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Rule 110

This page generates patterns based on Rule 110. Enter a starting string of ones and zeros, and 100 more lines of the pattern will be printed.

Rule 110 is the simplest proven Turing complete cellular automaton. Cells are located on an infinite line. Each cell is live or not live. The life value of each cell at any instant in time is determined by the life value of the cell and it's two neighbors at the previous instant of time. Here are our rules:

Rule 110 rules

In short, any sort of logic may be programmed into this system. Anything that any computer may do, may be achieved, albiet slowly, by an infinitely long line of cells following these rules.


Berlekamp, E. R., Conway, J. H., & Guy, R. K. (1982). Winning ways for your mathematical plays. London: Academic Press.

Cook, M. (2004). Universality in cellular automata. Complex Systems, 15, 1-40.

Cook, M. (2008). A Concrete View of Rule 110 Computation. In T. Neary, D.Woods, A. K. Seda, and N. Murphy (Eds.), The Complexity of Simple Programs 31-55.

Gardner, M. (1970). Mathematical games: The fantastic combinations of John Conways new solitaire game Life. Scientific American 223(10), 120-123.

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