Notes

Chapter 3: The World of Simple Programs

Section 2: More Cellular Automata


Rule 225

The width of the pattern after t steps varies between Sqrt[3/2] Sqrt[t] (achieved when t = 3 × 2^2n+1]) and Sqrt[9/2] Sqrt[t] (achieved when t = 2^2n+1). The pattern scales differently in the horizontal and vertical direction, corresponding to fractal dimensions Log[2, 5] and Log[4, 5] respectively. Note that with more complicated initial conditions rule 225 often no longer yields a regular nested pattern, as shown on page 951. The resulting patterns typically grow at a roughly constant average rate.

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