Been working on my path tracer program again for a little artistic outlet 😃 here’s a rendering of a limit set from a kleinian group (acting on the boundary of hyperbolic 4-space) made of colored glass! The entire material is homogeneous, with the qualitative differences coming from internal reflections and subsurface scattering amongst the many tiny spheres.

Distance estimation to the limit set is via Jos Leys’ “escape time algorithm”

@stevejtrettel oh these are absolutely gorgeous, thank you for sharing and keep up the good work! 🧡

@stevejtrettel Now to figure out how to 3D-print such a thing.  

In the meantime, these make great wallpapers too!

@stevejtrettel Beautiful! Having one question: Why do you say "it's a Kleinian group acting on the boundary of hyperbolic 4-space"? What's the group here? I have this question because I have also rendered some sphere-packing images resulting from some Coxeter groups acting on the hyperbolic 4-space, but they do not have spiral patterns like yours. I'm wondering if there are any connections...