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.