Square Quilts 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 12 different types of repeating pattern that can be supported on
the square lattice. 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 Symmetry in Chaos
for more details.