Rigorous and Empirical Analysis of Random Cellular Automata

随机元胞自动机的严格实证分析

• 批准号: 9626152
• 负责人: David Griffeath
• 金额: $ 12.9万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626152&HistoricalAwards=false
• 关键词: Rigorous; Empirical; Analysis; Random; Cellular

9626152 Griffeath The current and planned research of David Griffeath focuses on an interplay between mathematical theory and computer visualization for complex, random and deterministic lattice dynamics. Griffeath exploits this "symbiosis" in his theoretical and empirical studies of cellular automaton dynamics and other nonlinear spatial interactions. On the theoretical side, this work is giving rise to an increasingly rich and illuminating rigorous theory of Threshold Growth, a new paradigm for discrete-time parallel updating of lattice configurations. On the empirical side, Griffeath is developing effective, interactive simulation tools for the study of complex spatial systems, designing two platforms in parallel: (a) a high-end simulator based on the new CAM8 cellular automaton machine from MIT, of which he has one of the first few prototypes in the world; and (b) a low-end 32-bit Windows 95 simulator and graphical front end called WinCA. Over the next three years, among the types of dynamical system Griffeath intends to study using this hybrid methodology are various cellular automata, interacting particle systems, and individual-based models that serve as prototypes for such complex phenomena as nucleation, spiral formation in excitable media, the shape theory of crystal growth, flocking, host-parasite interactions, dendritic growth, and phase separation by surface tension. Mathematical models for growth and competition have played a key role in the development of spatial complex systems theory since the mid 1950's. An extensive body of theory and applications, for both random and deterministic systems, has been developed, especially over the past twenty years. Modeling of such fundamental phenomena as aggregation, emergence of shape, interfacial competition, and droplet interaction sheds new light on many areas of applied science. Griffeath's work during the next funding period will be motivated especially by problems elicited from the spatial mathematical ecology community, as identi fied during an interdisciplinary conference that he organized at the Santa Fe Institute during January, 1996. He expects that the various simulation tools he is developing will be able to provide new insights into questions of genuine interest to that clientele, and that a substantial body of interesting new pure mathematics will result as well.

9626152 Griffeath大卫Griffeath目前和计划的研究重点是数学理论和计算机可视化之间的相互作用复杂，随机和确定性的晶格动力学。Griffeath在他对元胞自动机动力学和其他非线性空间相互作用的理论和经验研究中利用了这种“共生”。在理论方面，这项工作正在产生一个日益丰富和启发严格的阈值增长理论，一个新的范例离散时间并行更新的晶格配置。在经验方面，Griffeath正在为复杂空间系统的研究开发有效的交互式仿真工具，并行设计两个平台：（a）基于麻省理工学院新的CAM 8元胞自动机的高端仿真器，他拥有世界上首批原型之一;（B）低端32位Windows 95仿真器和图形前端，称为WinCA。在接下来的三年里，Griffeath打算使用这种混合方法研究的动力系统类型包括各种细胞自动机，相互作用的粒子系统和基于个体的模型，这些模型可以作为成核，可激发介质中的螺旋形成，晶体生长的形状理论，植绒，宿主-寄生虫相互作用，树枝状生长和表面张力相分离等复杂现象的原型。 自20世纪50年代中期以来，增长和竞争的数学模型在空间复杂系统理论的发展中发挥了关键作用。特别是在过去的二十年里，已经发展了一套广泛的理论和应用，包括随机系统和确定性系统。对聚集、形状出现、界面竞争和液滴相互作用等基本现象的建模为应用科学的许多领域提供了新的视角。Griffeath的工作在下一个资助期间将特别是由问题引起的空间数学生态社区，作为identi fied在一个跨学科的会议期间，他组织在圣达菲研究所在1996年1月。他希望他正在开发的各种模拟工具能够为客户真正感兴趣的问题提供新的见解，并产生大量有趣的新纯数学。