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John Conway’s { Game of Life John von Neumann Wanted to find/create a machine that could replicate itself Found an answer, but it was very complex Conway assumed that there would be an easier solution. Who first posed it? A zero player, turn based games, based off of simple rules. This game exists in a 2 dimensional virtual world, on a grid with cell blocks Used to demonstrate how complexity can develop from extreme simplicity Named “Life” due to its complexity and unpredictability Conway’s Game of Life 2 primary rules (Note: every cell has 8 neighbors) An alive cell (a filled cell) with less than 2 or greater than 4 neighbors dies A dead cell (an empty cell) with 3 neighbors turns alive <2 – under population 2-3 – sustainable >3 – overcrowding =3 – reproduction (dead cell comes alive) Rules for the Game Some Interesting Shapes When Conway first created this notion, computers were relatively weak Offered a prize to anyone who could show that the game could continue indefinitely Prize collected shortly thereafter Conway originally played life with a “Go” board Each step very slow, when you consider that the game can continue indefinitely Games have continued past 6 octillion steps with a computer Why is this problem or idea so difficult for the time period? Rules slightly modeled real life. Also note correlation with Big Bang (small to big) Game itself creates unique problems: A glider gun that shoots gliders in intervals of prime numbers A gun that lets gliders travel faster than the speed of light (Stargate) 1 step is 1 unit of time. Stargate moves gliders ahead in steps. i.e. time travel It’s so difficult because… Family Life Parents were Agnes Boyce and Cyril Horton Conway Two sisters, Sylvia and Joan Grew up in Britain during wartime shortages At age 11, said he wanted to be a mathematician at Cambridge when he grew up John Conway’s Biographical Information Schooling Very successful at math during secondary school Went to Gonville and Caius College Cambridge to study math Earned his doctorate in 1964 Game of Life Created approximately 1970 “Often claimed that since 1970 more computer time worldwide has been devoted to the Game of Life than any other single activity” Opened the field of cellular automata Discovered surreal numbers Has done research in knot theory, number theory, game theory, quadratic forms, coding theory, and tilings Other Discoveries/Math Advancements http://www.cs4fn.org/alife/thegameoflife.php https://www.google.com/search?q=conway's+g ame+of+life&aq=0&oq=conway's+gam&aqs=chr ome.0.0j57j5j0j62l2.2058&sugexp=chrome,mod= 19&sourceid=chrome&http://itee.uq.edu.au/~co mp4006/life-patterns.gifie=UTF-8 http://www.ericweisstein.com/encyclopedias/lif e/R-Pentomino.html http://itee.uq.edu.au/~comp4006/Tutorial3.html http://www.math.cornell.edu/~lipa/mec/lesson6 .html Sources