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I've seen Conway's game of life mentioned in different circles and it seems many people (myself included) have made an implementation of it at one point or another. Other than the fact that it is inherently interesting that complex patterns can arise from such simple rules and the fact that its simple enough to make a good introductory programming exercise, is there anything important about Conways game of life in particular? Or does it just happen to be the most famous cellular automata by chance.

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I'd say it's "the most famous" cellular automaton, in the sense that the structures its rules generate have been studied and given names to.

One property that it does have, that makes it more interesting than other automata, is that stable structures are fairly common in Conway's game of life.

If you try and tweak the rules (by changing the population size for creation and death) you will realize that most of the versions of GOL tend to either die instantly or immediately start to grow, so they're not very interesting.

However, there are many other interesting cellular automata, for example you can create a cellular automaton with every geometric figure that tiles the plane, for example with hexagons, and the different number of neighbors changes what sets of rules are "stable". Also, you can change the type of neighborhood you're considering, or make a continuous automata, in which the cells are infinitesimal, and define the rules in the language of vector fields.

Conway's game of life's is probably the most famous one because it was made by Conway, a very influential mathematician, and it's defined "on a checkerboard", which makes it very easy to explain and understand.

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Two interesting properties: 1. There are states that have no predecessor. 2. Game of life is actually Turing complete!

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