Wolfram code

Article summary

Wolfram code is a widely used numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and popularized in his book A New Kind of Science. The code is based on the observation that a table specifying the new state of each cell in the automaton, as a function of the states in its neighborhood, may be interpreted as a k-digit number in the S-ary positional number system, where S is the number of states that each cell in the automaton may have, k = S 2n + 1 is the number of neighborhood configurations, and n is the radius of the neighborhood. Thus, the Wolfram code for a particular rule is a number in the range from 0 to S S − 1, converted from S-ary to decimal notation. It may be calculated as follows: # List all the S 2n + 1 possible state configurations of the neighbourhood of a given cell. # Interpreting each configuration as a number as described above, sort them in descending numerical order. # For each configuration, list the state which the given cell will have, according to this rule, on the next iteration. # Interpret the resulting list of states again as an S-ary number, and convert this number to decimal. The resulting decimal number is the Wolfram code. The Wolfram code does not specify the size (nor shape) of the neighbourhood, nor the number of states — these are assumed to be known from context.…

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