### Conway`s Game of Life

```John Conway’s
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Game of Life
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John von Neumann
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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?
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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
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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
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When Conway first created this notion,
computers were relatively weak
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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
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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
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It’s so difficult because…
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Family Life
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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
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Schooling
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Very successful at math during secondary school
Went to Gonville and Caius College Cambridge
to study math
Earned his doctorate in 1964
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Game of Life
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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
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Discovered surreal numbers
Has done research in knot theory, number
theory, game theory, quadratic forms, coding
theory, and tilings
Other Discoveries/Math
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http://www.cs4fn.org/alife/thegameoflife.php