The document presents a case study on cellular automata. It defines cellular automata as regular spatial lattices of cells that can have finite states, with cell states updated in discrete time steps according to the states of surrounding cells. The study discusses the history of cellular automata beginning with John von Neumann's work in 1947, presents examples of simple one-dimensional cellular automata and their rules, illustrates a predator-prey cellular automata model over generations, and discusses applications of cellular automata such as simulating biological and social systems.

1. A Case study of
Cellular Automata
Written and Presented by:
Devdutta Chakrabarti
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2. Cellular Automata-Summary
What is cellular automata?
History of cellular automata
Simple cellular automata
Rules
Applications
Summary
References
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3. What is Cellular Automata?
 Cellular Automata(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.
 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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4. How Cellular Automata 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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5. Simple Cellular Automata
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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6. Rules
This rule modeled a predator/prey relationship
Begins with a randomly distributed population of
fish, sharks, and empty cells in a 1000x2000 cell
grid (2 million cells)
Initially,
50% of the cells are occupied by fish
25% are occupied by sharks
25% are empty
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7. Here’s the number 2 million
• Fish: red; sharks: yellow; empty: black
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8. Rules in detail: Initial Conditions
Initially cells contain fish, sharks or are empty
Empty cells = 0 (black pixel)
Fish = 1 (red pixel)
Sharks = –1 (yellow pixel)
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9. Rules in detail: Breeding Rule
Breeding rule: if the current cell is empty
If there are >= 4 neighbors of one species, and >=
3 of them are of breeding age,
 Fish breeding age >= 2,
 Shark breeding age >=3,
and there are <4 of the other species:
then create a species of that type
 +1= baby fish (age = 1 at birth)
 -1 = baby shark (age = |-1| at birth)
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10. Breeding Rule: Before
EMPTY
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11. Breeding Rule: After
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12. GNIT_MTECH(CSE)
Rules in Detail: Fish Rules
If the current cell contains a fish:
• Fish live for 10 generations.
• If >=5 neighbors are sharks, fish dies (shark
food).
• If all 8 neighbors are fish, fish dies
(overpopulation).
• If a fish does not die, increment age.
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13. GNIT_MTECH(CSE)
Rules in Detail: Shark Rules
If the current cell contains a shark:
• Sharks live for 20 generations.
• If >=6 neighbors are sharks and fish
neighbors =0, the shark dies (starvation).
• A shark has a 1/32 (.031) chance of dying
due to random causes.
• If a shark does not die, increment age.
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14. GNIT_MTECH(CSE)
Shark Random Death: Before
I Sure Hope that the
random number
chosen is >.031
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15. GNIT_MTECH(CSE)
Shark Random Death: After
YES IT IS!!!
I LIVE 
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16. GNIT_MTECH(CSE)
Illustration
Next several screens show behavior over a
span of 10,000+ generations (about 25
minutes on a cluster of 20 processors).
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17. GNIT_MTECH(CSE)
Generation: 0
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18. GNIT_MTECH(CSE)
Generation: 100
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19. GNIT_MTECH(CSE)
Generation: 500
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20. GNIT_MTECH(CSE)
Generation: 1,000
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21. GNIT_MTECH(CSE)
Generation: 2,000
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22. GNIT_MTECH(CSE)
Generation: 4,000
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23. GNIT_MTECH(CSE)
Generation: 8,000
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24. GNIT_MTECH(CSE)
Generation: 10,500
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25. GNIT_MTECH(CSE)
Variations of Initial Conditions
Still using randomly distributed
populations:
Medium-sized population. Fish/sharks occupy:
1/16th
of total grid
Fish: 62,703; Sharks: 31,301
Very small population. Fish/sharks occupy:
1/800th
of total grid
Initial population:
Fish: 1,298; Sharks: 609
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26. Medium-sized population (1/16 of grid)
Generation 100 1000
2000 4000
8000
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27. GNIT_MTECH(CSE)
Very Small Populations
Random placement of very small
populations can favor one species over
another
Fish favored: sharks die out
Sharks favored: sharks predominate, but
fish survive in stable small numbers
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28. Applications of Cellular Automata
Simulation of Biological Processes
Simulation of Cancer cells growth
Predator – Prey Models
Art
Simulation of Forest Fires
Simulations of Social Movement
…many more.. It’s a very active area of
research.
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29. Summary
It excel at modelling physical systems because
the properties of the physical world and
cellular lattices are very similar.
Cellular automata has an old but brief history.
Simple cellular automata is very easy and quite
useful.
Could have many beneficial qualities if
researched and developed.
Play The Game of Life, its fun and interesting.
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30. References
http://www.mirwoj.opus.chelm.pl/ca
http://www.brainyencyclopedia.com/encyclopedia/c/ce/cellular_autom
aton.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/cellular
%20automaton
The New Turing Omnibus by A.K. Dewdney, ch. 44
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31. THANK YOU ALL !!
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