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The Ulam spiral as a Game of Life automaton


The Ulam Spiral is a rectangular grid created by Stanislaw Ulam in 1963 to help visualize prime numbers. It demonstrates the tendency of some polynomials to generate unusually large number of primes and the tendency for prime numbers to line up along diagonal lines.

The Game of Life is a zero-player game created by John Conway in 1970. It is a simplified cellular automaton whose outcome is entirely dependent on the initial state.

In this paper, I used a distribution of prime numbers within the Ulam Spiral as the starting point for an instance of Conway’s Game of Life cellular automaton. The results are fascinating.

Attached are the results: The Ulam spiral as a Game of Life automaton

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