Rule 30

For instance, a pattern resembling Rule 30 appears on the shell of the widespread cone snail species Conus textile.

Rule 30 has also been used as a random number generator in Mathematica,[3] and has also been proposed as a possible stream cipher for use in cryptography.

The following diagram shows the pattern created, with cells colored based on the previous state of their neighborhood.

[citation needed] Rule 30 meets rigorous definitions of chaos proposed by Devaney and Knudson.

Both of these characterizations of the rule's chaotic behavior follow from a simpler and easy to verify property of Rule 30: it is left permutative, meaning that if two configurations C and D differ in the state of a single cell at position i, then after a single step the new configurations will differ at cell i + 1.

Stephen Wolfram proposed using its center column as a pseudorandom number generator (PRNG); it passes many standard tests for randomness, and Wolfram previously used this rule in the Mathematica product for creating random integers.

[11][12] The state update can be done quickly by bitwise operations, if the cell values are represented by the bits within one (or more) computer words.