# Robert Spann

I am intrigued by the analogs between the compositional rules and color theory principles that artists use and the statistical properties of images. For example, the compositional principle that an image be balanced horizontally and vertically is equivalent to stating that the first horizontal and vertical geometric moments are zero. The principle of rhythm and repetition makes one think of repeated applications of group operations. A digital image is a map from the unit square to a set of n colors. I start with a set of desirable statistical properties for an image and then produce maps which have have these properties. I then refine these candidate images using digital manipulation based on my own aesthetic judgments.

I start with a generator that is a square subdivided into four differently colored squares. The four squares within the generator are labeled 0, 1, 2, 3 in clockwise order. I then translate the generator horizontally and vertically At each translation, I apply an element of the group of permutations of four items. This image contains the permutation (0,3)(1,2) --vertical reflections-- plus the permutations (1,3,2), (0,3,2), (1,2,3). The latter three permutations are not members of the dihedral group – that is they are not reflections or rotations of the generator. Finally, I convert the image to black and white and rotate the entire image 45 degrees.

I start with single generator: a square, which is subdivided into four different colored squares. The four squares within the generator are labeled 0, 1, 2, 3 in clockwise order. I then translate the generator horizontally and vertically. At each translation, I apply an element of the group of permutations of four items. This image contains the permutation (0,1)(3,2) (horizontal reflections) plus the permutations (1,0,2) and (0,2,3). These latter two permutations are not members of the dihedral group – that is they are not reflections or rotations of the generator. Finally, I experiment with different rotations of the entire image to arrive at an image that I find aesthetically pleasing.