Clifford A. Reiter, Cyclic Cellular Automata in 3D, Chaos, Solitons and Fractals, 44 (2011) 764-768

Cyclic cellular automata in two dimensions have long been intriguing because they self organize into spirals and that behavior can be analyzed. The form for the patterns that develop is highly dependent upon the form of the neigh- borhood. We extend this work to three dimensional cyclic cellular automata and observe self organization dependent upon the neighborhood type. This includes neighborhood types intermediate between Von Neumann and Moore neighborhoods. We also observe the patterns include nested shells with the appropriate forms but that the nesting is far more complex than the spirals that occur in two dimensions.

See also: · Clifford A. Reiter, Medley of Spirals from Cyclic Cellular Automata, Computers & Graphics 34 (2010) 72-76. Preprint, and some images, and animations related to the paper [Medley of Spirals from Cyclic Cellular Automata]