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Conclusions

* Given the common form shared by continuous cellular automata (CA) dynamics and numerical methods for differential equations, we might expect to approach some more accurate, more stable, ideal version of a self-organizing pattern by decreasing the step size dt.

* We’d be wrong! CA patterns are not generally more stable/accuracte at lower step size; instead they occupy specific ranges and a step size too small can be as catastrophic as one that is too large.

* Qualitative differences in behavior also become apparent at different step sizes for some patterns.

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