Chapter 4: Systems Based on Numbers

Section 7: Iterated Maps and the Chaos Phenomenon

Distribution of chaotic behavior

For iterated maps, unlike for discrete systems such as cellular automata, one can get continuous ranges of rules by varying parameters. With maps based on piecewise linear functions the regions of parameters in which chaotic behavior occurs typically have simple shapes; with maps based, say, on quadratic functions, however, elaborate nested shapes can occur. (See page 934.)

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