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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+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