# Jeffrey Stewart Ely

Associate Professor of Computer Science

The Department of Mathematical Sciences, Lewis and Clark College

Portland, Oregon, USA

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.

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.

Negative Butterflies

40 x 40 cm

Digital print on archival paper.

2016

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.

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.