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The people who believe (2) are being rather unimaginative, but in addition to imagination I can offer evidence.

Probably the best known example of a cellular automaton is the "Game of Life," devised by mathematician John Horton Conway in 1970 and popularized by mathematics journalist Martin Gardner in the same year.

This web page is concerned only with showing that (2) is not valid reasoning, and does not constitute a proof of (3).

I assert that statement (2) is mathematically just plain wrong -- and I assert that the wrongness of (2) is not merely opinion, but fact.

Featured prominently in the book is one class of 256 experiments which might be termed the simplest possible cellular automata; they are simpler than the "game of life." Each of these automata acts on a row (i.e., a one-dimensional array) of black and white squares, but we get an interesting two-dimensional picture by stacking the rows -- i.e., the row at time 1, and below it the row at time 2, and below it the row at time 3, etc.

Each picture is generated by an extremely simple rule -- one that could easily occur "by accident" in nature, as it were -- but many of the pictures show incredible ordered complexity.