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23 Sep 2021 20:53:45 EDT (-0400)
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From: Dave Matthews
Subject: Re: Indra's deep sea life
Date: 6 Jun 2005 10:50:00
Message: <web.42a4615ad40151ad8c7259570@news.povray.org>
Kevin Wampler <wam### [at] cswashingtonedu> wrote:
> Just a couple of images obtained with a few reflective objects.  JPG did
> some pretty bad blurring to the first one, but I don't know how to fix
> that without increasing the file size probably a bit too high.
>
> This ideas for these came from the book I'm reading "Indra's Pearls"
> which so far I would recommend.  It gives a very accessible and pretty
> picture filled description of the symmetries of Kleinian groups.  Sounds
> dry, but they make some dang nice fractals and are very elegant
> mathematically as well.

Thanks for the reference and the source code!  I've been playing with
similar constructions (in the fractal contest from last year I placed
tangent spheres at the vertices of a cube:

http://astronomy.swin.edu.au/~pbourke/povray/povfrac/final/0002.html

and have since been working with other constructions.)  But yours came out
way cooler, and with new variations I hadn't thought of.  I'll have to get
the book.  I have seen the name "Indra's Pearls" on some fractals scattered
throughout the internet, but wasn't aware of their construction.

Very nice!

Dave Matthews


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From: Kevin Wampler
Subject: Re: Indra's deep sea life
Date: 6 Jun 2005 15:45:37
Message: <42a4a7e1$1@news.povray.org>
Dave Matthews wrote:
> Kevin Wampler <wam### [at] cswashingtonedu> wrote:
> 
> and have since been working with other constructions.)  But yours came out
> way cooler, and with new variations I hadn't thought of.  I'll have to get
> the book.  I have seen the name "Indra's Pearls" on some fractals scattered
> throughout the internet, but wasn't aware of their construction.

Nice image!  I should note that neither of the images I posted is 
actually the sort of think that would be generated by a Kleinian Group. 
  Intuitively they're similar, but the stuff covered in the book takes 
place entirely in the complex plane, so rather than optical reflection 
you have circle inversion for example.  You can see pictures more like 
those in the actual book at its web site:

http://klein.math.okstate.edu/IndrasPearls/

and also at:

http://klein.math.okstate.edu/kleinian/


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From: bugman
Subject: Re: Indra's deep sea life
Date: 5 May 2006 02:35:01
Message: <web.445af0fdd40151ad7acd794a0@news.povray.org>
I've been experimenting with some Kleinian Groups in POV-Ray, and just
thought I'd share it here:
http://bugman123.com/Fractals/DoubleCusp-large.jpg


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From: PM 2Ring
Subject: Re: Indra's deep sea life
Date: 5 May 2006 04:25:00
Message: <web.445b0b30d40151ad1bd1c060@news.povray.org>
"bugman" <nomail@nomail> wrote:
> I've been experimenting with some Kleinian Groups in POV-Ray, and just
> thought I'd share it here:
> http://bugman123.com/Fractals/DoubleCusp-large.jpg

Pretty! I like circular inversions. And who needs UltraFractal when we have
POV? :)

On a closely related note, do you happen to know how to do a 3D version of
Poincare's disk projection of hyperbolic space in POV? I know it can be
done, I once saw a hyperbolic tessellation using dodecahedra and I'm pretty
sure it was rendered using POV.


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From: bugman
Subject: Re: Indra's deep sea life
Date: 7 Jul 2006 22:35:00
Message: <web.44af19a8d40151ad7acd794a0@news.povray.org>
By the way, here is some POV-Ray code for the double cusp group:
http://bugman123.com/Fractals/DoubleCusp.zip


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From: bugman
Subject: Re: Indra's deep sea life
Date: 22 Jul 2006 16:10:01
Message: <web.44c2859cd40151ad7acd794a0@news.povray.org>
"PM 2Ring" <nomail@nomail> wrote:
> On a closely related note, do you happen to know how to do a 3D version of
> Poincare's disk projection of hyperbolic space in POV? I know it can be
> done, I once saw a hyperbolic tessellation using dodecahedra and I'm pretty
> sure it was rendered using POV.

I don't know if this is exactly what you had in mind, but it might be
helpful:
http://bugman123.com/Math/Poincare.zip


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