Chapter 5: Two Dimensions and Beyond

Section 3: Turing Machines

Rules [for 2D Turing machines] based on turning

The rules used in the main text specify the displacement of the head at each step in terms of fixed directions in the underlying grid. An alternative is to specify the turns to make at each step in the motion of the head. This is how turtles in the Logo computer language are set up. (Compare the discussion of paths in substitution systems on page 892.)

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