Two color repeating patterns are constructed using either a determinstic symmetric dynamical
system or a random symmetric dynamical system. In either case, the images shown
can be thought of as colored realizations of chaotic symmetric attractors.
There are a total of 6 different types of two color repeating pattern that can be supported on the hexagonal lattice. A description of all the two color repeating patterns can be found in Symmetries of Culture, by Washburn and Crowe.
For determinsitic dynamics, each image is constructed using iteration of an appropriately symmetric torus map. Typically, each such map can be represented as a trigonometric polynomial. We refer to `Harmony, Chromatics, and Chaos', In: Proc. Bridges Conference, 1999, Southwestern College, Kansas, 1-21, and `Designer chaos', J. Computer Aided Design, vol 33, to appear 2001, for more details on constructing two-color patterns using chaotic dynamics.