Rule 30: one black cell
Rule 30 is a one-dimensional cellular automaton that produces complex, seemingly random patterns from a very simple set of rules. Despite its simplicity, the behavior of its center column remains a subject of mathematical mystery and open challenges.
Why it matters
It highlights the intersection of simple computational rules and complex emergent behavior, which has implications for cryptography and scientific modeling.
Start with a single black square. Apply one tiny rule, row after row. What grows is part orderly, part wild, and nobody can yet prove whether the column running straight down its middle ever repeats.
Picture a row of squares, each black or white. To make the next row, every square looks at three squares above it: the one directly above, and that one's left and right neighbours. Those three colours can come in eight combinations, and the rule simply says, for each combination, what colour the new square is.
Write the eight answers as a binary number and you get 00011110, which is 30. That is the whole of Rule 30. Below, the rule is applied one square at a time: the three boxed squares decide the new one, and the matching entry of the rule lights up.
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