My work is composed primarily of computer generated, mathematically-inspired, abstract images. I draw from the areas of geometry, fractals and numerical analysis, and combine them with image processing technology. The resulting images powerfully reflect the beauty of mathematics that is often obscured by dry formulae and analyses.
An overriding theme that encompasses all of my work is the wondrous beauty and complexity that flows from a few, relatively simple, rules. Inherent in this process are feedback and connectivity; these are the elements that generate the patterns. They also demonstrate to me that mathematics is, in many cases, a metaphor for the beauty and complexity in life. This is what I try to capture.
This image examines the chaotic nature that Newton's method can exhibit. Here, the routine attempts to solve two real equations independently, however, the equations (x^2 = -1 and y^2 = -1) have no solutions. To exacerbate the chaos, the routine was modified to include a weight, making the process unstable. Each solution proceeded independent of the other, but the values were combined to generate the color of each pixel.
This image examines the chaotic nature that Newton's method can exhibit. Here, the routine attempts to solve a system of two real equations in two variables, using the matrix formulation of Newton's method. The method has been augmented through the inclusion of a matrix weight, whose elements were chosen to prevent finding a solution. A complex number was formed using the variables as components and the image was colored by the polar angle of the complex combination.