# 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. For example, equations, just like images, have symmetries. A digital image is a map from the unit square to a set of k colors. Equations with symmetries can be used to produce images with those same symmetries. Currently, I am experimenting with combinations of equations (formed using Discrete Cosine Transforms) that have different symmetries and/or parities. Combining equations with different symmetries can be used to produce images which have structure, but no symmetries. I then refine these images using digital manipulation based on my own aesthetic judgments.

I start with a map from the unit square onto the set of integers 1,..,k. This map is constructed using Discrete Cosine Transforms (DCT). Each integer is assigned a color. The DCT’s are construct so that the resulting image is symmetric with respect to a 180 degree rotation. Additionally, the edges are are symmetric with respect to a diagonal reflection and exhibit an orientation reversing symmetry with respect to horizontal and vertical reflections. I then create a copy of this image, rotate it by 90 degrees, and attach it to the original image. The resulting image is digitally manipulated to achieve a desired aspect ratio and further refined based on my own aesthetic judgments.

Stepping Stones is constructed using the same mathematical process as the image Autumn Evening. The two images use different palettes --both in terms of color and the number of colors used. Since the coloring algorithm maps a continuous function onto a set of integers--each of which is assigned a different color, changing the number of colors changes the way in which the space is divided into areas of color. Additionally, the image Stepping Stones is rotated and resized. The comparison between the two images illustrates the importance of palette choice in mapping the mathematics behind an image to the resulting visual experience produced by the image.