{ 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

  ame+of+life&aq=0&oq=conway's+gam&aqs=chr ome.0.0j57j5j0j62l2.2058&sugexp=chrome,mod= 19&sourceid=chrome& mp4006/life-patterns.gifie=UTF-8  e/R-Pentomino.html   Sources