我们研究定义在任意群宇宙 $G$ 与字母表 $A$ 上的最基础一类元胞自动机：懒惰元胞自动机（lazy cellular automata）。此类自动机在配置空间 $A^G$ 上作用为恒等映射，除非其读取到唯一的活跃转移模式 $p \in A^S$，此时它输出一个固定的符号 $a \in A$。如预期所料，懒惰元胞自动机的动力学行为相对简单，但由于其行为完全取决于 $p$ 与 $a$ 的选取，仍会产生微妙的问题。本文考察懒惰元胞自动机 $τ: A^G \to A^G$ 的阶，即集合 $\{ τ^k : k \in \mathbb{N} \}$ 的基数。特别地，我们基于 $p$ 的纤维（fibers）给出了 $τ$ 阶的一个通用上界，并证明当 $p$ 为拟常值模式（quasi-constant pattern）时该上界可达。

We study the most elementary family of cellular automata defined over an arbitrary group universe $G$ and an alphabet $A$: the lazy cellular automata, which act as the identity on configurations in $A^G$, except when they read a unique active transition $p \in A^S$, in which case they write a fixed symbol $a \in A$. As expected, the dynamical behavior of lazy cellular automata is relatively simple, yet subtle questions arise since they completely depend on the choice of $p$ and $a$. In this paper, we investigate the order of a lazy cellular automaton $τ: A^G \to A^G$, defined as the cardinality of the set $\{ τ^k : k \in \mathbb{N} \}$. In particular, we establish a general upper bound for the order of $τ$ in terms of the fibers of $p$, and we prove that this bound is attained when $p$ is a quasi-constant pattern.