Chapter 8: Implications for Everyday Systems

Section 7: Biological Pigmentation Patterns

Scales of patterns [on animals]

The visual appearance of a pattern on an actual animal depends greatly on the scale of the pattern relative to the whole animal. Pandas and anteaters, for example, typically have just a few regions of different color, while other animals can have hundreds of regions. Studies based on linear reaction-diffusion equations sometimes assume that patterns correspond to stationary modes of the equations, which inevitably depend greatly on boundary conditions. But in more realistic models patterns emerge from long time behavior with generic initial conditions, making boundary conditions—and effects such as changes in them associated with growth of an embryo—much less important.

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