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
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+game+of+life&aq=0&oq=conway's+gam&aqs=chrome.0.0j57j5j0j62l2.2058&sugexp=chrome,mod=19&sourceid=chrome&http://itee.uq.edu.au/~comp4006/life-patterns.gifie=UTF-8
http://www.ericweisstein.com/encyclopedias/life/R-Pentomino.html
http://itee.uq.edu.au/~comp4006/Tutorial3.html http://www.math.cornell.edu/~lipa/mec/
lesson6.html
Sources