The automation known as "Langton's ant" exhibits a propagation phase where the particle dynamics (the ant) produces a regular periodic pattern (called "highway''). Despite the simplicity of its basic algorithm, Langton's ant has remained a puzzle in terms of analytical description. Here I show that propagation dynamics obeys a general difference equation for a class of automata which includes 1-D. 2-D triangular and square lattice models. In the case of Langton's ant, thc speed of the ant in the highway (c=root2/52) follows exactly from the equation. [References: 10]
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机译：被称为“ Langton蚂蚁”的自动化系统表现出传播阶段，在该阶段，粒子动力学（蚂蚁）产生规则的周期性模式（称为“高速公路”），尽管其基本算法简单，但在以下方面，Langton蚂蚁仍然是一个难题。分析性描述。在这里，我证明了传播动力学服从一类自动机的一般差分方程，其中包括一维，二维三角形和正方形网格模型。对于兰顿蚂蚁，该蚂蚁在高速公路上的速度（ c = root2 / 52）完全从方程式得出[参考文献：10]
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