2.8 Summary of construction choices

In this chapter we have discussed the different choices one has to make in the construction of cellular automata and presented some techniques to help in the construction. The particular choices and most common selections are:

• Lattice geometry: 1-d, 2-d square or hexagonal, 3-d.
• Neighborhood: square (Moore) neighborhood of radius $r$ or nearest neighbors only.
• Boundary conditions: periodic or reflective.
• Initial conditions: problem dependent.
• State set: problem dependent.
• Transition rules: probabilistic, symmetric, often outer totalistic.
• Reversible models: block-CA and partitioned CA.

We have demonstrated the choices using the simple example of the Greenberg-Hastings cellular automaton, which we have extended in many different directions.