标题： 由细胞自动机形成的循环模式 显示英文标题

标题： Loop Patterns Formed by Cellular Automata

摘要： 提出了一种元胞自动机（CA）规则，可以在二维网格的固定边界条件下生成“环路图案”。 环路是由零单元包围的一单元组成的循环闭合路径。 环路图案可以包含多个不允许相互接触的环路。 该问题通过设计适当的可以重叠的瓦片集合来解决，这些瓦片被用于CA规则中。 从这些瓦片中衍生出模板，用于局部图案匹配。 为了驱动演化以达到期望的图案，如果模板不匹配或未满足其他约束条件，则注入噪声。 通用的CA规则可以通过启用某些条件来专门化，解释了五种规则变体的特性。 模拟表明，CA规则可以安全地演化出稳定的环路图案。 对所得环路图案的初步理论分析提出了许多有趣的未来研究问题——其中一些已简要讨论。 显示英文摘要

摘要： A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain several loops that are not allowed to touch each other. The problem is solved by designing an appropriate set of tiles that can overlap and which are used in the CA rule. Templates are derived from the tiles which are used for local pattern matching. In order to drive the evolution to the desired patterns, noise is injected if the templates do not match or other constraints are not fulfilled. The general CA rule can be specialized by enabling certain conditions, and the characteristics of five rule variants are explained. Simulations illustrate that the CA rule can securely evolve stable loop patterns. The preliminary theoretical analysis of the obtained loop patterns raises many interesting research problems for the future -- several of them have been briefly discussed.