POV-Ray : Newsgroups : povray.advanced-users : Pappus Chain Server Time
10 Dec 2024 06:23:28 EST (-0500)
  Pappus Chain (Message 25 to 34 of 44)  
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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 17 Jun 2024 17:50:00
Message: <web.6670af7f3bd24dfe1f9dae3025979125@news.povray.org>
MichaelJF <fri### [at] t-onlinede> wrote:

> It took me a while to understand this weird javascript recursion and I
> mixed up some - with + or vice versa:

Excellent!
Now that there's some working SDL, I can try to understand where things went off
the rails, and try to make some variations.

Maybe a nested Appolonian gasket, but also one with circles in between 2
straight lines (circles with infinite radius, curvature of zero, resulting in
"Ford circles)

Thanks so much, Michael!

- BW


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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 17 Jun 2024 18:35:00
Message: <web.6670b9c03bd24dfe1f9dae3025979125@news.povray.org>
But for now...


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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 17 Jun 2024 18:35:00
Message: <web.6670b9d73bd24dfe1f9dae3025979125@news.povray.org>
And


#macro DrawCircle (C, PigmNr)

 //#debug concat( "C = ", vstr(3, C, ", ", 0, 3), " \n")
 //torus {abs(C.z), Line texture {pigment {colour Colours[PigmNr]} finish
{emission 1}} rotate x*90 translate <C.x, C.y, 0>}
 #if (C.z > 0 & C.z < 0.6)
 sphere {0, abs(C.z) scale <1, 1, 1+pow(abs(C.z), 0.001)> texture {pigment
{colour Colours[PigmNr]} finish {specular 0.4}} translate <C.x, C.y, 0>}
 #end
#end


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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 17 Jun 2024 18:55:00
Message: <web.6670bdb23bd24dfe1f9dae3025979125@news.povray.org>
And of course, because the Appollonian gasket is a foam, . . .

bubbles!


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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 17 Jun 2024 20:05:00
Message: <web.6670ce7d3bd24dfe1f9dae3025979125@news.povray.org>
and with a nested gasket, we could do a sort of Sierpinski triangle.

There's some kind of transformation that makes them isomorphic.


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From: kurtz le pirate
Subject: Re: Pappus Chain
Date: 18 Jun 2024 11:28:16
Message: <6671a790$1@news.povray.org>
On 17/06/2024 23:49, Bald Eagle wrote:
> Excellent!
> Now that there's some working SDL, I can try to understand where things went off
> the rails, and try to make some variations.


I've updated my page and published the code (at the very bottom).
<http://louisbel.free.fr/scenes/scene038.shtml>


Sorry, still in French
-- 
Kurtz le pirate
Compagnie de la Banquise


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From: kurtz le pirate
Subject: Re: Pappus Chain
Date: 18 Jun 2024 11:29:05
Message: <6671a7c1$1@news.povray.org>
On 18/06/2024 00:50, Bald Eagle wrote:
> And of course, because the Appollonian gasket is a foam, . . .
> 
> bubbles!
> 


GREAT Bubbles. Very good job.


-- 
Kurtz le pirate
Compagnie de la Banquise


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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 18 Jun 2024 16:05:00
Message: <web.6671e8453bd24dfec74cee8225979125@news.povray.org>
Just posting this here for reference.

https://www.johndcook.com/blog/2023/12/19/conformal-map-disk-triangle/

Would be cool to apply this to the gasket to see what pops out - probably a
Sierpinski Triangle.

Search: conformal mapping of circle to a triangle

- BE


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From: Bald Eagle
Subject: Re: Pappus Chain
Date: 18 Jun 2024 20:40:00
Message: <web.667228173bd24dfe1f9dae3025979125@news.povray.org>
Now with lenses!


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From: MichaelJF
Subject: Re: Pappus Chain
Date: 19 Jun 2024 07:49:27
Message: <6672c5c7$1@news.povray.org>
Am 19.06.2024 um 02:36 schrieb Bald Eagle:
> Now with lenses!
somewhat crazy, but very interesting;)

Best regards
Michael


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