of mine:
>
> https://i.ibb.co/sbv82dd/image.png
[...]

Fwiw, tightened up the algorithm a bit:
___________________________________________
float
ct_test_algo_for_dj(
ct::plot::cairo::plot_2d& scene,
float unit,
bool plot,
unsigned long yn
) {
float max_dis = 0;

// DIRECTION DATA
std::array<direction, 4> directions = { {
{ { 1, 0 }, CT_RGBF(1, 0, 0) }, // right, red
{ { 0, 1 }, CT_RGBF(0, 1, 0) }, // up, green
{ { -1, 0 }, CT_RGBF(0, 0, 1) }, // left, blue
{ { 0, -1 }, CT_RGBF(0, 1, 1) } // down, cyan
} };

// DIRECTION MOD DATA
std::array<direction_mod, 4> direction_mods = { {
{ { 1, 1 }, 2 },
{ { -1, 1 }, -1 },
{ { -1, -1 }, 2 },
{ { 1, -1 }, -1 }
} };

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

unsigned long n = 1;
float normal_color = 1.f / yn;

for (unsigned long y = 0; y < yn; ++y)
{
float color = normal_color * y;
direction_mod const& dmod = direction_mods[y %
direction_mods.size()];
n += dmod.m_addend;

for (unsigned long x = 0; x < n * 2; ++x)
{
direction const& dir = directions[x % (directions.size() / 2)];
glm::vec2 next = current + dir.m_normal * dmod.m_normal * unit;

float dis = glm::length(next);

max_dis = glm::max(max_dis, dis);

if (plot)
{
plot_arrow_line(scene, current, next, CT_RGBF(color, 1
- color, 1), 3);
}

current = next;
}
}

return max_dis;
} ___________________________________________

This may be of use to you. It produces:

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

When called with:
___________________________________________
{ float unit = 1;
unsigned long yn = 32;

float max_dis = ct_test_algo_for_dj(scene, unit, false, yn);
unit = unit / max_dis;

ct_test_algo_for_dj(scene, unit, true, yn);
} ___________________________________________

As you can see, I can set yn to anything I want to. There are several
more improvements than can be made. However, am I on the right track
with this, Dan?

Thanks.

On 6/7/2023 11:12 PM, Chris M. Thomasson wrote:
> On 6/7/2023 10:47 PM, Chris M. Thomasson wrote:
>> Not sure if this can help you, however, this is what I got with a
>> crude test algorithm of mine:
>>
>> https://i.ibb.co/sbv82dd/image.png
> [...]
>
> Fwiw, tightened up the algorithm a bit:
> ___________________________________________
[snip my code]
> This may be of use to you. It produces:
>
> https://i.ibb.co/cJLpGNQ/image.png
>
> When called with:
> ___________________________________________
> {
>     float unit = 1;
>     unsigned long yn = 32;
>
>     float max_dis = ct_test_algo_for_dj(scene, unit, false, yn);
>     unit = unit / max_dis;
>
>     ct_test_algo_for_dj(scene, unit, true, yn);
> }
> ___________________________________________
>
> As you can see, I can set yn to anything I want to. There are several
> more improvements than can be made. However, am I on the right track
> with this, Dan?
>
> Thanks.

Its pretty dense here... ;^)

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

Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person

Chris Thomasson testing Sarmat from London flat. Yeh, Chris, what was the wind pressure??

Pentcho Valev spamming as China under Russian Sarmats. Does it remind Pentcho of Nero fiddling while Rome burnt???

Shanghai, Beijing, Shenzhen, Guangzhou, Chongqing, Tianjin, Chengdu, Hangzhou, Nanjing, Wuhan, Xi'An, Suzhou, Harbin, Shenyang, Qingdao, Zhengzhou, Dongguan, Foshan, Dalian, Jinan, Changchun, Hefei

Shenzhen▂▄▅█████████▅▄▃▂ Xi as Putin's stooge when Russia vaporizes Shenzhen with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person

On Thursday, March 30, 2023 at 11:56:20 PM UTC-5, Volney wrote:
> Botfly of Math and Blowfly of Physics "Putin's stooge"
>"wasn't bolted down too tight in the first place"

On Friday, September 9, 2022 at 1:16:55 AM UTC-5, Michael Moroney wrote:
> "Imp of Science"
>"not one single marble of commonsense in my entire brain"




& wrote:
> _And as the Baby Xi grew up, surrounded by concubines, from the rice paddies and reeds of Outer


> Manchuria, stolen by the Naxi and Zani Dictator Putin in Moscow, Xi
> learned in school in chemical engineering that Taiwan was 1/28 the size
> of Outer Manchuria, Emperor Qing's homeland, now occupied by homeless Russians drinking vodka, as Putin bombs Ukraine. And the nascent Xi orders
> 1,000 divisions to the Outer Manchuria border to regain back the stolen

> > Why Putin is 2X smarter than Xi as dictators// SCIENCE COUNCIL RULES EARTH, not petty dictators
> > 2m views
> >
> >
3> If Putin pushes nuclear buttons, he drags down China along with Russia into a nuclear ash waste pile, and this means Xi is a inferior junior partner to Putin. Putin will drag down Xi's China, never the reverse.
> >
4> So, one can look at the present situation on Earth and ask several logical questions about the 2 dictators of Putin's Russia and China's Xi.
> >
> > It is little wonder that both Russia and China dictators are combative towards the West. Because dictators never want to give up on power but stay in power all their life long. So they oppose the West because the West has grown up to democracy-- let the people have power, not one single idiot having power all his life time.
> >
5 > Naturally, Putin will want to keep the Russian people suppressed and have Russia be a second rate government as a dictator. Same goes for China-- they never want to give up power so the people themselves choose their leader.
> >
> > But can we find differences in Putin and Xi themselves? Well in the West we call the Chinese inscrutable-- meaning -- little logical commonsense. And is this a valid description?? Yes of course, considering that Russia had stolen the lands of Outer Manchuria, some 28 times larger of a land mass than is Taiwan island. Yet there is Xi, spending so much time on wanting to invade Taiwan, when it is Outer Manchuria and Vladivostok (Haishenwai) that he should be focusing attention upon. And while Putin is distracted with Ukraine, is the time for Xi to recapture Outer Manchuria, the Qing dynasty empire, Qing's Manchurian homeland.
> >
> > What does Xi do instead??? He focuses on Taiwan and befriends Russia. Why, at this rate, if Russia takes Inner Manchuria, we can expect Xi and the Chinese Communist Party to become even more loving of Russia for stealing more land of China.
> >
> > And there is Xi, whose China has become rich with trading with the West, yet every day, Xi foaming at the mouth in hatred of the West.
> >
> > So yes, Putin is 2X smarter as a dictator than is Xi, as if Putin has Xi in his side pocket.
> >
> > Is there some scientific explanation as to why Xi is 2X dumber than Putin?? Perhaps, in that China is densely populated and the air pollution over all of China is worse than most countries. That Xi probably has 1/2 of his brain filled with CO and CO2 isomers and lead, and mercury and nitrous oxide and sulfur dioxide from just living in that air polluted hellhole of Beijing. Xi studied chemistry and should know this. Whereas Putin likely detox...s every evening with breathing in pure oxygen at his residence and takes oxygen breathing tanks to office and work. This easily can explain the light-headed reasoning that Xi and his foreign diplomats Wang Yi display, where Putin plays them like a chess game, --- checkmate in 7 moves.
> >
> > This explains why Xi hates the West for not stealing any Chinese lands and making China rich in trade, while loving Putin for stealing Outer Manchuria, and proposing having Russia push nuclear buttons, making both Russia and China a nuclear waste site after ICBMs wipe China off the map.
> >
> > Xi's brain is full of air pollution toxins from the nasty Chinese air. They still build a new coal fired plant in China every day. The air in China is the worst air in the entire world.
> >
6 > Why Putin is 2X smarter than Xi as dictators// SCIENCE COUNCIL RULES EARTH, not petty dictators.

Pentcho is this what happens to China when they follow the insane Putin, tag-a-long, tag-a-long and then all of a sudden--- dragged into a mushroom cloud

On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
> Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
[...]

Do you have an 8-bit mentality?

https://youtu.be/cRAmtrnOXWc

Btw, I think the voice in this is computed generated. All on an 8-bit
computer?

On Thursday, June 8, 2023 at 2:53:14 AM UTC-4, Chris M. Thomasson wrote:
> On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
> > Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
> [...]
>
> Do you have an 8-bit mentality?
>
> https://youtu.be/cRAmtrnOXWc
>
> Btw, I think the voice in this is computed generated. All on an 8-bit
> computer?
You are on the right track but you have to close in that outward path.
The first instruction RU is only run once --
RU=1 --- then the next 4 instructions LD =2, RD=1,RU=3, LU=2, --- Now again in the same order--
LD=4, RD=3,RU=5,LU=4 --- again in the same order ---- taking each integer from the outgiong
sequence. As simple as that.
I believe now you got it.

On Thursday, June 8, 2023 at 6:38:25 AM UTC-4, Dan joyce wrote:
> On Thursday, June 8, 2023 at 2:53:14 AM UTC-4, Chris M. Thomasson wrote:
> > On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
> > > Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
> > [...]
> >
> > Do you have an 8-bit mentality?
> >
> > https://youtu.be/cRAmtrnOXWc
> >
> > Btw, I think the voice in this is computed generated. All on an 8-bit
> > computer?
> You are on the right track but you have to close in that outward path.
> The first instruction RU is only run once --
> RU=1 --- then the next 4 instructions LD =2, RD=1,RU=3, LU=2, --- Now again in the same order--
> LD=4, RD=3,RU=5,LU=4 --- again in the same order ---- taking each integer from the outgiong
> sequence. As simple as that.
> I believe now you got it
..
For the sake of argument here. Say a picture of a large square lattice with thousands of cells was
shown to you and the person said, can you duplicate this lattice useing a pencil without crossing
a line or retracing a line and at no time not lifting the pencil from the paper. What would you say to
him. Oh yeah it can be done or it is impossible?
Just wondering.

On 6/8/2023 11:00 AM, Dan joyce wrote:
> On Thursday, June 8, 2023 at 6:38:25 AM UTC-4, Dan joyce wrote:
>> On Thursday, June 8, 2023 at 2:53:14 AM UTC-4, Chris M. Thomasson wrote:
>>> On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
>>>> Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
>>> [...]
>>>
>>> Do you have an 8-bit mentality?
>>>
>>> https://youtu.be/cRAmtrnOXWc
>>>
>>> Btw, I think the voice in this is computed generated. All on an 8-bit
>>> computer?
>> You are on the right track but you have to close in that outward path.
>> The first instruction RU is only run once --
>> RU=1 --- then the next 4 instructions LD =2, RD=1,RU=3, LU=2, --- Now again in the same order--
>> LD=4, RD=3,RU=5,LU=4 --- again in the same order ---- taking each integer from the outgiong
>> sequence. As simple as that.
>> I believe now you got it
> .
> For the sake of argument here. Say a picture of a large square lattice with thousands of cells was
> shown to you and the person said, can you duplicate this lattice useing a pencil without crossing
> a line or retracing a line and at no time not lifting the pencil from the paper. What would you say to
> him. Oh yeah it can be done or it is impossible?
> Just wondering.

Not sure. I need to create the other path that goes from the end point
back to the origin point. This is the key that can create the squares
our of the spiral, I think...? Let me start small. This is only 18
iterations:

The circle in red is the origin, the one in green is the end:

https://i.ibb.co/R70XGkz/image.png

So, after this spiral, I would want to go from green to red in the
closing spiral. The anti-spiral, so to speak...? ;^)

Fair enough? Or am I somehow "missing" your main point?

Thanks. I only have perhaps two hours to work on your work today. Sorry!

On 6/8/2023 11:00 AM, Dan joyce wrote:
> On Thursday, June 8, 2023 at 6:38:25 AM UTC-4, Dan joyce wrote:
>> On Thursday, June 8, 2023 at 2:53:14 AM UTC-4, Chris M. Thomasson wrote:
>>> On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
>>>> Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
>>> [...]
>>>
>>> Do you have an 8-bit mentality?
>>>
>>> https://youtu.be/cRAmtrnOXWc
>>>
>>> Btw, I think the voice in this is computed generated. All on an 8-bit
>>> computer?
>> You are on the right track but you have to close in that outward path.
>> The first instruction RU is only run once --
>> RU=1 --- then the next 4 instructions LD =2, RD=1,RU=3, LU=2, --- Now again in the same order--
>> LD=4, RD=3,RU=5,LU=4 --- again in the same order ---- taking each integer from the outgiong
>> sequence. As simple as that.
>> I believe now you got it
> .
> For the sake of argument here. Say a picture of a large square lattice with thousands of cells was
> shown to you and the person said, can you duplicate this lattice useing a pencil without crossing
> a line or retracing a line and at no time not lifting the pencil from the paper. What would you say to
> him. Oh yeah it can be done or it is impossible?
> Just wondering.

This is just me drawing on my result trying to sketch my way back in
through the spiral. I think I got it?

https://i.ibb.co/4ZVTwtf/image.png

Humm... Any thoughts?

Thanks. :^)

On Thursday, June 8, 2023 at 2:52:45 PM UTC-4, Chris M. Thomasson wrote:
> On 6/8/2023 11:00 AM, Dan joyce wrote:
> > On Thursday, June 8, 2023 at 6:38:25 AM UTC-4, Dan joyce wrote:
> >> On Thursday, June 8, 2023 at 2:53:14 AM UTC-4, Chris M. Thomasson wrote:
> >>> On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
> >>>> Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
> >>> [...]
> >>>
> >>> Do you have an 8-bit mentality?
> >>>
> >>> https://youtu.be/cRAmtrnOXWc
> >>>
> >>> Btw, I think the voice in this is computed generated. All on an 8-bit
> >>> computer?
> >> You are on the right track but you have to close in that outward path.
> >> The first instruction RU is only run once --
> >> RU=1 --- then the next 4 instructions LD =2, RD=1,RU=3, LU=2, --- Now again in the same order--
> >> LD=4, RD=3,RU=5,LU=4 --- again in the same order ---- taking each integer from the outgiong
> >> sequence. As simple as that.
> >> I believe now you got it
> > .
> > For the sake of argument here. Say a picture of a large square lattice with thousands of cells was
> > shown to you and the person said, can you duplicate this lattice useing a pencil without crossing
> > a line or retracing a line and at no time not lifting the pencil from the paper. What would you say to
> > him. Oh yeah it can be done or it is impossible?
> > Just wondering.
> This is just me drawing on my result trying to sketch my way back in
> through the spiral. I think I got it?
>
> https://i.ibb.co/4ZVTwtf/image.png
>
> Humm... Any thoughts?
>
> Thanks. :^)
I have just made a correction. The top part where it ends going out 2 lines can be elliminated
to draw a rectangular border around this lattice nothing will protrude beyond the border as
it does in your rendering and mine. The last integer (n) in the first sequence is reduced by n=n-1
Also the correction has to go over to the coming in sequence (2nd sequence) first integer (n)
has to be reduces by n=n-1
I didn't actually try this yet but I believe it should correct the protruding portion of this lattice.
Giving a nice, close to square, border around this lattice with no protruding cells..
How is it going with the going in lines?

On Friday, June 9, 2023 at 2:42:32 PM UTC-4, Dan joyce wrote:
> On Thursday, June 8, 2023 at 2:52:45 PM UTC-4, Chris M. Thomasson wrote:
> > On 6/8/2023 11:00 AM, Dan joyce wrote:
> > > On Thursday, June 8, 2023 at 6:38:25 AM UTC-4, Dan joyce wrote:
> > >> On Thursday, June 8, 2023 at 2:53:14 AM UTC-4, Chris M. Thomasson wrote:
> > >>> On 6/7/2023 11:32 PM, Archimedes Plutonium wrote:
> > >>>> Moscow▂▄▅█████████▅▄▃▂ Beijing mushroom cloud, Xi as Putin's stooge when Russia vaporizes Beijing with its RS-28 Sarmat "Satan II", all because Xi was too dumb to realize you can never trust an insane person
> > >>> [...]
> > >>>
> > >>> Do you have an 8-bit mentality?
> > >>>
> > >>> https://youtu.be/cRAmtrnOXWc
> > >>>
> > >>> Btw, I think the voice in this is computed generated. All on an 8-bit
> > >>> computer?
> > >> You are on the right track but you have to close in that outward path.
> > >> The first instruction RU is only run once --
> > >> RU=1 --- then the next 4 instructions LD =2, RD=1,RU=3, LU=2, --- Now again in the same order--
> > >> LD=4, RD=3,RU=5,LU=4 --- again in the same order ---- taking each integer from the outgiong
> > >> sequence. As simple as that.
> > >> I believe now you got it
> > > .
> > > For the sake of argument here. Say a picture of a large square lattice with thousands of cells was
> > > shown to you and the person said, can you duplicate this lattice useing a pencil without crossing
> > > a line or retracing a line and at no time not lifting the pencil from the paper. What would you say to
> > > him. Oh yeah it can be done or it is impossible?
> > > Just wondering.
> > This is just me drawing on my result trying to sketch my way back in
> > through the spiral. I think I got it?
> >
> > https://i.ibb.co/4ZVTwtf/image.png
> >
> > Humm... Any thoughts?
> >
> > Thanks. :^)
> I have just made a correction. The top part where it ends going out 2 lines can be elliminated
> to draw a rectangular border around this lattice nothing will protrude beyond the border as
> it does in your rendering and mine. The last integer (n) in the first sequence is reduced by n=n-1
> Also the correction has to go over to the coming in sequence (2nd sequence) first integer (n)
> has to be reduces by n=n-1
> I didn't actually try this yet but I believe it should correct the protruding portion of this lattice.
> Giving a nice, close to square, border around this lattice with no protruding cells..
> How is it going with the going in lines?

I just made the above corrections and it worked the first time so it gives a nice almost square
lattice with no protruding cells beyond the drawn border around the lattice..
By the way, When drawing a lattice in this manner and putting a border around it creates a
rectanglear shape of 9 * 11.25 or that ratio.
The exact measurement for a lattice with 32 cells and each cell measures 1X1 then the
exact border around that lattice is --- 5.6565542... * 7.0710678... =40 minus the spaces added
up =8 within the border that are not within any 1*1 cells = 32 cells within the border
So it is really not a square lattice the way it is constructed. Many more of these longer and longer
rectangular lattices with shorter and shorter ends can be constructed with out lifting the pencil.