Artist Statement

“Without mathematics there is no art.”

Luca Pacioli (da Vinci’s teacher)


Can ideas from mathematics open pathways to new and unexpected visual images?  Can the very formal inspire the subjective and personal?  Throughout my life, I’ve been fascinated and driven by the idea of using exotic mathematical tools to create unusual and unexpected images.  When I generate an image, I’m trying to share my own subjective perceptions of the enormous complexity and unity that can emerge from simulations based on mathematical processes.

An artist often creates a body or work by making one piece at a time but my approach is somewhat different. I design a single algorithm as a tool to create a coherent collection of images that reflect my own artistic intentions. At heart, I’m an experimentalist.  I make tiny changes to my unique computer code and look at the visual results.  Based on what I see, I make another small change and this process can go on months, even years, until I’m satisfied the algorithm is giving me a significant number of images that I like. Most often, my ideas fail to produce results that satisfy me artistically and I give up and try another approach.

The computer code I’ve shaped incrementally over the last thirty years contains subroutines that define the composition, colour and texture of each piece.  One of the processes I use is based on the extraordinary and often chaotic behaviour that emerges from the feedback loop xn+1  = f ( xn ) which is currently  under intense study by mathematicians.  Recently, I’ve been constructing “vector fields” on photographs and using that structure to create images containing figurative elements.   Currently, I’m experimenting with images based on networks of random data that have been mixed together with data from photographs.


Bill Ralph