1. Theory of nonlinear dynamic systems Practice 12
Juhász János
Szélig Ádám
Goda Márton

2. Cellular automata in 1D:
ca1d_3.m
28 =256 rules
88 fundamentally inequivalent rules
E.g.: rule 30=
Famous rules:
Rule 30: pseudo random pattern
Rule 90: Sierpinsky triangle
Rule 110: Turing complete

3. Cellular automata 2D: Conway’s Game of Life
Rules:
Cell with less than 2 neighbors: cell die
Cell with more than 3 neighbors: cell die
Cell with 2 or 3 neighbors: cell lives
Empty place with 3 neighbors: cell is born

4. Cellular automata 2D: Conway’s Game of Life
Pattern library: lifex.m
Can produce for example:
Spaceships (move): e.g.: glider, spaceship
Oscillators: e.g.: pulsar
Game of life game: lifegenesis.m

5. Cellular automata 2D: Logic gates with Conway’s Game of Life
put_gliders.m
AND and OR
gates with glider guns:

6. Cellular automata 2D: epidemics (SIR) modell
where

7. Thank you for your whole semester attention!

8. Matlab® supplement
[X,Y] = meshgrid(x,y) replicates the grid vectors x and y to produce a full grid.
[y(2); y(1)]; [1. equ of the system; 2. equ of the system]
[t,y]=ode45(equation, [t0,tmax][Xinit,Yinit]); there are other solvers as well, first we try this
figure creates figure graphics objects. Figure objects are the individual windows on the screen in which the MATLAB software displays graphical output.
plot(x,y,how…) drawing, has many options
subplot(m,n,p) (divide the figure m*n parts, draws in the p th region)
contour(X,Y,Z), contour(X,Y,Z,n), and contour(X,Y,Z,v) draw contour plots of Z using X and Y to determine the x- and y-axis limits.