Chapter 5: Two Dimensions and Beyond

Section 2: Cellular Automata

Limiting shapes [in 2D cellular automata]

When growth occurs at the maximum rate the outer boundaries of a cellular automaton pattern reflect the neighborhood involved in its underlying rule (in rough analogy to the Wulff construction for shapes of crystals). When growth occurs at a slower rate, a wide range of polygonal and other shapes can be obtained, as illustrated in the main text.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]