Presentation adv theo cs fadhil

CELLULAR AUTOMATA AND CELLULAR AUTOMATA AND APPLICATIONS – Conway’s Game of APPLICATIONS – Conway’s Game of

LifeLifePresentation on Adv. Theories of Computer Presentation on Adv. Theories of Computer

ScienceScienceFADHIL NOER AFIF – MC112075FADHIL NOER AFIF – MC112075

Self-replicating Self-replicating SystemSystem

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John von Neumann Stanislaw Ulam

• In 1940s, working on a problem “how to construct a

self – replicating system?“

• Born a mathematical model named Cellular

Automata (CA)

Cellular AutomataCellular Automata

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What is Cellular Automata ?

• Discrete, dynamical system

• Consists of network of finite state cells

• Changes state homogenously depending on

states of neighbors and local update rule

Cellular AutomataCellular Automata

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What is Cellular Automata ?

• Discrete, dynamical system

• Consists of network of finite state cells

• Changes state homogenously depending

on states of neighbors and local update

rule

Simple Example of CASimple Example of CA

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One-dimensional CA, • Two-state automaton (black / white)• Each cell has three neighbors (including itself)• Rules : – If all three == WHITE WHITE– If all three == BLACK WHITE– Else, BLACK

• Initial State :

Simple Example of CASimple Example of CA

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• Initial State (1st generation):

• 2nd generation ?

Simple Example of CASimple Example of CA

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• 2nd generation :

• 3rd generation ?

• If this continues what will happen ?

Simple Example of CASimple Example of CA

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• n th generation :

A complex

pattern !

Simple Example of CASimple Example of CA

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• Another 1-D CA with different rule (rule 30) :

Math. Definition of Math. Definition of CACA

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By Definition, CA is a 4-tuple (Kari, 2011)

A = (d, S, N, f), where

• dimensional cellular space, d Є Z

• finite state set S,

• neighborhood vector N = (n1, n2, ..., nm), and

• local update rule f: Sm S

Cellular AutomataCellular Automata

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• What’s interesting about this CA?

• Any applications of CA?

Applications of CAApplications of CA

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CA has been implemented in fields such as :

• Cryptography

• Parallel Computing

• Modeling and Simulation

– Crowd Simulation

– Traffic Simulation

• Artificial Life

• Multimedia Content

Conway’s Game of Conway’s Game of LifeLife

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Artificial Life

Conway’s Game of

Life(1970)

Conway’s Game of Conway’s Game of LifeLife

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Two-dimensional CA,

• Two-state automaton,– Life (denoted by marker)– Dead (no marker)

• Each cell has 8 neighbors (horizontal, vertical, diagonal)

n n n

n n

n n n

A LIVE cell with its neighbors

Conway’s Game of Conway’s Game of LifeLife

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Rules : • A dead cell with exactly three live neighbors becomes live cell (a

birth)

• A live cell with two or three live neighbors stays alive (survival)

• In all other cases, a cell dies or remains dead (as if overcrowding or loneliness).

n n n

n N n

n n n

n n n

n N n

n n n

n n n

n N n

n n n

n n n

n N n

n n n

Conway’s Game of Conway’s Game of LifeLife

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Game of Life can create complex behavior by only simple rules.

n n n

n n

n n n

cell configuration called “glider”

Click here for simulations

GliderGlider

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A pattern called “glider”

• When simulated, evolves periodically

• But, location is moved in diagonal direction

• Glider “moves” even though there is no rules about movement

n n n

n n

n n n

cell configuration called “glider”

R-pentominoR-pentomino

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A pattern called R-pentomino

• When simulated, grows with a complex manner, creating new pattern through time.

• Shows a complexity of “life”

n n n

n n

n n n

cell configuration called R-pentomino

Conway’s Game of Conway’s Game of LifeLife

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Artificial Life

Conway’s Game of

Life

Invented by J. Conway (1970)

Shows that patterns can evolve

Example of emergence and self-organization

Complexity can arise from simple rules

Theoretically, model the life itself??

Four-cell Embryo

Applications of CAApplications of CA

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CA has been implemented in fields such as :

• Cryptography

• Parallel Computing

• Modeling and Simulation

• Artificial Life

• Multimedia Content

OtomataOtomata

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Multimedia Content

Batuhan Bozkurt’s OTOMATA

ConclusionConclusion

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• Cellular Automata is a discrete system which states depending on neighbors.

• Potentially able to model complex system.

• Conway’s Game of Life model simulates natural behavior, and probably the complexity, unpredictable behavior of life itself.

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Thank You - Terima Kasih - Hatur Nuhun

Snail named Conus

Textile. Researchers

believe that the shell

exhibits cellular

automaton pattern, as

shown in example of 1D

CA.

ReferencesReferences

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Miranda, E. (2002) Cellular Automata Music: From Sound Synthesis to Musical Forms. Evolutionary Computer Music. Pp 170-193

Kari, Jarkko. (2011). Cellular Automata. Lecture Notes. Part 1, Taken from http://users.utu.fi/jkari/ca/

Sarkar, Palash. (2000). A Brief History of Cellular Automata, ACM Computing Surveys, 32(1), pp 80-107.