Hexagonal 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 5 different types of repeating pattern that can be supported on the hexagonal 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 - which are quite complicated.