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Nawaf M Albadia 427121532
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Introduction.Components.Behavior & Characteristics.Classes & Rules.Grid Dimensions.Evolving Cellular Automata using Genetic Algorithms.Applications.Conclusion.References.
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Some of the contents of this presentation is assembled and adopted from multifarious resources, see the
references for more details
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What are Cellular Automata?A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, theoretical biology and microstructure modeling
CA are discrete dynamic systems. CA's are said to be discrete because they operate in finite space and
time and with properties that can have only a finite number of states.
CA's are said to be dynamic because they exhibit dynamic behaviors.Basic Idea: Simulate complex systems by interaction of cells following
easy rules.
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Original concept of CA is most strongly associated with John von Neumann.
von Neumann was interested in the connections between biology and the new study of automata theory
Stanislaw Ulam suggested that von Neumann use a cellular automata as a framework for researching these connections.
The original concept of CA can be credited to Ulam, while the early development of the concept is credited to von Neumann.
Ironically, although von Neumann made many contributions and developments in CA, they are commonly referred to as “non-von Neumann style”, while the standard model of computation (CPU, globally addressable memory, serial processing) is know as “von Neumann style”.
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GridMesh of cells.Simplest mesh is one dimensional.
CellBasic element of a CA.Cells can be thought of as memory elements
that store state information.All cells are updated synchronously according
to the transition rules.Rules
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Local interaction leads to global dynamics.One can think of the behavior of a cellular automata like
that of a “wave” at a sports event.Each person reacts to the state of his neighbors (if they
stand, he stands).
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Rule ApplicationNext state of the core cell is related to the states of
the neighborhood cells and its current state. An example rule for a one dimensional CA: 011->x0x All possible states must be described.
Next state of the core cell is only dependent upon the sum of the states of the neighborhood cells. For example, if the sum of the adjacent cells is 4 the
state of the core cell is 1, in all other cases the state of the core cell is 0.
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John H. Conway developed “the Game of Life” in the 1970’s.
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First Generation
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Second Generation
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Discrete lattice of cells.Homogeneity – all of the cells of the lattice are
equivalent.Discrete states – each cell takes on one of a finite
number of possible discrete states.Local interactions – each cell interacts only with cells
that are in its local neighbourhood.
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CA typically fall into 4 classes:Class 1: system freezes into a fixed state after a short
time.Class 2: system develops periodic behaviours, which
repeat continuously.Class 3: system becomes a periodic, in which it
continuously changes in unpredictable ways.Class 4: system can develop in highly patterned but
unstable ways.
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A computational Model with discrete cells updated synchronously.
………..
outputInput
Combinational Logic
Clock
From Left Neighbor
From Right Neighbor
0/1
2 – State, 2-Neighborhood, 3 -CA Cells
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Combinational Logic can be of 256 typeseach type is called a rule
Each cell can have 256 different rules
………..
98 236 226 107
4 cell CA with different rules at each cell15
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von Neumann neighborhoodMoore neighbourhood.
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The cyclic cellular automaton is a cellular automaton rule developed by David Griffeath
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Melanie Mitchell, working on sophisticated micro level structures designed at network. Inspired by complex natural systems like insect colonies.
Mitchell and collaborators have applied Genetic Algorithms to evolve patterns in cellular automata.
In their results they were able to show that the GA discovered rules that gave rise to sophisticated emergent computational strategies.
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Cryptography use, Rule 30Simulations
Gas behaviour.Forest fire propagation.Urban development.Traffic flow.Air flow.Crystallization process.
Alternative to differential equations
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Natural biotic types.Chemical types.Computer processors CAM-6Error correction coding
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Discrete dynamical system simulator.Allow for a systematic investigation of complex
phenomena.Original models of fundamental physics.
Instead of looking at the equations of fundamental physics, consider modelling them with CA.
Can mimic complex operationsProblem – How to find the exact CA rules
which will model a particular application
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Introduction to Cellular automata, http://www.rennard.org/alife/english/acintrogb01.html
Derek Horton “Cellular Automata”, April 14, 2003 Jean-Philippe Rennard Ph.D.ز "Introduction to Cellular
automata", 12/2000Wikipedia, “Cellular automaton”
http://en.wikipedia.org/wiki/Cellular_automataWikipedia Rule 30, http://en.wikipedia.org/wiki/Rule_30Wikipedia Rule 110 ,
http://en.wikipedia.org/wiki/Rule_110_cellular_automaton
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