There should be initial patterns that apparently do grow without limit.There should be no initial pattern for which there is a simple proof that the population can grow without limit.The Game of Life rules were carefully chosen by Conway to satisfy three simple criteria (Gardner, 1970): Time steps are sometimes called ‘generations’. The initial state of the game is the ‘seed’ and all cells are updated simultaneously. Rule 1 represents ‘death by under-population’ rule 2 represents ‘sustainable life’ rule 3 represents ‘death by over-population’, and rule 4 represents ‘birth’. These rules can be thought to represent basic processes of life and death, motivating the name ‘Game of Life’. And ‘off’ cell (t -1) with exactly three ‘on’ neighbours (t -1) transitions to an ‘on’ state at time t.Any ‘on’ cell (t -1) with more than three ‘on’ neighbours (t -1) transitions to an ‘off’ state at time t.
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