Wolfram code is a naming system often used for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and used 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 = S2n + 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 SS2n + 1 − 1, converted from S-ary to decimal notation. It may be calculated as follows: