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This guide introduces you to cellular automata (CA), demonstrating how to create and visualize live cells using draw mode. You’ll learn to generate live cells and observe their evolution through iterations by stepping through cycles. Key concepts include survival and birth conditions based on nearest neighbor rules. We'll also explore limit cycles, such as transient behavior in the system and examples of both periodic limits and chaotic attractors. Understand how starting values influence outcomes in CA and discover the fascinating complexity within simple rules.
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Zoom to 10 That will allow you to see the grid and individual cells
2) Select draw mode 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
Transient as the CA settles into its 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.
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 Starting at xt= 0.2 and R = 4 we see a chaotic attractor. The values will never repeat.
