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List of Figures

  1. Two most common 2-D CA neighborhood templates.
  2. Three classes of attractor.
  3. Wolfram class examples. Each image a time-evolution of a 2-state CA on a circle using neighborhood size of 3 (central cell and its two neighbors).
  4. For selected $ \lambda $-values, a 256 step time-evolution of a corresponding CA.
  5. Schematic drawing of CA rule space indicating relative location of periodic, chaotic, and ``complex'' transition regimes.
  6. Schematic drawing of CA rule space showing the relationship between the Wolfram classes and the underlying phase-transition structure.
  7. Schematic drawing of computation space, indicating relative location of halting, non-halting, and undecidable regimes.
  8. Comparison between schematic of CA rule space and bifurcation diagram of the phase portrait of olfactory bulb states.

Jeremy Avnet (brainsik); Senior Thesis, Mathematics; University California, Santa Cruz; 6th June 2000; email: jeremy (at)