  Step size in continuous cellular automata (CA) plays an important role in the
stability and behavior of self-organizing patterns. Continous CA dynamics are
defined by formula very similar to numerical estimation of physics-based
ordinary differential equations, specifically Euler's method, for which a large
step size is often inaccurate and unstable. Rather than asymptotically
approaching more accurate estimates of CA dynamics with decreasing step size,
continuous CA may support different self-organizing patterns at different
ranges of step size. We discuss several examples of mobile patterns that become
unstable at step sizes that are too small as well as too large. Additionally,
an individual mobile pattern may exhibit qualitatively different behavior
across a range of step sizes. We demonstrate examples of the effects of step
size in pattern stability and qualitative behavior in continuous CA implemented
in the Lenia framework and its variant, Glaberish.
