CELLULAR AUTOMATON Presented by Rajini Singh.

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CELLULARAUTOMATONPresented by Rajini Singh.
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• CELLULAR AUTOMATON
• Discrete Model
• Infinite Regular Grid of cells.
• Finite number of States.
• State of a cell is a function of the States of
  its neighborhood.
• Every cell has the same rule for updating.
• New generation is created every time rules are
  applied to the whole grid.

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• CELLULAR AUTOMATON
• Simulated on a Finite Grid.
• In Two Dimensions, the universe would be a
  rectangle.
• The edge cells are handled with a toroidal
  arrangement.

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• EXAMPLE
• Infinite sheet of graph paper.
• Every cell (square) has 2 states.
• Neighborhood are the 8 squares.
• 29512 patterns.

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• CELLULAR AUTOMATON
• Simplest non trivial CA is one-dimensional, with
  two States per cell.
• Every cells neighborhood are the cells on
  adjacent sides of it.
• A cell and its 2 neighbors form a neighborhood of
  3 cells, so there are 23 8 possible patterns
  for a neighborhood and 28 256 possible rules.
• These 256 CAs are referred to using a standard
  naming convention invented by Wolfram.

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• CELLULAR AUTOMATON
• The name of the CA is the decimal number, which,
  in binary, gives the rule table, with the eight
  possible neighborhoods listed in reverse counting
  order.
• Examples are
• Rule 30 CA (binary - 11110)
• Rule 110 CA (binary 1101110)

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• EXAMPLES OF CELLULAR AUTOMATON
• RULE 30 CELLULAR AUTOMATION

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• RULE 30 CELLULAR AUTOMATON

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• CELLULAR AUTOMATON
• RULE 110 CELLULAR AUTOMATON

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• RULE 110 CELLULAR AUTOMATION

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• CELLULAR AUTOMATION
• Table completely defines a CA rule.
• For example, Rule 30 table says that if 3
  adjacent cells in the CA currently have the
  pattern 100, then the middle cell will become 1
  on the next time step
• Rule 110 table says the opposite of it for that
  particular case.

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REVERSIBLE

• CELLULAR AUTOMATONS
• CATEGORIES OF CELLULAR AUTOMATON
• Reversible
• Totalistic

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• REVERSIBLE
• A CA is said to be Reversible if for every
  configuration of the CA there is exactly one past
  configuration (preimage)
• For one dimensional CA, preimages can be found,
  and any 1D rule can be proved either reversible
  or irreversible.
• For CA of two or more dimensions, reversibility
  is undecidable for arbitrary rules.

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• TOTALISTIC
• The State of each cell in a Totalistic CA is
  represented by a number, which is a value, and
  this value of the cell at time t depends on the
  sum of the values of the cells in its
  neighborhood (including itself) at time t-1.
• If the state of the cell at time t does depend
  on its own state at time t-1 then the CA is
  called outer totalistic.
• An example of the above is Conways Game of Life
  with cell values 0 and 1.

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• CONWAYS GAME OF LIFE

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• CONWAYS GAME OF LIFE
• Devised by a British Mathematician- John Horton
  Conway.
• The evolution of the game is determined by its
  initial state.
• Its universe is a 2-D square grid.
• Every cell has a state - live or dead, and
  interacts with its 8 neighbors.

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• At each step in time,
• A dead cell with exactly 3 live neighbors comes
  to life.
• 2. A live cell with two or three live neighbors
  stay alive.
• 3. In all other cases, a cell dies or remains
  dead.

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• Initial pattern constitutes first Generation of
  the system.
• The above rules are applied to every cell in the
  first generation, and the discrete moment at
  which this happens is called a tick.
• Births and deaths happen simultaneously in this
  phase.
• The rules continue to be applied repeatedly to
  create further generations.

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• The kinds of Objects that emerge in Life
• Still Life Objects.
• Block 2 x 2 square
• Beehive
• Boat
• Ship
• Loaf
• Oscillators
• Objects that change but eventually repeat
  themselves.
• Gliders
• Moving patterns consisting of 5 cells.
• Guns
• Generates an endless stream of new
  patterns.

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• Guns and Gliders Turing Complete.

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• CONCLUSION
• Behavior of cells or animals can be better
  understood using simple rules.
• Computer viruses are also examples of Cellular
  Automaton. Finding the cure could be hidden in
  the patterns of this game.
• Human diseases could be cured if we better
  understand why cells live and die.
• Cryptography.

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• REFERENCES
• http//www.stephenwolfram.com/publications/articl
  es/ca/
• http//www.santafe.edu/shlizi/notebooks/cellular
  -automata.html
• http//www.stephenwolfram.com/publications/articl
  es/ca/85-cryptography/1/text.html

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• THANK YOU.