Rule 30
Eine Zelle kaskadiert unter Wolframs Regel 30 ins strukturierte Chaos · das Muschelmuster. Säe eine Zeile und spiel abwärts
Rule 30 derives each new row from the one above it: every cell looks at its left, centre, and right neighbours, and the result follows the binary form of the number 30 · new cell = left XOR (centre OR right). One simple line produces endless structured chaos.
About Rule 30
Rule 30 is a calm, watchable cellular automaton · the elementary rule Stephen Wolfram catalogued in 1983 and made the emblem of how simple programs create complexity. It belongs to the PlayMemorize Idle Games collection alongside Game of Life and Langton's Ant: systems that are satisfying to watch, simple to nudge, and faithful to their underlying rules. There is no score and nothing to lose · you seed the top row and watch the cascade grow.
The rule. Each cell of a row looks at itself and its two neighbours, and the next row follows from the binary expansion of the number 30 (00011110): the new cell is left XOR (centre OR right). From a single dark cell this produces a triangle whose left flank is orderly and whose interior never settles · so unpredictable that its centre column once served as a random-number generator, and so natural that the same pattern grows on the Conus textile seashell.
Starting rows. Begin from the canonical single centre cell, or seed a random first row and watch a completely different cascade unfold. Tap or click any column to flip a cell of the newest row · the accent line marks it · and the change ripples into every row that follows. The cascade keeps a fixed number of rows on screen and scrolls as it grows, so it can run forever.
Controls. Play or pause, step a single row, reset to the current starting row, and set the speed up to a bounded maximum. A running generation count is always on screen. The full keyboard works too: Space plays or pauses and the Right arrow steps.
Calm by design. The simulation pauses itself when you switch tabs, and it never auto-animates when your device asks for reduced motion · you simply step rows by hand instead. It runs entirely in your browser and works offline as part of the PlayMemorize app. Part of the PlayMemorize family.
FAQ
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What rule does Rule 30 run?
The elementary cellular automaton numbered 30 in Wolfram's catalogue. Every cell looks at (left, centre, right) and the eight outcomes follow 30's binary form 00011110 · equivalently, the new cell is left XOR (centre OR right). Each press of Step derives exactly one new row from the newest one. -
Why is Rule 30 famous?
Because two lines of arithmetic produce genuine chaos. Its centre column passes randomness tests and was used as the random-number source in early Mathematica, and essentially the same triangle pattern grows naturally on the shell of the Conus textile sea snail. It is the standard example that simple rules can generate endless complexity. -
How do I change the cascade?
Pick a starting row · the canonical single centre cell or a random row · then tap or click any column to flip a cell of the newest row (marked by the accent line). Press Play to run, Step to add one row, Reset to restore the current starting row, and drag the speed control up to a bounded maximum. -
Does the cascade grow forever?
The pattern does, but the memory does not. Only a fixed number of recent rows is kept on screen; once the window is full, the oldest row scrolls away as each new one arrives, while the generation counter keeps counting. You can leave it running as long as you like. -
Does it respect reduced motion and hidden tabs?
Yes. The simulation pauses itself whenever the tab is hidden, and if your device requests reduced motion it never auto-animates · you step rows by hand with the Step button or the Right arrow key instead, with the current state always visible.