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Any chance someone here could render a sphere packing image similar to this, except fully raytraced (preferably with specular reflections, and global illumination so that colours leak from sphere to sphere). I haven't ever seen such an image, but I bet it would look completely breathtaking.

http://www.josleys.com/show_image.php?galid=225&imageid=6753

No, I'm not bothered about how long it would take to render  :D

If not, maybe someone could recommend a good 3D program to achieve this?

I have not a clue. I have bee trying around with creating a formula like that, but I failed and Jos Ley's Formulas aren't public domain yet.

Oh isn't it just Apollonian sphere packing? I thought that was widely known...

heya twinbee, i suppose almost any 3d renderer could render it given a suitable scene definition; i suppose your best bet would be indigo, which is free to use and offers by far the best results of any renderer out there today ;)

i'm also working on some new rendering code, but it's a while to go still before it's working... in any case, the big thing is to get the sphere pos/radius/colours, which i'd need to study more of indra's pearls to be able to set up.

let us know how you get on!  O0

Hi Lycium, that Indigo looks good, though I was thinking along that maybe something like povray would be suitable too since it allows direct 'programming' of the object? Dunno if POVray can export .3ds models and the scene xml file - then one could use those in Indigo.

This looks like it could be a fun project :D

oh, indigo also supports (perfect) sphere primitives, so no need to go the polygon mesh route. if you can write povray-script, no reason you can't write it in another script that will just output a whole bunch of sphere definitions :)

Could you not do this in Incendia?

unfortunately incendia doesn't support ray tracing; this was planned for a while but in the end aexion decided to use his own rendering engine instead of mine :-\

Ah. Tho to be honest I'm not quite sure what ray tracing is

Well after a few tricky bits, I've got the 2D coords/sizes for the Apollonian gasket all sorted out. Now on to the 3D stuff :)

It should be easyish, but I'm having trouble finding 3D equivalents to the Complex Descartes' theorem (http://en.wikipedia.org/wiki/Descartes'_theorem#Complex_Descartes_theorem), which is what's needed for the full blown Apollonian sphere packing.

In the meantime, here are some tasty renderings from an excellent little program which I found here (http://www.geocities.com/thomas_r_bonner/fract/fract.htm). The pics below contain around 5 million spheres (renders very quickly actually). I'm eager to see how much slower full blown raytracing is. As good as this looks, it lacks decent shadowing, reflections, and all the other goodies raytracing would bring...

Larger resolutions are available here (http://www.skytopia.com/stuff/apollospheres1.png) and here (http://www.skytopia.com/stuff/apollospheres2.png).

(http://www.skytopia.com/stuff/apollospheres1s.png)
(http://www.skytopia.com/stuff/apollospheres2s.png)

Just thought I'd link this thread up to Ron's thread:

http://www.fractalforums.com/3d-fractal-generation/sphere-inversion-fractals/ (http://www.fractalforums.com/3d-fractal-generation/sphere-inversion-fractals/)