Cellular Automata

In this chapter, the biological roots of cellular automata are described and formal definitions of cellular automata (CA) are provided. CA are characterized by a regular lattice, a set of elementary states, a local interaction interaction local , a neighborhood template cellular automaton neighborhood , and a space- and time-independent transition rule cellular automaton transition rule which is applied to each cell in the lattice. In particular, we introduce deterministic, probabilistic, and lattice-gas cellular automata cellular automaton probabilistic cellular automaton deterministic lattice-gas cellular automaton (LGCA) . Furthermore, we present strategies to analyze spatio-temporal pattern formation in cellular automaton models. In subsec. 4.4.2, the so-called mean-field theory mean-field theory approximations is presented as an approximative method to study dynamic properties of cellular automata.