We consider a generative art scheme that uses zero-one labelings of the edges of all the cells of a grid and chaotic one-dimensional cellular automata to assign hexadecimal digits to the cells of the grid. This allows us to color all the cells by mapping hex digits to colors. We invoke a genetic algorithm to maximize the number of occurrences of two hex digits thereby evolving what we call hex-chaos compositions. Using elementary group theory we prove, up to equivalence, there are thirteen different types of hex-chaos compositions.