Kerry Mitchell
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.
Every fraction has a decimal expansion that either terminates or repeats. This image represents those conditions for fractions with denominators from 2 to 101 (rows), expressed in number bases from 2 to 101 (columns). The color of each disk represents how many digits are in its repeating block of decimals, from 0 (terminating) in yellow to denominator - 1 for full reptend primes (blue-gray). The bright main diagonal includes denominators expressed in that base (such as 1/10 in base 10), which are terminating fractions.
This image contains several visual demonstrations that (a + b)^2 can be expanded into a^2 + 2ab + b^2. Disregarding the white borders, the yellow region in the lower left can be taken as a square with side length a and area of a^2. Likewise, the blue region in the upper right can be taken as a square with side length b and area of b^2. Consequently, the entire region is a square with side length (a + b). The green and purple regions comprise rectangles with area a x b and b x a, rounding out the expansion. The same analysis can be done within the yellow region (using the dark and bright squares) and within the blue region. Also, using the four squares individually, the entire piece also represents the expansion of (a + b + c + d)^2.