# Jeffrey Stewart Ely

I am interested in applying computer graphical techniques to illuminate mathematical processes and

objects. Ideally, this can lead to a deeper understanding or at least to an increased appreciation and awareness of the process or object. Some of my projects are implemented as billions of particles, others use the ray tracing technique and hundreds of millions of rays. In either case, I do not use "canned" software, preferring to write the code myself to first principles.

The spherical chandelier is composed of squarish lenses. Inside the chandelier is a cubical

object that has been painted with the Mandelbrot set. Each of the lenses gives us a different

view of this object. This interior object and the individual lenses are all variations of

the quartic surface, x^4 + y^4 + z^4 = 1. The image was constructed using the ray

tracing technique and required the solution of over a billion quartic equations,

At^4 + Bt^3 + Ct^2 + Dt + E = 0, as the individual rays through each pixel were followed into this mathematical world of quartic surfaces. Snell's law was used to correctly model the

refraction of the rays as they passed through the lenses. Finally, the background also shows

a portion of the Mandelbrot set.