Mathematical Sciences: Attracting Sets in Cellular Automata

数学科学：元胞自动机中的吸引集

• 批准号: 8800758
• 负责人: Michael Hurley
• 金额: $ 4.01万
• 依托单位: Case Western Reserve University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800758&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Attracting; Sets; Cellular

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.

迈克尔·赫尔利将进行动力系统的研究。 特别是他将研究元胞自动机。这些是相关的 数据的磁性存储。赫尔利的目标是 研究各种最近的数学解释 经验观察。对细胞生物学感兴趣的一个原因 自动机的一个重要特征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。 元胞自动机可以被认为是一个双重的映射 无穷序列的移位交换。赫尔利将学习 这些地图的动态。自我组织表现在 观察到随机序列变得更高 在重复迭代下的模式和渐近模式是 独立于原始序列。的两大目标 赫尔利的研究是为了了解 一个自动机的吸引子的集合，并描述 动力学的限制，其有趣的吸引子。