While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. If you want to go deeper, you'll likely want to download one of the many Game of Life software packages that are freely available online. There's a solid Web-based game of life implementation here that will let you experiment with basic patterns. If you'd like to try out Conway's Game of Life, it's easy to do. Game of Life enthusiasts have made thousands of posts at the site's forums. The website has an extensive Wiki documenting hundreds of interesting Game of Life patterns. More than 50 years after Conway invented the Game of Life, it continues to have an active community of both professional mathematicians and amateurs. So it's theoretically possible, if not particularly efficient, to compute any function using the right arrangement of Game of Life cells. The Church-Turing thesis tells us that a Turing machine is theoretically capable of computing any function we can compute on modern computers-at least given enough time and storage space. Mathematicians have demonstrated that it is possible to construct a Turing machine on a Game of Life board. These elements, in turn, can become building blocks for still more complex structures. Otherwise, the cell becomes-or stays-dead. If a dead cell has three live neighbors, it switches to black and becomes alive. If a live square has two or three live neighbors (counting diagonals), it stays alive. ![]() Simple deterministic rules dictate how the state of the board in one step leads to the next step. Each square can be either black ("alive") or white ("dead"). ![]() (Don't confuse it with Milton Bradley's board game of the same name.)Ĭonway's Game of Life is played on a two-dimensional plane with square cells. It was made famous by a 1970 Scientific American article and has had a lively community around it ever since then. He made contributions in various areas of mathematics but is best known for his invention of Conway's Game of Life, a cellular automaton in which simple rules give rise to surprisingly complex behaviors. The British-born Conway spent the early part of his career at Cambridge before moving to Princeton University in the 1980s. Princeton mathematician John Conway has died of the coronavirus.
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