As a computer scientist, I have long been fascinated with the intersection of art, mathematics, and computer science. Abstract visual artists who have enlightened and inspired me include the Constructivist artists Josef Albers, Ellsworth Kelly, and Piet Mondrian. Recently, I have written software specifically for generating mathematically based abstract art. The software uses geometric transformations as its underlying principle, while also allowing for the precise specification of color, texture, and opacity; it has a rich, descriptive input language as well as a high quality rendering engine. This software has enabled me to explore abstract, mathematically oriented art which computer generation makes feasible.
I have long enjoyed looking at harmonographs; they were the initial inspiration for these images. The curve represented in each of these images is defined by a parametric equation; the curve serves as a guide for a series of plates which are placed at a calculated constant distance along the curve from its initial point. The shape, color, and opacity of the plates are functions of the distance along the curve. The number of possibilities and opportunities for satisfying results are endless. Often a more aesthetically pleasing final image can be obtained by applying a conformal map to the image. Even though each image is based on a single continuous two-dimensional curve, the results can have a very three-dimensional look.