Intro to Life32
1) Zoom to 10
(magnifying
glass)
That will allow
you to see the
grid and
individual cells
2) Select draw mode in options
That will allow you to create “live” cells (dark)
3) Draw 3 live cells, and press the “step” to see what
happens in each iteration
4) Under the “Game” menu look at the “rules”.
1
2
3
8
2
4
7
6
5
Every cell has 8 nearest neighbors
Survival: how many neighbors to stay alive
Birth: how many to go from dead to alive
Limit cycles in cellular automata
Repeated behavior is a limit cycle, just like we saw in logistic map.
Starting at xt = 0.5 and R = 3.2 we
have a 2 period limit cycle
Add one cell atop the center. We see a transient as
the CA settles into a new basin of attraction
After 9 steps, this CA settles into a limit cycle.
At R= 3.2, and starting from x=0.5, it
takes about 9 steps before the
logistic map settles into its limit
cycle.
4 period Limit cycle in CA
Starting at xt = 0.5 and R = 3.5
4 period in logistic map.
CA can also create deterministic chaos
From games menu, open folder lifep,
and select Acorn. This is not true deterministic
chaos but it takes 5206 generations to stabilize!
Chaos in a 1D CA. The pattern one row; each
Starting at xt = 0.2 and R = 4 we see a
iteration provides the next row as it moves down
chaotic attractor. The values will never
the screen. If the width is unlimited, the time to
repeat.
stabilize can be unlimited as well: deterministic chaos.