Cellular automata
Grid, states, neighbourhood and a local rule applied everywhere at once; elementary automata and the Wolfram number; Conway's Game of Life and its patterns.
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Cellular automaton: what is it?
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A grid of cells, each in one of a few states, that change at every generation according to the same local rule, read from the state of the neighbouring cells.
The update is synchronous: all new values are computed from the previous generation, then written together.
A live cell has four live neighbours. What does it become in the next generation?
- It dies, from overcrowding
- It survives, since it does not have fewer than 2 neighbours
- It survives and a neighbour is born next to it
- It survives, as with 2 or 3 neighbours
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It dies, from overcrowding
Survival takes exactly 2 or 3 live neighbours. With 4 or more the cell dies, and so it does with 0 or 1 (loneliness).
In a cellular automaton, all cells are updated …, from the state of the … generation.
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In a cellular automaton, all cells are updated at the same time, from the state of the previous generation.
Updating one cell after another and reusing the new values would make the result depend on the scan order, and it would no longer be the same automaton.
Moore neighbourhood: what is it?
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The eight cells surrounding a cell on a grid: the four sides and the four diagonals.
It is the neighbourhood of the Game of Life. The von Neumann neighbourhood is limited to the four sides.