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From: sobriquet <dohduhdah@yahoo.com>
Newsgroups: sci.math
Subject: Re: n-poly from a line...
Date: Tue, 1 Apr 2025 00:53:12 +0200
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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