J. B. Coe et al 2008 EPL 84 50005 doi:10.1209/0295-5075/84/50005
When are cellular automata random?
J. B. Coe1,3, S. E. Ahnert4 and T. M. A. Fink1,2,3,5
Show affiliationsA random cellular automaton is one in which a cell's behaviour is independent of its previous states. We derive analytical conditions which must be satisfied by random cellular automata and find deterministic and probabilistic cellular automata that satisfy these conditions. Many random cellular automata are seen to have a flow as they are updated through time. We define a correlation current that describes this flow and develop an analytical expression for its size. We compare results from this analytical expression with those from simulation. The randomness in a cell comes from randomness in adjacent cells or from the stochastic nature of update rules. We give an expression for how much randomness comes from each of these two sources.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.50.-r Probability theory, stochastic processes, and statistics
- Subjects
- Dates
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Issue 5 (December 2008)
Received 29 July 2008, accepted for publication 20 October 2008
Published 16 December 2008
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When are cellular automata random?
J. B. Coe et al 2008 EPL 84 50005
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