标题： 广义模糊基本细胞自动机的模式形成 显示英文标题

标题： Pattern formation of generalized fuzzy elementary cellular automaton

摘要： 我们提出了一种从给定的细胞自动机构造模糊细胞自动机的一般方法。 与之前使用模糊独特正规形式的方法不同，其更新函数被限制为三阶多项式，我们的方法可以容纳广泛的模糊化函数，从而生成简单启发式模型无法实现的多样且复杂的时间演化模式。 我们证明，通过改变模糊化函数的参数或两种不同演化规则之间的混合比例，可以观察到模式形成中的相变。 值得注意的是，所得的广义模糊基本细胞自动机即使在仅由三个细胞组成的最小系统中也表现出丰富的动态特性，包括稳定流形和混沌。 显示英文摘要

摘要： We propose a general method for constructing a fuzzy cellular automaton from a given cellular automaton. Unlike previous approaches that use fuzzy distinctive normal form, whose update function is restricted to third-order polynomials, our method accommodates a wide range of fuzzification functions, enabling the generation of diverse and complex time-evolution patterns that are unattainable with simpler heuristic models. We demonstrate that phase transitions in pattern formation can be observed by changing the parameters of the fuzzification function or the mixing ratio between two distinct evolution rules of elementary cellular automata. Remarkably, the resulting generalized fuzzy elementary cellular automata exhibit rich dynamical properties, including stable manifolds and chaos, even in minimal systems composed of just three cells.