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tech / sci.math / Re: for Dan... Check this out:

SubjectAuthor
* for Dan... Check this out:Chris M. Thomasson
+* Re: for Dan... Check this out:Chris M. Thomasson
|`* Re: for Dan... Check this out:Chris M. Thomasson
| +- Re: for Dan... Check this out:Chris M. Thomasson
| +- Re: for Dan... Check this out:Dan joyce
| `- Re: for Dan... Check this out:Dan joyce
`* Re: for Dan... Check this out:Dan joyce
 `* Re: for Dan... Check this out:Chris M. Thomasson
  `* Re: for Dan... Check this out:Chris M. Thomasson
   `* Re: for Dan... Check this out:Dan joyce
    +* Re: for Dan... Check this out:Chris M. Thomasson
    |+* Re: for Dan... Check this out:Dan joyce
    ||`- Re: for Dan... Check this out:Dan joyce
    |`* Re: for Dan... Check this out:Ben Bacarisse
    | `- Re: for Dan... Check this out:Dan joyce
    +- Re: for Dan... Check this out:Chris M. Thomasson
    `* Re: for Dan... Check this out:Chris M. Thomasson
     `- Re: for Dan... Check this out:Dan joyce

1
for Dan... Check this out:

<u8dler$22n6e$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139870&group=sci.math#139870

  copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: for Dan... Check this out:
Date: Sat, 8 Jul 2023 23:52:12 -0700
Organization: A noiseless patient Spider
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 06:52 UTC

0123456789
10111213141516171819
20212223242526272829
30313233343536373839
40414243444546474849

Notice the pattern using your command map as in:

// command map
const command_map = new Map([
["R", [[1, 0], [255, 0, 0, 255]]],
["U", [[0, 1], [0, 255, 0, 255]]],
["L", [[-1, 0], [0, 255, 255, 255]]],
["D", [[0, -1], [255, 255, 0, 255]]],

// Dan's map
["1", [[1, 0], [255, 0, 0, 255]]],
["4", [[0, 1], [0, 255, 0, 255]]],
["3", [[-1, 0], [0, 255, 255, 255]]],
["2", [[0, -1], [255, 0, 255, 255]]]
]);

in:

http://fractallife247.com/test/cmd_plot/ct_main.js

These commands should work fine for you in my plotter:

https://i.ibb.co/f2Km3KN/image.png

Nice! I wonder what it would look like with larger numbers.

Or a special mapping for 10-ary pi2 / 10 angle:

0123456789

Ten symbols to map.

Re: for Dan... Check this out:

<u8dm2f$22n6b$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139872&group=sci.math#139872

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 00:02:40 -0700
Organization: A noiseless patient Spider
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 07:02 UTC

On 7/8/2023 11:52 PM, Chris M. Thomasson wrote:
> 0123456789
> 10111213141516171819
> 20212223242526272829
> 30313233343536373839
> 40414243444546474849
>
> Notice the pattern using your command map as in:
>
>     // command map
>     const command_map = new Map([
>         ["R", [[1, 0], [255, 0, 0, 255]]],
>         ["U", [[0, 1], [0, 255, 0, 255]]],
>         ["L", [[-1, 0], [0, 255, 255, 255]]],
>         ["D", [[0, -1], [255, 255, 0, 255]]],
>
>         // Dan's map
>         ["1", [[1, 0], [255, 0, 0, 255]]],
>         ["4", [[0, 1], [0, 255, 0, 255]]],
>         ["3", [[-1, 0], [0, 255, 255, 255]]],
>         ["2", [[0, -1], [255, 0, 255, 255]]]
>     ]);
>
> in:
>
> http://fractallife247.com/test/cmd_plot/ct_main.js
>
> These commands should work fine for you in my plotter:
>
> https://i.ibb.co/f2Km3KN/image.png
>
> Nice! I wonder what it would look like with larger numbers.
>
> Or a special mapping for 10-ary pi2 / 10 angle:
>
> 0123456789
>
> Ten symbols to map.

Well, it seems to be fractal in nature!

https://i.ibb.co/gJ0882k/image.png

Humm... I need to assign an 10-ary set of directions to it, pi2 / 10

Re: for Dan... Check this out:

<u8dn0j$22sfg$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139873&group=sci.math#139873

  copy link   Newsgroups: sci.math
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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 00:18:42 -0700
Organization: A noiseless patient Spider
Lines: 22
Message-ID: <u8dn0j$22sfg$1@dont-email.me>
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 07:18 UTC

On 7/9/2023 12:02 AM, Chris M. Thomasson wrote:
> On 7/8/2023 11:52 PM, Chris M. Thomasson wrote:
[...]
>> Nice! I wonder what it would look like with larger numbers.
>>
>> Or a special mapping for 10-ary pi2 / 10 angle:
>>
>> 0123456789
>>
>> Ten symbols to map.
>
> Well, it seems to be fractal in nature!
>
> https://i.ibb.co/gJ0882k/image.png
>
> Humm... I need to assign an 10-ary set of directions to it, pi2 / 10

It is a fractal! This is mapping 10 directions to 0...9 symbols:

https://i.ibb.co/mv37r1h/image.png

Re: for Dan... Check this out:

<u8dn8s$22sfg$2@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139874&group=sci.math#139874

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 00:23:09 -0700
Organization: A noiseless patient Spider
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 07:23 UTC

On 7/9/2023 12:18 AM, Chris M. Thomasson wrote:
> On 7/9/2023 12:02 AM, Chris M. Thomasson wrote:
>> On 7/8/2023 11:52 PM, Chris M. Thomasson wrote:
> [...]
>>> Nice! I wonder what it would look like with larger numbers.
>>>
>>> Or a special mapping for 10-ary pi2 / 10 angle:
>>>
>>> 0123456789
>>>
>>> Ten symbols to map.
>>
>> Well, it seems to be fractal in nature!
>>
>> https://i.ibb.co/gJ0882k/image.png
>>
>> Humm... I need to assign an 10-ary set of directions to it, pi2 / 10
>
> It is a fractal! This is mapping 10 directions to 0...9 symbols:
>
> https://i.ibb.co/mv37r1h/image.png
>
>

Strange shit is occurring with the simple pattern:

https://i.ibb.co/nm5FQHT/image.png

Re: for Dan... Check this out:

<e43d491c-aa00-4125-b38c-d2ac41e53f9bn@googlegroups.com>

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https://www.novabbs.com/tech/article-flat.php?id=139878&group=sci.math#139878

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
Injection-Date: Sun, 09 Jul 2023 11:25:13 +0000
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 by: Dan joyce - Sun, 9 Jul 2023 11:25 UTC

On Sunday, July 9, 2023 at 3:18:53 AM UTC-4, Chris M. Thomasson wrote:
> On 7/9/2023 12:02 AM, Chris M. Thomasson wrote:
> > On 7/8/2023 11:52 PM, Chris M. Thomasson wrote:
> [...]
> >> Nice! I wonder what it would look like with larger numbers.
> >>
> >> Or a special mapping for 10-ary pi2 / 10 angle:
> >>
> >> 0123456789
> >>
> >> Ten symbols to map.
> >
> > Well, it seems to be fractal in nature!
> >
> > https://i.ibb.co/gJ0882k/image.png
> >
> > Humm... I need to assign an 10-ary set of directions to it, pi2 / 10
> It is a fractal! This is mapping 10 directions to 0...9 symbols:
>
> https://i.ibb.co/mv37r1h/image.png
So you can even do certain fractals with this algorithm.
How cool is that!

Re: for Dan... Check this out:

<47df57bc-96f7-496e-bf61-868b39296f7cn@googlegroups.com>

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https://www.novabbs.com/tech/article-flat.php?id=139882&group=sci.math#139882

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sun, 9 Jul 2023 12:04 UTC

On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
> 0123456789
> 10111213141516171819
> 20212223242526272829
> 30313233343536373839
> 40414243444546474849
>
> Notice the pattern using your command map as in:
>
> // command map
> const command_map = new Map([
> ["R", [[1, 0], [255, 0, 0, 255]]],
> ["U", [[0, 1], [0, 255, 0, 255]]],
> ["L", [[-1, 0], [0, 255, 255, 255]]],
> ["D", [[0, -1], [255, 255, 0, 255]]],
>
> // Dan's map
> ["1", [[1, 0], [255, 0, 0, 255]]],
> ["4", [[0, 1], [0, 255, 0, 255]]],
> ["3", [[-1, 0], [0, 255, 255, 255]]],
> ["2", [[0, -1], [255, 0, 255, 255]]]
> ]);
>
> in:
>
> http://fractallife247.com/test/cmd_plot/ct_main.js
>
> These commands should work fine for you in my plotter:
>
> https://i.ibb.co/f2Km3KN/image.png
>
> Nice! I wonder what it would look like with larger numbers.
>
> Or a special mapping for 10-ary pi2 / 10 angle:
>
> 0123456789
>
> Ten symbols to map.
Neat! That 10 directions would be a lot of angles.
If the mapping of the 10 is possible, now your talking fractals.

Re: for Dan... Check this out:

<a17a134f-0626-4440-a1a8-769a073306a1n@googlegroups.com>

  copy mid

https://www.novabbs.com/tech/article-flat.php?id=139883&group=sci.math#139883

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sun, 9 Jul 2023 12:33 UTC

On Sunday, July 9, 2023 at 3:18:53 AM UTC-4, Chris M. Thomasson wrote:
> On 7/9/2023 12:02 AM, Chris M. Thomasson wrote:
> > On 7/8/2023 11:52 PM, Chris M. Thomasson wrote:
> [...]
> >> Nice! I wonder what it would look like with larger numbers.
> >>
> >> Or a special mapping for 10-ary pi2 / 10 angle:
> >>
> >> 0123456789
> >>
> >> Ten symbols to map.
> >
> > Well, it seems to be fractal in nature!
> >
> > https://i.ibb.co/gJ0882k/image.png
> >
> > Humm... I need to assign an 10-ary set of directions to it, pi2 / 10
> It is a fractal! This is mapping 10 directions to 0...9 symbols:
>
> https://i.ibb.co/mv37r1h/image.png
Nice work Chris.

Re: for Dan... Check this out:

<u8f414$27mp0$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139941&group=sci.math#139941

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 13:07:01 -0700
Organization: A noiseless patient Spider
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 20:07 UTC

On 7/9/2023 5:04 AM, Dan joyce wrote:
> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
>> 0123456789
>> 10111213141516171819
>> 20212223242526272829
>> 30313233343536373839
>> 40414243444546474849
>>
>> Notice the pattern using your command map as in:
>>
>> // command map
>> const command_map = new Map([
>> ["R", [[1, 0], [255, 0, 0, 255]]],
>> ["U", [[0, 1], [0, 255, 0, 255]]],
>> ["L", [[-1, 0], [0, 255, 255, 255]]],
>> ["D", [[0, -1], [255, 255, 0, 255]]],
>>
>> // Dan's map
>> ["1", [[1, 0], [255, 0, 0, 255]]],
>> ["4", [[0, 1], [0, 255, 0, 255]]],
>> ["3", [[-1, 0], [0, 255, 255, 255]]],
>> ["2", [[0, -1], [255, 0, 255, 255]]]
>> ]);
>>
>> in:
>>
>> http://fractallife247.com/test/cmd_plot/ct_main.js
>>
>> These commands should work fine for you in my plotter:
>>
>> https://i.ibb.co/f2Km3KN/image.png
>>
>> Nice! I wonder what it would look like with larger numbers.
>>
>> Or a special mapping for 10-ary pi2 / 10 angle:
>>
>> 0123456789
>>
>> Ten symbols to map.
> Neat! That 10 directions would be a lot of angles.

Actually, it is rather straight forward:
___________________________
// build n-ary map
{
var n = 10;
var angle_base = Math.PI * 2 / n;

for (var i = 0; i < 10; ++i) {
var angle = angle_base * i;
var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
0, 255]];
command_map.set(i.toString(), command);
}
}
____________________________

The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
can make it use any number of unique symbols... :^)

> If the mapping of the 10 is possible, now your talking fractals.

;^)

Re: for Dan... Check this out:

<u8f4ke$27mp0$3@dont-email.me>

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Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 13:17:19 -0700
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 20:17 UTC

On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
> On 7/9/2023 5:04 AM, Dan joyce wrote:
>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
>>> 0123456789
>>> 10111213141516171819
>>> 20212223242526272829
>>> 30313233343536373839
>>> 40414243444546474849
>>>
>>> Notice the pattern using your command map as in:
>>>
>>> // command map
>>> const command_map = new Map([
>>> ["R", [[1, 0], [255, 0, 0, 255]]],
>>> ["U", [[0, 1], [0, 255, 0, 255]]],
>>> ["L", [[-1, 0], [0, 255, 255, 255]]],
>>> ["D", [[0, -1], [255, 255, 0, 255]]],
>>>
>>> // Dan's map
>>> ["1", [[1, 0], [255, 0, 0, 255]]],
>>> ["4", [[0, 1], [0, 255, 0, 255]]],
>>> ["3", [[-1, 0], [0, 255, 255, 255]]],
>>> ["2", [[0, -1], [255, 0, 255, 255]]]
>>> ]);
>>>
>>> in:
>>>
>>> http://fractallife247.com/test/cmd_plot/ct_main.js
>>>
>>> These commands should work fine for you in my plotter:
>>>
>>> https://i.ibb.co/f2Km3KN/image.png
>>>
>>> Nice! I wonder what it would look like with larger numbers.
>>>
>>> Or a special mapping for 10-ary pi2 / 10 angle:
>>>
>>> 0123456789
>>>
>>> Ten symbols to map.
>> Neat! That 10 directions would be a lot of angles.
>
> Actually, it is rather straight forward:
> ___________________________
>     // build n-ary map
>     {
>         var n = 10;
>         var angle_base = Math.PI * 2 / n;
>
>         for (var i = 0; i < 10; ++i) {
^^^^^^^^^^^^^^^^^^^

I hard coded 10 here to experiment with different n's using the same
angle_base. This is still in pre-alpha stage. Fun times!

:^)

>             var angle = angle_base * i;
>             var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
> 0, 255]];
>             command_map.set(i.toString(), command);
>         }
>     }
> ____________________________
>
> The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
> in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
> can make it use any number of unique symbols... :^)
>
>> If the mapping of the 10 is possible, now your talking fractals.
>
> ;^)
>

Re: for Dan... Check this out:

<ae46f506-ea2b-406e-9056-f4793d14d465n@googlegroups.com>

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sun, 9 Jul 2023 20:56 UTC

On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
> > On 7/9/2023 5:04 AM, Dan joyce wrote:
> >> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
> >>> 0123456789
> >>> 10111213141516171819
> >>> 20212223242526272829
> >>> 30313233343536373839
> >>> 40414243444546474849
> >>>
> >>> Notice the pattern using your command map as in:
> >>>
> >>> // command map
> >>> const command_map = new Map([
> >>> ["R", [[1, 0], [255, 0, 0, 255]]],
> >>> ["U", [[0, 1], [0, 255, 0, 255]]],
> >>> ["L", [[-1, 0], [0, 255, 255, 255]]],
> >>> ["D", [[0, -1], [255, 255, 0, 255]]],
> >>>
> >>> // Dan's map
> >>> ["1", [[1, 0], [255, 0, 0, 255]]],
> >>> ["4", [[0, 1], [0, 255, 0, 255]]],
> >>> ["3", [[-1, 0], [0, 255, 255, 255]]],
> >>> ["2", [[0, -1], [255, 0, 255, 255]]]
> >>> ]);
> >>>
> >>> in:
> >>>
> >>> http://fractallife247.com/test/cmd_plot/ct_main.js
> >>>
> >>> These commands should work fine for you in my plotter:
> >>>
> >>> https://i.ibb.co/f2Km3KN/image.png
> >>>
> >>> Nice! I wonder what it would look like with larger numbers.
> >>>
> >>> Or a special mapping for 10-ary pi2 / 10 angle:
> >>>
> >>> 0123456789
> >>>
> >>> Ten symbols to map.
> >> Neat! That 10 directions would be a lot of angles.
> >
> > Actually, it is rather straight forward:
> > ___________________________
> > // build n-ary map
> > {
> > var n = 10;
> > var angle_base = Math.PI * 2 / n;
> >
> > for (var i = 0; i < 10; ++i) {
> ^^^^^^^^^^^^^^^^^^^
>
> I hard coded 10 here to experiment with different n's using the same
> angle_base. This is still in pre-alpha stage. Fun times!
>
> :^)
> > var angle = angle_base * i;
> > var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
> > 0, 255]];
> > command_map.set(i.toString(), command);
> > }
> > }
> > ____________________________
> >
> > The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
> > in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
> > can make it use any number of unique symbols... :^)
> >
> >> If the mapping of the 10 is possible, now your talking fractals.
> >
> > ;^)
> >
You can track the digits in p1?

Re: for Dan... Check this out:

<u8f7br$2848p$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139951&group=sci.math#139951

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From: chris.m....@gmail.com (Chris M. Thomasson)
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Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 14:03:56 -0700
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 21:03 UTC

On 7/9/2023 1:56 PM, Dan joyce wrote:
> On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
>> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
>>> On 7/9/2023 5:04 AM, Dan joyce wrote:
>>>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
>>>>> 0123456789
>>>>> 10111213141516171819
>>>>> 20212223242526272829
>>>>> 30313233343536373839
>>>>> 40414243444546474849
>>>>>
>>>>> Notice the pattern using your command map as in:
>>>>>
>>>>> // command map
>>>>> const command_map = new Map([
>>>>> ["R", [[1, 0], [255, 0, 0, 255]]],
>>>>> ["U", [[0, 1], [0, 255, 0, 255]]],
>>>>> ["L", [[-1, 0], [0, 255, 255, 255]]],
>>>>> ["D", [[0, -1], [255, 255, 0, 255]]],
>>>>>
>>>>> // Dan's map
>>>>> ["1", [[1, 0], [255, 0, 0, 255]]],
>>>>> ["4", [[0, 1], [0, 255, 0, 255]]],
>>>>> ["3", [[-1, 0], [0, 255, 255, 255]]],
>>>>> ["2", [[0, -1], [255, 0, 255, 255]]]
>>>>> ]);
>>>>>
>>>>> in:
>>>>>
>>>>> http://fractallife247.com/test/cmd_plot/ct_main.js
>>>>>
>>>>> These commands should work fine for you in my plotter:
>>>>>
>>>>> https://i.ibb.co/f2Km3KN/image.png
>>>>>
>>>>> Nice! I wonder what it would look like with larger numbers.
>>>>>
>>>>> Or a special mapping for 10-ary pi2 / 10 angle:
>>>>>
>>>>> 0123456789
>>>>>
>>>>> Ten symbols to map.
>>>> Neat! That 10 directions would be a lot of angles.
>>>
>>> Actually, it is rather straight forward:
>>> ___________________________
>>> // build n-ary map
>>> {
>>> var n = 10;
>>> var angle_base = Math.PI * 2 / n;
>>>
>>> for (var i = 0; i < 10; ++i) {
>> ^^^^^^^^^^^^^^^^^^^
>>
>> I hard coded 10 here to experiment with different n's using the same
>> angle_base. This is still in pre-alpha stage. Fun times!
>>
>> :^)
>>> var angle = angle_base * i;
>>> var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
>>> 0, 255]];
>>> command_map.set(i.toString(), command);
>>> }
>>> }
>>> ____________________________
>>>
>>> The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
>>> in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
>>> can make it use any number of unique symbols... :^)
>>>
>>>> If the mapping of the 10 is possible, now your talking fractals.
>>>
>>> ;^)
>>>
> You can track the digits in p1?

Sure. Since I have the 10-ary digit map of 0...9, lets see here. I will use:

https://i.ibb.co/GJqLDyW/image.png
_______________________________
3141592653589793238462643383279502884
1971693993751058209749445923078164062
8620899862803482534211706798214808651
3282306647093844609550582231725359408
1284811174502841027019385211055596446
2294895493038196442881097566593344612
8475648233786783165271201909145648566
9234603486
_______________________________

Keep in mind that this version is not uploaded to my website, yet... ;^)

Re: for Dan... Check this out:

<u8f82h$2848p$2@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=139955&group=sci.math#139955

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Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 14:16:02 -0700
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 21:16 UTC

On 7/9/2023 1:56 PM, Dan joyce wrote:
> On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
>> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
>>> On 7/9/2023 5:04 AM, Dan joyce wrote:
>>>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
[...]
> You can track the digits in p1?

Any digits in base ten, or any base:

00112233445566778899

in ten-ary wrt angles of pi2 / 10:

https://i.ibb.co/646xKT5/image.png

Re: for Dan... Check this out:

<u8fc3d$28rb5$1@dont-email.me>

  copy mid

https://www.novabbs.com/tech/article-flat.php?id=139964&group=sci.math#139964

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Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Sun, 9 Jul 2023 15:24:46 -0700
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 by: Chris M. Thomasson - Sun, 9 Jul 2023 22:24 UTC

On 7/9/2023 1:56 PM, Dan joyce wrote:
> On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
>> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
>>> On 7/9/2023 5:04 AM, Dan joyce wrote:
>>>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
>>>>> 0123456789
>>>>> 10111213141516171819
>>>>> 20212223242526272829
>>>>> 30313233343536373839
>>>>> 40414243444546474849
>>>>>
>>>>> Notice the pattern using your command map as in:
>>>>>
>>>>> // command map
>>>>> const command_map = new Map([
>>>>> ["R", [[1, 0], [255, 0, 0, 255]]],
>>>>> ["U", [[0, 1], [0, 255, 0, 255]]],
>>>>> ["L", [[-1, 0], [0, 255, 255, 255]]],
>>>>> ["D", [[0, -1], [255, 255, 0, 255]]],
>>>>>
>>>>> // Dan's map
>>>>> ["1", [[1, 0], [255, 0, 0, 255]]],
>>>>> ["4", [[0, 1], [0, 255, 0, 255]]],
>>>>> ["3", [[-1, 0], [0, 255, 255, 255]]],
>>>>> ["2", [[0, -1], [255, 0, 255, 255]]]
>>>>> ]);
>>>>>
>>>>> in:
>>>>>
>>>>> http://fractallife247.com/test/cmd_plot/ct_main.js
>>>>>
>>>>> These commands should work fine for you in my plotter:
>>>>>
>>>>> https://i.ibb.co/f2Km3KN/image.png
>>>>>
>>>>> Nice! I wonder what it would look like with larger numbers.
>>>>>
>>>>> Or a special mapping for 10-ary pi2 / 10 angle:
>>>>>
>>>>> 0123456789
>>>>>
>>>>> Ten symbols to map.
>>>> Neat! That 10 directions would be a lot of angles.
>>>
>>> Actually, it is rather straight forward:
>>> ___________________________
>>> // build n-ary map
>>> {
>>> var n = 10;
>>> var angle_base = Math.PI * 2 / n;
>>>
>>> for (var i = 0; i < 10; ++i) {
>> ^^^^^^^^^^^^^^^^^^^
>>
>> I hard coded 10 here to experiment with different n's using the same
>> angle_base. This is still in pre-alpha stage. Fun times!
>>
>> :^)
>>> var angle = angle_base * i;
>>> var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
>>> 0, 255]];
>>> command_map.set(i.toString(), command);
>>> }
>>> }
>>> ____________________________
>>>
>>> The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
>>> in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
>>> can make it use any number of unique symbols... :^)
>>>
>>>> If the mapping of the 10 is possible, now your talking fractals.
>>>
>>> ;^)
>>>
> You can track the digits in p1?

oops! for some reason I thought you meant the digits in pi! Sorry. What
is p1?

Re: for Dan... Check this out:

<478a68df-539b-4093-a09a-21a3da60a92bn@googlegroups.com>

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Date: Sun, 9 Jul 2023 15:42:30 -0700 (PDT)
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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sun, 9 Jul 2023 22:42 UTC

On Sunday, July 9, 2023 at 6:24:55 PM UTC-4, Chris M. Thomasson wrote:
> On 7/9/2023 1:56 PM, Dan joyce wrote:
> > On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
> >> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
> >>> On 7/9/2023 5:04 AM, Dan joyce wrote:
> >>>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
> >>>>> 0123456789
> >>>>> 10111213141516171819
> >>>>> 20212223242526272829
> >>>>> 30313233343536373839
> >>>>> 40414243444546474849
> >>>>>
> >>>>> Notice the pattern using your command map as in:
> >>>>>
> >>>>> // command map
> >>>>> const command_map = new Map([
> >>>>> ["R", [[1, 0], [255, 0, 0, 255]]],
> >>>>> ["U", [[0, 1], [0, 255, 0, 255]]],
> >>>>> ["L", [[-1, 0], [0, 255, 255, 255]]],
> >>>>> ["D", [[0, -1], [255, 255, 0, 255]]],
> >>>>>
> >>>>> // Dan's map
> >>>>> ["1", [[1, 0], [255, 0, 0, 255]]],
> >>>>> ["4", [[0, 1], [0, 255, 0, 255]]],
> >>>>> ["3", [[-1, 0], [0, 255, 255, 255]]],
> >>>>> ["2", [[0, -1], [255, 0, 255, 255]]]
> >>>>> ]);
> >>>>>
> >>>>> in:
> >>>>>
> >>>>> http://fractallife247.com/test/cmd_plot/ct_main.js
> >>>>>
> >>>>> These commands should work fine for you in my plotter:
> >>>>>
> >>>>> https://i.ibb.co/f2Km3KN/image.png
> >>>>>
> >>>>> Nice! I wonder what it would look like with larger numbers.
> >>>>>
> >>>>> Or a special mapping for 10-ary pi2 / 10 angle:
> >>>>>
> >>>>> 0123456789
> >>>>>
> >>>>> Ten symbols to map.
> >>>> Neat! That 10 directions would be a lot of angles.
> >>>
> >>> Actually, it is rather straight forward:
> >>> ___________________________
> >>> // build n-ary map
> >>> {
> >>> var n = 10;
> >>> var angle_base = Math.PI * 2 / n;
> >>>
> >>> for (var i = 0; i < 10; ++i) {
> >> ^^^^^^^^^^^^^^^^^^^
> >>
> >> I hard coded 10 here to experiment with different n's using the same
> >> angle_base. This is still in pre-alpha stage. Fun times!
> >>
> >> :^)
> >>> var angle = angle_base * i;
> >>> var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
> >>> 0, 255]];
> >>> command_map.set(i.toString(), command);
> >>> }
> >>> }
> >>> ____________________________
> >>>
> >>> The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
> >>> in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
> >>> can make it use any number of unique symbols... :^)
> >>>
> >>>> If the mapping of the 10 is possible, now your talking fractals.
> >>>
> >>> ;^)
> >>>
> > You can track the digits in p1?
> oops! for some reason I thought you meant the digits in pi! Sorry. What
> is p1?
Sorry, I meant pi

Re: for Dan... Check this out:

<3ecc4473-563b-473c-8a34-9cdc7eff1b67n@googlegroups.com>

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sun, 9 Jul 2023 22:47 UTC

On Sunday, July 9, 2023 at 5:04:06 PM UTC-4, Chris M. Thomasson wrote:
> On 7/9/2023 1:56 PM, Dan joyce wrote:
> > On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
> >> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
> >>> On 7/9/2023 5:04 AM, Dan joyce wrote:
> >>>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
> >>>>> 0123456789
> >>>>> 10111213141516171819
> >>>>> 20212223242526272829
> >>>>> 30313233343536373839
> >>>>> 40414243444546474849
> >>>>>
> >>>>> Notice the pattern using your command map as in:
> >>>>>
> >>>>> // command map
> >>>>> const command_map = new Map([
> >>>>> ["R", [[1, 0], [255, 0, 0, 255]]],
> >>>>> ["U", [[0, 1], [0, 255, 0, 255]]],
> >>>>> ["L", [[-1, 0], [0, 255, 255, 255]]],
> >>>>> ["D", [[0, -1], [255, 255, 0, 255]]],
> >>>>>
> >>>>> // Dan's map
> >>>>> ["1", [[1, 0], [255, 0, 0, 255]]],
> >>>>> ["4", [[0, 1], [0, 255, 0, 255]]],
> >>>>> ["3", [[-1, 0], [0, 255, 255, 255]]],
> >>>>> ["2", [[0, -1], [255, 0, 255, 255]]]
> >>>>> ]);
> >>>>>
> >>>>> in:
> >>>>>
> >>>>> http://fractallife247.com/test/cmd_plot/ct_main.js
> >>>>>
> >>>>> These commands should work fine for you in my plotter:
> >>>>>
> >>>>> https://i.ibb.co/f2Km3KN/image.png
> >>>>>
> >>>>> Nice! I wonder what it would look like with larger numbers.
> >>>>>
> >>>>> Or a special mapping for 10-ary pi2 / 10 angle:
> >>>>>
> >>>>> 0123456789
> >>>>>
> >>>>> Ten symbols to map.
> >>>> Neat! That 10 directions would be a lot of angles.
> >>>
> >>> Actually, it is rather straight forward:
> >>> ___________________________
> >>> // build n-ary map
> >>> {
> >>> var n = 10;
> >>> var angle_base = Math.PI * 2 / n;
> >>>
> >>> for (var i = 0; i < 10; ++i) {
> >> ^^^^^^^^^^^^^^^^^^^
> >>
> >> I hard coded 10 here to experiment with different n's using the same
> >> angle_base. This is still in pre-alpha stage. Fun times!
> >>
> >> :^)
> >>> var angle = angle_base * i;
> >>> var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
> >>> 0, 255]];
> >>> command_map.set(i.toString(), command);
> >>> }
> >>> }
> >>> ____________________________
> >>>
> >>> The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
> >>> in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
> >>> can make it use any number of unique symbols... :^)
> >>>
> >>>> If the mapping of the 10 is possible, now your talking fractals.
> >>>
> >>> ;^)
> >>>
> > You can track the digits in p1?
> Sure. Since I have the 10-ary digit map of 0...9, lets see here. I will use:
>
> https://i.ibb.co/GJqLDyW/image.png
> _______________________________
> 3141592653589793238462643383279502884
> 1971693993751058209749445923078164062
> 8620899862803482534211706798214808651
> 3282306647093844609550582231725359408
> 1284811174502841027019385211055596446
> 2294895493038196442881097566593344612
> 8475648233786783165271201909145648566
> 9234603486
> _______________________________
>
> Keep in mind that this version is not uploaded to my website, yet... ;^)
Nice!

Re: for Dan... Check this out:

<bf145bad-b132-409a-b17f-3b7051c9c5den@googlegroups.com>

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sun, 9 Jul 2023 23:25 UTC

On Sunday, July 9, 2023 at 6:47:24 PM UTC-4, Dan joyce wrote:
> On Sunday, July 9, 2023 at 5:04:06 PM UTC-4, Chris M. Thomasson wrote:
> > On 7/9/2023 1:56 PM, Dan joyce wrote:
> > > On Sunday, July 9, 2023 at 4:17:28 PM UTC-4, Chris M. Thomasson wrote:
> > >> On 7/9/2023 1:07 PM, Chris M. Thomasson wrote:
> > >>> On 7/9/2023 5:04 AM, Dan joyce wrote:
> > >>>> On Sunday, July 9, 2023 at 2:52:22 AM UTC-4, Chris M. Thomasson wrote:
> > >>>>> 0123456789
> > >>>>> 10111213141516171819
> > >>>>> 20212223242526272829
> > >>>>> 30313233343536373839
> > >>>>> 40414243444546474849
> > >>>>>
> > >>>>> Notice the pattern using your command map as in:
> > >>>>>
> > >>>>> // command map
> > >>>>> const command_map = new Map([
> > >>>>> ["R", [[1, 0], [255, 0, 0, 255]]],
> > >>>>> ["U", [[0, 1], [0, 255, 0, 255]]],
> > >>>>> ["L", [[-1, 0], [0, 255, 255, 255]]],
> > >>>>> ["D", [[0, -1], [255, 255, 0, 255]]],
> > >>>>>
> > >>>>> // Dan's map
> > >>>>> ["1", [[1, 0], [255, 0, 0, 255]]],
> > >>>>> ["4", [[0, 1], [0, 255, 0, 255]]],
> > >>>>> ["3", [[-1, 0], [0, 255, 255, 255]]],
> > >>>>> ["2", [[0, -1], [255, 0, 255, 255]]]
> > >>>>> ]);
> > >>>>>
> > >>>>> in:
> > >>>>>
> > >>>>> http://fractallife247.com/test/cmd_plot/ct_main.js
> > >>>>>
> > >>>>> These commands should work fine for you in my plotter:
> > >>>>>
> > >>>>> https://i.ibb.co/f2Km3KN/image.png
> > >>>>>
> > >>>>> Nice! I wonder what it would look like with larger numbers.
> > >>>>>
> > >>>>> Or a special mapping for 10-ary pi2 / 10 angle:
> > >>>>>
> > >>>>> 0123456789
> > >>>>>
> > >>>>> Ten symbols to map.
> > >>>> Neat! That 10 directions would be a lot of angles.
> > >>>
> > >>> Actually, it is rather straight forward:
> > >>> ___________________________
> > >>> // build n-ary map
> > >>> {
> > >>> var n = 10;
> > >>> var angle_base = Math.PI * 2 / n;
> > >>>
> > >>> for (var i = 0; i < 10; ++i) {
> > >> ^^^^^^^^^^^^^^^^^^^
> > >>
> > >> I hard coded 10 here to experiment with different n's using the same
> > >> angle_base. This is still in pre-alpha stage. Fun times!
> > >>
> > >> :^)
> > >>> var angle = angle_base * i;
> > >>> var command = [[Math.cos(angle), Math.sin(angle)], [255, 0,
> > >>> 0, 255]];
> > >>> command_map.set(i.toString(), command);
> > >>> }
> > >>> }
> > >>> ____________________________
> > >>>
> > >>> The sets up a mapping of the 10-ary symbols "0123456789" to ten angles
> > >>> in pi2 / 10, where n = 10 for the n-ary mapping. Since this is n-ary I
> > >>> can make it use any number of unique symbols... :^)
> > >>>
> > >>>> If the mapping of the 10 is possible, now your talking fractals.
> > >>>
> > >>> ;^)
> > >>>
> > > You can track the digits in p1?
> > Sure. Since I have the 10-ary digit map of 0...9, lets see here. I will use:
> >
> > https://i.ibb.co/GJqLDyW/image.png
> > _______________________________
> > 3141592653589793238462643383279502884
> > 1971693993751058209749445923078164062
> > 8620899862803482534211706798214808651
> > 3282306647093844609550582231725359408
> > 1284811174502841027019385211055596446
> > 2294895493038196442881097566593344612
> > 8475648233786783165271201909145648566
> > 9234603486
> > _______________________________
> >
> > Keep in mind that this version is not uploaded to my website, yet... ;^)
> Nice!
I will have to plot reciprocals like 1/pn like I sent to you from the start
where most of the primes leave a nice complex pattern showing many
angles in the rendering. If your 1/pn matches mine that would be fantastic..

Re: for Dan... Check this out:

<87mt047gd2.fsf@bsb.me.uk>

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https://www.novabbs.com/tech/article-flat.php?id=139982&group=sci.math#139982

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: sci.math
Subject: Re: for Dan... Check this out:
Date: Mon, 10 Jul 2023 01:35:53 +0100
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 by: Ben Bacarisse - Mon, 10 Jul 2023 00:35 UTC

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> On 7/9/2023 1:56 PM, Dan joyce wrote:

>> You can track the digits in p1?
>
> Sure. Since I have the 10-ary digit map of 0...9, lets see here. I will use:
>
> https://i.ibb.co/GJqLDyW/image.png
> _______________________________
> 3141592653589793238462643383279502884
> 1971693993751058209749445923078164062
> 8620899862803482534211706798214808651
> 3282306647093844609550582231725359408
> 1284811174502841027019385211055596446
> 2294895493038196442881097566593344612
> 8475648233786783165271201909145648566
> 9234603486
> _______________________________
>
> Keep in mind that this version is not uploaded to my website, yet... ;^)

Some time ago I posted a picture of this for 1,000,000 digits of pi:

http://www.bsb.me.uk/tmp/pi-walk.png
http://www.bsb.me.uk/tmp/pi-walk-col.png

The lines are not opaque, so darker areas are ones visited often (like
overdrawing with a felt-tip pen). In the coloured version, the path
starts red and goes through orange, yellow, green and then blue.

--
Ben.

Re: for Dan... Check this out:

<55666cdf-120c-486f-85f8-d2605264c6can@googlegroups.com>

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Subject: Re: for Dan... Check this out:
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Mon, 10 Jul 2023 03:12 UTC

On Sunday, July 9, 2023 at 8:36:06 PM UTC-4, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>
> > On 7/9/2023 1:56 PM, Dan joyce wrote:
>
> >> You can track the digits in p1?
> >
> > Sure. Since I have the 10-ary digit map of 0...9, lets see here. I will use:
> >
> > https://i.ibb.co/GJqLDyW/image.png
> > _______________________________
> > 3141592653589793238462643383279502884
> > 1971693993751058209749445923078164062
> > 8620899862803482534211706798214808651
> > 3282306647093844609550582231725359408
> > 1284811174502841027019385211055596446
> > 2294895493038196442881097566593344612
> > 8475648233786783165271201909145648566
> > 9234603486
> > _______________________________
> >
> > Keep in mind that this version is not uploaded to my website, yet... ;^)
> Some time ago I posted a picture of this for 1,000,000 digits of pi:
>
> http://www.bsb.me.uk/tmp/pi-walk.png
> http://www.bsb.me.uk/tmp/pi-walk-col.png
>
> The lines are not opaque, so darker areas are ones visited often (like
> overdrawing with a felt-tip pen). In the coloured version, the path
> starts red and goes through orange, yellow, green and then blue.
>
> --
> Ben.
I assume the lower right is the x\y axis of x=0 and y=0.
Nice random walk on the x\y plain mostly in the second quadrant.

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server_pubkey.txt

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