Random sequence generation by cellular automata

Authors:
Stephen Wolfram
Affiliations:
Thinking Machines Corporation, 245 First Street, Cambridge, Massachusetts 02142 USA and The Institute for Advanced Study, Princeton, New Jersey 08540 USA
Venue:
Advances in Applied Mathematics
Year:
1986

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Abstract

A 1-dimensional cellular automaton which generates random sequences is discussed. Each site in the cellular automaton has value 0 or 1, and is updated in parallel according to the rule a'"i = a"i" "-" "1 XOR (a"i OR a"i" "+" "1) (a'"i = (a"i" "-" "1 + a"i + a"i" "+" "1 + a"ia"i" "+" "1) mod 2). Despite the simplicity of this rule, the time sequences of site values that it yields seem to be completely random. These sequences are analysed by a variety of empirical, combinatorial, statistical, dynamical systems theory and computation theory methods. An efficient random sequence generator based on them is suggested.