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Conway’s Game of Life
Charles Burnell
Jordan Engstrom
Department of Mathematics
Boise State University
March, 31, 2015
Lindsey Gentry
Outline
Origins
Basic Rules
Lifeforms
Still Life
Movers
Generators
Variations on Conway’s
References
Origins
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Created in 1970 by John Conway
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Extension of John Von Neumann’s work
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Simplified Neumann’s machine
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More of a machine than a game
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Cellular Automaton - a machine that can replicate itself
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Biological, chemical, and computer science applications
Basic Rules
Ca = number of adjacent cells that are alive
Each iteration is called a generation
The heat of a life form is average number of cells that change each
generation.
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If cell is alive and Ca < 2 cell dies
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If cell is alive and 1 < Ca < 4 cell lives to
next generation
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If cell is alive and Ca > 3 cell dies
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If cell is dead and Ca = 3 then the cell
becomes alive.
Basic types of Life Forms
We are going to define a life form as a group of cells that stay
together and have a predictable pattern.
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Still
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Spaceships
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Puffers
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Guns
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Oscillators
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Wicks
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Methuselahs
Still Life
Still life is exactly what it sounds like. They are lifeforms that do
not evolve over generations.
Special Still Life
There is a very special configuration that can only occur at
generation 0 and can never be generated by later generations.
These formations are called Gardens of Eden.
It doesn’t meant hat they don’t require support to stay alive
though.
First Garden of Eden discovered.
Most recent smallest Garden of Eden.
Space Ships
Space ships are life forms that have a predictable period of
movement.
This period normally is how long it takes to progress 1 cell so
different spaceships have different speeds.
Life cycle of the glider
Puffers are just spaceships that leave behind live cells. This can
sometimes be a benefit to larger systems that use the oscillators or
still life that is left behind.
Other Movers
An Oscilator is a life form that has a set number of generations
that take it from a state back to that state.
Wicks are life forms that oscillates and can be made to ”burn” an
end.
Movers Cont’d
Methuselah is a relatively small starting life form that uses many
generations to expand to a larger size.
=⇒
This is what is called an particular Methuselah is called an acord.
Guns
Guns are ”stationary” creations that through their life cycle creates
spaceships. Smallest glider generator is called the Gosper Glider
Gun.
This is a state of the Gosper Glider Gun.
Variations of the Game of Life
Regular rules are symbolized as B3/S23, meaning: Born if 3
contacts and stays alive if 2 or 3 contacts. Dies otherwise
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B6/S16 is another popular rule set
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Highlife is described as: B36/S23 causes frequent replicators
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Immagration: two ON states (expressed in 2 colors) if a new
cell is born, it takes the ON state of the majority of its parents
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Quadlife: four ON states, if a cell is born from 3 different ON
states it takes on a new ON state, otherwise behaves like
immagration
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http://pmav.eu/stuff/javascript-game-of-life-v3.1.1/
Variations of the Game of Life
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3D Game of Life
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Same basic rules, squares converted to boxes
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https://scratch.mit.edu/projects/615879/
References
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n.p. Conways Game of Life. LifeWiki. 06/25/2012.
Electronic. 03/30/2015.
http://www.conwaylife.com/wiki/Conway
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Winsh. Conways Game of Life. 2014. Electronic. 03/30/2015.
http://conwaysgameoflife.appspot.com/#links
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Weisstein, Eric W. ”Cellular Automaton.” From Math
World–A Wolfram Web Resource. http:
//mathworld.wolfram.com/CellularAutomaton.html