Mathematical Sciences: Attracting Sets in Cellular Automata

迈克尔·赫尔利将进行动力系统方面的研究。特别是，他将学习细胞自动机。这些都与数据的磁性存储有关。赫尔利的目标是研究对最近各种经验观察的数学解释。对元胞自动机感兴趣的一个原因是，它们中的一些表现出自组织行为。用数学术语来说，这意味着吸引子的存在。细胞自动机可以被认为是双无限序列上的一个映射，它可以通过移位进行交换。赫尔利将研究这类地图的动态。自组织表现在观察到的随机序列在重复迭代下变得更加高度模式化，并且渐近模式独立于原始序列。赫尔利研究的两个主要目标是了解自动机吸引子集合的层次结构，并描述其对有趣吸引子的限制的动力学。

Michael Hurley will carry out research in dynamical systems. In particular he will study cellular automata. These are related to the magnetic storage of data. Hurley's objective is to investigate the mathematical explanations of various recent empirical observations. One reason for interest in cellular automata is that some of them exhibit self-organizing behavior. In mathematical terms this suggests the existence of attractors. A cellular automaton can be thought of as a map on doubly infinite sequences which commutes with shifts. Hurley will study the dynamics of such maps. Self-organization manifests itself in the observation that random sequences become more highly patterned under repeated iterations and the asymptotic pattern is independent of the original sequence. The two major goals of Hurley's research are to understand the hierarchy of the collection of attractors of an automaton and to describe the dynamics of its restriction to its interesting attractors.