Chapter 9: Fundamental Physics

Section 4: Conserved Quantities and Continuum Phenomena

Diffusion equation

In an appropriate limit the density distribution for cellular automaton (d) appears to satisfy the usual diffusion equation tf[x, t] c xxf[x, t] discussed on page 163. The solution to this equation with an impulse initial condition is Exp[-x2/t], and with a block from -a to a it is (Erf[(a - x)/t] + Erf[(a + x)/t])/a.

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