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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: n-poly from a line...
Date: Mon, 31 Mar 2025 21:54:26 -0700
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On 3/31/2025 9:48 PM, Chris M. Thomasson wrote:
> On 3/31/2025 3:53 PM, sobriquet wrote:
>> Op 31/03/2025 om 23:05 schreef Chris M. Thomasson:
>>> On 3/31/2025 6:40 AM, sobriquet wrote:
>>>> Op 30/03/2025 om 08:24 schreef Chris M. Thomasson:
>>>>> Well, according to some AI's, lol, my ability to find an n-poly 
>>>>> from a single line, its incircle, outcircle and center point is 
>>>>> supposedly something good. Some of them claim it's not enough info 
>>>>> to gain the poly from the line and number of vertices alone. Well, 
>>>>> my function only takes two points (p0, p1) and a number of vertices 
>>>>> (n) for the result. Then renders all of them. Does this sound like 
>>>>> anything worthwhile to you? I just did it for a new fractal I am 
>>>>> tinkering around with for fun. I did not think it was anything all 
>>>>> that special. Fwiw, here is a render:
>>>>>
>>>>> https://i.ibb.co/Y7G4C80t/image.png
>>>>>
>>>>> Notice how the red circles are all tangent along a "path". The 
>>>>> green circles intersect. The number of polys are decreased as they 
>>>>> extend out. This starts from a single line and the number of 
>>>>> vertices. I am thinking about doing something interesting with it. 
>>>>> It might look fairly nice.
>>>>>
>>>>> :^)
>>>>>
>>>>> Thanks.
>>>>>
>>>>> Kind of interesting at all? Or been there, done that. :^)
>>>>
>>>> Nice! Looks a bit like a polyhedron that has been unfolded.
>>>>
>>>> Not sure how you scaled it relative to the unit circle.
>>>>
>>>> https://www.desmos.com/calculator/3izjfv3yma
>>>
>>> Thanks. Well, my algorithm starts off with only three relevant inputs:
>>>
>>> p0 = start of line
>>> p1 = end of line
>>> n = the n in n-poly
>>>
>>>  From that information alone, I create the fractal. So, it's not 
>>> scaled to the unit circle, its basically scaled from that line (p0, 
>>> p1). So, it can grow out of bounds, if we treat the unit circle as a 
>>> sort of "boundary". Now, you read my mind a bit. I have a way to 
>>> scale the fractal as a whole inside of any circle. Just need to port 
>>> my older code to this. Fwiw, these types of things can get pretty 
>>> dense, using the tangent circles instead of n-poly. Actually, its a 
>>> different generator algo using the same intersection avoidance algo:
>>>
>>> https://www.facebook.com/photo? 
>>> fbid=1377765076715820&set=pcb.1377765353382459
>>>
>>> Can you get to that FB link? Sorry... ;^o
>>
>> Yes, looks cool.. Can you also shade those fractals?
>>
>> In desmos it's a bit cumbersome, but still kinda cool effect:
>>
>> https://www.desmos.com/calculator/kuw9d9ftim
>>
> 
> I got it in 3d now. Here is an example:
> 
> https://i.ibb.co/CkHZ98P/ct-p4-Copy.png

https://www.facebook.com/photo/?fbid=1378008770024784&set=pcb.1378008916691436