celaut

Prev: Rock of Gibraltar =Cellular Automata=

Pioneered by Ulam and von Neumann, a cellular automaton (CA) is a formalism with the following characteristics. CAs have been used mainly as experimental mathematics (Ulam), artificial physics (Ulam), "new" physics (Wolfram), artificial life (von Neumann, Langton) or as a modelling tool (Toffoli). In biology the last case is the most interesting one. The features that make a CA a (good) model are: People started studying 1D elementary CAs and attempted to classify them by the temporal-spatial pattern they generated. The well-known classification by Wolfram is listed in the table below.
 * there is a grid or lattice
 * each gridcell is a finite state machine (FSM), but as simple as possible. The entire grid is an autonomous FSM again.
 * there is speed of "light", the velocity at which information can travel across the grid
 * "the whole is //less// than the sum of its parts", since the input of the small FSMs is not arbitrary, but constrained to its neighbours
 * structural stability: stable, but not too stable. When changing any parameter doesn't result in a structural effect, the model has no meaning (is not "saying" anything)
 * multiple stable points: starting in a certain initial state, a lot of stable states are possible
 * local optima: f.i. additive voting rules can be seen as minimizing the zero-one borderline
 * variable/FSM identification: the correspondence between the real world and the features in the model. The active components in CAs are not the FSMs but the spaces
 * dynamical systems constraints: fixed set of FSMs. When one relaxes these constraints, one gets individual oriented models


 * **Class** || **Spatial pattern** || **Non-spatial equivalent** ||
 * I || to uniform pattern || fixed point ||
 * IIa || domains, localized: patches || limit cycles ||
 * IIb || domains, non-stationary: waves || limit cycles ||
 * III || non-periodic, non-localized || chaos ||
 * IV || localized, long transient || universal computation ||

Particle conservation, biological models vs physical models Space time scaling behavior scaling Synchronous vs asynchronous critically slowing down phenomena travelling patterns

Crutchfield's rule 54 (mesoscale pattern algebra)

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