Chapter 9: Fundamental Physics

Section 6: The Nature of Space

Symmetry [of discrete space]

A system like a cellular automaton that consists of a large number of identical cells must in effect be arranged like a crystal, and therefore must exhibit one of the limited number of possible crystal symmetries in any particular dimension, as discussed on page 929. And even a generalized cellular automaton constructed say on a Penrose tiling still turns out to have a discrete spatial symmetry.

Image Source Notebooks:

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