Chapter 5: Two Dimensions and Beyond

Section 3: Turing Machines

Visualization [of 2D Turing machines]

The pictures below show the 2D position of the head at 500 successive steps for the rules on page 185.

Some 2D Turing machines exhibit elements of randomness at some steps, but then fill in every so often to form simple repetitive patterns. An example is the 3-state rule

Image Source Notebooks:

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