growth
and
self-similar structures
diffusion limited aggregation
DLA
•
we start with N diffusing
particles
•
plus a nucleation site
•
when diffusing particles touch
the nucleation site the attach
•
new particles are introduced
in the periphery of the system
pure diffusion
noise and attraction
pure attraction
pure noise
characterizing growth geometry
fractal dimension
measure it
dimension of DLA
not one dimensional not two dimensional but something in
between
D=1.36
D=1.41
D=1.20
consider this
consider this
consider this
finite area
infinitely long boundary
consider this
finite area
infinitely long boundary
DLA and Automata
cellular automata
example: the game of life
•
cells can be dead or alive
•
Every living cell considers 8 nearest
neighbors and counts living neighbors
K
•
when K<2 the cell dies
•
when K=2 or K=3 the cell lives
•
when K>3 the cell dies
•
a dead cell is born when 3
neighbors are alive
one dimensional cellular automata
the next state of a unit is determined by the states of the
neighboring units
each state can be 1 or 0
1 = alive
0 = dead
example
starvation
invasion
competition
cooperation
an isolated dead “cell” will remain dead
example
show muscheln
another example
another example
stochastic cellular automata