In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential update modes, regardless of the initial configuration. In this context, we classify these rules according to whether all initial configurations converge under all, some, one or none sequential update modes, depending on if they have fixed points under synchronous (or parallel) update modes.

翻译：本文对至少具有一个不动点的基本元胞自动机在顺序更新模式下的收敛性进行了理论分析。我们的目标是确定哪些基本规则在顺序更新模式下，无论初始配置如何，总能达到不动点。在此背景下，我们根据这些规则在同步（或并行）更新模式下是否具有不动点，将其按照所有初始配置在所有、部分、一种或无顺序更新模式下收敛的情况进行分类。