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.
Iterated function systems are a rich source of fractals. As a
rule, one sees two-dimensional
images that have been generated from a small set of contractive,
affine transformations.
As well-known examples, the Sierpinski gasket can be specified
with a system of three
affine transformations and the Koch curve with four.
It is natural and simple to extend these systems to three
dimensions but my own experiments
at this were not visually intriguing. I believe I overcame this
when I was willing to consider
non-affine transformations that utilize the trigonometric
functions. This image is the result
of one such choice.