Intro to Life32

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 7 6 5 8 2 4 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 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 iteration provides the next row as it moves down the screen. If the width is unlimited, the time to stabilize can be unlimited as well: deterministic chaos. Starting at xt = 0.2 and R = 4 we see a chaotic attractor. The values will never repeat.