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Generalized Langton's Ant: Dynamical Behavior and Complexity

机译:广义兰顿的蚂蚁:动态行为和复杂性

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Langton's ant is a simple discrete dynamical system, with a surprisingly complex behavior. We study its extension to general planar graphs. First we give some relations between characteristics of finite graphs and the dynamics of the ant on them. Then we consider the infinite bi-regular graphs of degrees 3 and 4, where we prove the universality of the system, and in the particular cases of the square and the hexagonal grids, we associate a P-hard problem to the dynamics. Finally, we show strong spatial restrictions on the trajectory of the ant in infinite bi-regular graphs with degrees strictly greater than 4, which contrasts with the high unpredictability on the graphs of lower degrees.
机译:Langton的蚂蚁是一种简单的离散动态系统,具有令人惊讶的复杂性行为。我们研究其扩展到一般平面图。首先,我们在有限图和蚂蚁的动态之间提供一些关系。然后我们考虑中度3和4的无限双常规图,我们证明了系统的普遍性,并且在广场和六边形网格的特定情况下,我们将P-Coll问题与动态相关联。最后,我们对无限的双常规图表中的蚂蚁轨迹表现出严格大于4的轨迹的强烈空间限制,这与较低程度的图表的高不可预测性形成鲜明对比。

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