# Random Walks in Elementary Cellular Automata

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This Demonstration illustrates the pseudorandomness capabilities of certain class 3 cellular automata in Wolfram's behavioral classification. For example, the center column of rule 30 appears effectively random and the accumulation of its values apparently produces a random walk. The random walk can be used as a test to tell apart complex from simple behavior. However, some complex class 3 cellular automata are capable of intrinsic randomness starting from the simplest initial configuration (one black cell), such as rule 30 and symmetric rules; other class 3 cellular automata such as rule 22 require some random seed to produce randomness.

Contributed by: Hector Zenil (January 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The central column (column 0) of rule 30 was for a long time used as the default pseudorandom number generator in *Mathematica* and it is still available among the various methods to produce pseuorandom numbers in *Mathematica*. This Demonstration also lets you explore certain properties of the rules listed. For example, the left-hand side evolution of rule 30 displays some transitional regularities and therefore produces a deficient "random walk". However, from one point on, rule 30 starts producing a high-quality random walk just as it would if taking the central column or any other on the right-hand side of its evolution.

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