1. CELLULAR AUTOMATA AND APPLICATIONS –CELLULAR AUTOMATA AND APPLICATIONS –
Conway’s Game of LifeConway’s Game of Life
Presentation on Adv. Theories of Computer SciencePresentation on Adv. Theories of Computer Science
FADHIL NOER AFIF – MC112075FADHIL NOER AFIF – MC112075

2. Self-replicating SystemSelf-replicating System
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)

3. 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

4. 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

5. 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 :

6. Simple Example of CASimple Example of CA
6
• Initial State (1st generation):
• 2nd generation ?

7. Simple Example of CASimple Example of CA
7
• 2nd generation :
• 3rd generation ?
• If this continues what will happen ?

8. Simple Example of CASimple Example of CA
8
• n th
generation :
A complex
pattern !

9. Simple Example of CASimple Example of CA
9
• Another 1-D CA with different rule (rule 30) :

10. Math. Definition of CAMath. Definition of CA
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

11. Cellular AutomataCellular Automata
11
• What’s interesting
about this CA?
• Any applications of
CA?

12. 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

13. Conway’s Game of LifeConway’s Game of Life
13
Artificial Life
Conway’s
Game of Life
(1970)

14. Conway’s Game of LifeConway’s Game of Life
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

15. Conway’s Game of LifeConway’s Game of Life
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

16. Conway’s Game of LifeConway’s Game of Life
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

17. 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”

18. 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

19. Conway’s Game of LifeConway’s Game of Life
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

20. 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

21. OtomataOtomata
21
Multimedia Content
Batuhan
Bozkurt’s
OTOMATA

22. 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. 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.

24. 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.