presentation adv theo cs fadhil
TRANSCRIPT
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
2
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
3
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
4
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
5
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
6
• Initial State (1st generation):
• 2nd generation ?
Simple Example of CASimple Example of CA
7
• 2nd generation :
• 3rd generation ?
• If this continues what will happen ?
Simple Example of CASimple Example of CA
8
• n th generation :
A complex
pattern !
Simple Example of CASimple Example of CA
9
• Another 1-D CA with different rule (rule 30) :
Math. Definition of Math. Definition of CACA
10
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
11
• What’s interesting about this CA?
• Any applications of CA?
Applications of CAApplications of CA
12
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
13
Artificial Life
Conway’s Game of
Life(1970)
Conway’s Game of Conway’s Game of LifeLife
14
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
15
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
16
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
17
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
18
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
19
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
20
CA has been implemented in fields such as :
• Cryptography
• Parallel Computing
• Modeling and Simulation
• Artificial Life
• Multimedia Content
OtomataOtomata
21
Multimedia Content
Batuhan Bozkurt’s OTOMATA
ConclusionConclusion
22
• 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.
23
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
24
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.