标题： 步长是连续细胞自动机中的关键参数 显示英文标题

标题： Step Size is a Consequential Parameter in Continuous Cellular Automata

摘要： 连续细胞自动机(CA)中的步长在自组织模式的稳定性和行为中起着重要作用。 连续CA的动力学由非常类似于基于物理的常微分方程数值估计的公式定义，特别是欧拉方法，对于该方法，较大的步长通常不准确且不稳定。 与随着步长减小逐渐接近更精确的CA动力学估计不同，连续CA在不同的步长范围内可能支持不同的自组织模式。 我们讨论了一些移动模式的例子，这些模式在步长过小或过大时都会变得不稳定。 此外，一个单独的移动模式在不同范围的步长下可能表现出定性不同的行为。 我们展示了在Lenia框架及其变体Glaberish中实现的连续CA中步长对模式稳定性及定性行为的影响示例。 显示英文摘要

摘要： 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.