What is the smallest number of live cells needed

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Reference no: EM131318954

Erik's puzzle. In a stripped-down version of Conway's game of life, cells are arranged on a square grid. Each cell is either alive or dead. Live cells do not die. Dead cells become alive if two or more of their immediate neighbours are alive. (Neighbours to north, south, east and west.) What is the smallest number of live cells needed in order that these rules lead to an entire N × N square being alive?

In a d-dimensional version of the same game, the rule is that if d neighbours are alive then you come to life. What is the smallest number of live cells needed in order that an entire N × N × · · · × N hypercube becomes alive? (And how should those live cells be arranged?)

Reference no: EM131318954

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