Cellular Automaton

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Cellular Automaton

• Written and Presented by
• Craig Schweitzer

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Cellular Automaton-Summary

• What is cellular automaton?
• History of cellular automaton
• Simple cellular automata
• The practical uses of cellular automaton
• The Game of Life

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What is Cellular Automaton?
Cellular Automaton(CA) A regular spatial lattice
of cells, each of which can have a finite number
of states. The cell states are updated in
discrete time steps and defined by its original
state and the state of the cells surrounding it.
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How Cellular Automaton Began
In 1947, John von Neumann was working in the
field of science, focusing on biology. He was
studying a self-replicating machine when he
designed a two-dimensional CA model of the
physics of our universe. He mathematically
proved that the universe he made acted like a
self-replicating machine and that it would make
endless copies of itself.
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What is Cellular Automaton?(contd)
Every separate cell can be described as its own
finite state machine. The finite state machines
are determined by different sets of information.
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Simple Cellular Automaton

• The simplest CA is one dimensional with only
  two states for each cell. A cell and the cell on
  each side make up a neighborhood. These cells
  are the deciding factors as to what state is
  chosen for the element.

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Practical Uses of CA

• For Rule 30, there has been thought that it
  could be used as a stream cipher for use in
  cryptography. CA has been used for public key
  cryptography. You can find the next state
  easily, but it is almost impossible to determine
  the last states.
• Much more complex two dimensional cellular
  automaton has many uses, one of which is the
  evolution of population in an area.
• Can also be a very interesting game

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Creating Life

• In the late 60s and early 70s, a man named
  James Conway created a two-dimensional CA called
  The Game of Life that popularized CA. The rules
  to Life are simple
• If a live cell has two or three live neighbors,
  it stays live
• If a dead cell has three live neighbors it
  changes to live
• For any other case, it becomes dead

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The Evolution of Life
for i 1 to 100 for j 1 to 100
s0 for p i-1 to i1
for q j-1 to j1 s sL(p,q)
ss-L(i,j) if s 3 or sL(i,j) 3
X(i,j) 1 else X(i,j)
0 for i 1 to 100 for j 1 to 100
L(i,j) X(i,j) display L(i,j)
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The Evolution of Life(contd)

• Conway originally believed that no population
  could grow without limit.
• Every population would either die out or repeat a
  pattern.
• Students at MIT proved this incorrect.
• They created a glider gun which would emit a
  glider every 30 generations and in turn create an
  endlessly growing life.

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Popularity of Life
Life was a simple little game until Martin
Gardner brought it to the attention of millions.
He wrote a column in Popular Science about it and
sparked the evolution of CA from a researching
standpoint to the gaming aspect. Millions of
technical minded people began playing The Game of
Life.
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Nowhere to Go
Still Life Objects-Very common in Life are groups
of cells that remain constant through the many
steps of life.Some types of still life objects
are blocks, beehives, boats, ships, and loafs.
Block
Ship
Beehive
Loaf
Boat
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Keep on Moving
Oscillators-objects that change from step to
step, but eventually repeat themselves. These
include, but are not limited to, period 2
oscillators, including the blinker and the toad.
Blinker
Toad
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Gliding Through Life
Glider-A commonly found arrangement of cells (5
in total) that move themselves across a grid in
the Game of Life
Glider
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A Little Lesson on Life
Initial Setup
After Pass 1
Number of Neighbors
After Pass 2
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Puffertrain
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Double-Barreled Gun
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Edge Shooter
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Gosper Gun
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Where Has Life Taken Us?
Unfortunately for the computing society, after
Conway released The Game of Life, most people did
not look at CA the same way. CA became a source
of entertainment instead of a science and it has
not advanced much further than that of the days
of Life
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Summary

• Cellular automaton has an old but brief history.
• Simple cellular automaton is very easy and quite
  useful
• Could have many beneficial qualities if
  researched and deveoped
• Play The Game of Life, its fun and interesting

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References

• http//www.mirwoj.opus.chelm.pl/ca
• http//www.brainyencyclopedia.com/encyclopedia/c/c
  e/cellular_automaton.html
• http//www.frank-buss.de/automaton
• http//www.hyperdictionary.com/dictionary/cellular
  automaton
• http//www.wordiq/defintion/Cellular_automaton
• http//mathworld.wolfram.com/CellularAutomaton
• http//computing-dictionary.thefreedictionary.com/
  cellular20automaton
• The New Turing Omnibus by A.K. Dewdney, ch. 44