Chapter 7: Mechanisms in Programs and Nature

Section 9: Origins of Simple Behavior

Origins of localized structures

Much as with other features of behavior, one can identify several mechanisms that can lead to localized structures. In 1D, localized structures sometimes arise as defects in largely repetitive behavior, or more generally as boundaries between states with different properties—such as the different phases of the repetitive background in rule 110. In higher dimensions a common source—especially in systems that show some level of continuity—are point, line or other topological defects (see page 1045), of which vortices are a typical example.

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