Chapter 9: Fundamental Physics

Section 4: Conserved Quantities and Continuum Phenomena

PDE approximations [to cellular automata]

Cellular automaton (d) in the main text can be viewed as minimal discrete approximations to the diffusion equation. The evolution of densities in the ensemble average is analogous to a traditional finite difference method with a real number at each site. The cellular automaton itself uses in effect a distributed representation of the density.

Image Source Notebooks:

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