# Robert Spann

I am intrigued by analogs between the compositional rules and color theory principles that artists use and the mathematical/statistical properties of images. A digital image is a map from the unit square to a set of k colors. I start with a set of desirable mathematical and statistical properties for an image and then produce maps which have these properties. Currently, I am experimenting with combinations of equations (formed using Discrete Cosine Transforms) that have different symmetries and/or parities. I use the resulting maps to produce candidate images for further refinement. I then refine these candidate images using digital manipulation based on my own aesthetic judgments.

I start with two maps, f(x,y) and g(x,y); each a map from the unit square onto the set of integers 1,..,n and 1,..,m respectively. Each is constructed using Discrete Cosine Transforms. I combine these two maps to form a map from the unit square onto the integers 1,..,mn. Each integer is assigned a color. In Frolic, f(x,y) is symmetric with respect to a diagonal mirror and is also symmetric with respect to a 180 degree rotation. The function g(x,y) has odd parity with respect to a vertical reflection and no symmetry or parity with respect to horizontal reflections or diagonal mirrors. The result is an image which has structure, but no symmetries. The initial image is further refined based on my own aesthetic judgments.

I start with two maps, f(x,y) and g(x,y); each is a map from the unit square onto the set of integers 1,..,n and 1,..,m respectively. Each is constructed using Discrete Cosine Transforms. I combine these two maps to form a map from the unit square onto the integers 1,..,mn. Each integer is assigned a color. In Time Travel f(x,y) has odd parity with respect to a diagonal axis. The function g(x,y) has even parity with respect to horizontal reflections, odd parity with respect to vertical reflections and odd parity when rotated through 180 degrees. When the resulting image is rotated 180 degrees, the shapes do not change and each color is mapped to a neighboring hue. There are no symmetries with respect to horizontal or vertical reflections.