Chapter 5: Two Dimensions and Beyond

Section 7: Systems Based on Constraints

Non-computable [2D] patterns

It is known to be possible to set up constraints that will force patterns in which finding the color of a particular cell can require doing something like solving a halting problem—which cannot in general be done by any finite computation. (See also page 1139.)

Image Source Notebooks:

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