The Game of LifeThe Game of Life, which is not actually a game, is addictive nonetheless. The Game of Life, or simply Life, has been invented by the famous mathematician John H. Conway, now of Princeton University, in the late 1960s. It was popularized by Martin Gardner in three Scientific American columns starting 1970. All three have been republished in one of his books. Life is also the subject of the last chapter of a mathematical gamer bible, The Winning Ways for Your Mathematical Plays. Life is a cellular automaton with transition rules for birth, survival and death of individual cells. On a square grid, a cell has 8 neighbors, corresponding to the notion of 8-connectedness. With a reference to a grid square, the terms "empty" and "dead" cell are interchangeable. The rules define a community of organisms that interact in order to reproduce and compete for the living space in the following manner:
It follows that a live cell with fewer than 2 or with more than 3 neighbors dies, apparently of loneliness in the former case and of overcrowding in the latter. The applet below implements Conway's transition rules. It offers the following controls:
Finally, at the bottom of the applet a drop-down control allows for a selection of some known shapes, some static, some dynamic.
(Another implementation allows one to define the birth and survival rules.) Where is mathematics in all that? you may ask. Well, it may not be apparent, but there is a plenty, although, as the authors of Winning Ways write assertively, "Life's problems are hard!" Many among the finest mathematicians devoted their time to the study of cellular automata: John von Neumann and Stanislaw Ulam were among the pioneers in the field. Are all Life configurations have an ancestor? According to Winning Ways, the answer is No. There is also a proof that such a configuration, which are appropriately called Garden(s) of Eden, exists that fits into a 2325816000×2325816000 grid square. A smaller paradise has been found with the help of computers, the size of 9×33. The authors of Winning Ways also show how Life patterns can imitate computers. The gliders, that is, the patterns that move across the board staying in a fixed size moving frame, play an important role in their theory. This alone may justify a widespread involvement of Life enthusiasts in the search for glider patterns. David Epstein's site is a good starting point for the curious. References
 Cellular Automaton
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