Generating textures

As discussed on page 217, it is in general difficult to find 2D patterns which at all points match some definite set of templates. With 2×2 templates, there turn out to be just 7 minimal such patterns, shown below. Constructing patterns in which templates occur with definite densities is also difficult, although randomized iterative schemes allow some approximation to be obtained.

One-dimensional cellular automata are especially convenient generators of distinctive textures. Indeed, as was noticed around 1980, generalizations of additive rules involving cells in different relative locations can produce textures with similar statistics, but different visual appearance, as shown below. (All the examples shown turn out to correspond to ordinary, sequential and reversible cellular automata seen elsewhere in this book.) (See also page 1018.)