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.