Theory and applications of cellular automata and iterated systems

元胞自动机和迭代系统是离散的动力系统，可用于模拟各种科学中感兴趣的许多过程。例如，它们已被用于构建晶体生长、化学反应、螺旋星系、社会互动和车辆交通的模型。它们被应用于计算机芯片设计、密码学和伪随机数生成器中。在这个建议中提出的程序包括对元胞自动机和迭代系统的数学特性的分析研究，以及它们在构建简单模型中的应用，这些模型说明了复杂系统的一般原理。例如，最近的工作考虑了稳定性和灵活性之间的权衡，并表明在随机波动发生的环境中，优先选择两种稳定类型中的一种或另一种，不稳定类型（即通过自我监控和适应性控制在不同的行为反应之间保持“平衡”的类型）可能会占主导地位，即使它付出了死亡率增加的代价。另一项为后续工作提出的研究将考虑对威胁情况的快速反应和准确感知之间的权衡：快速反应增加了逃离危险的可能性，但也增加了错过机会的可能性，而这些机会本可以通过更仔细的考虑来感知。这类案例的简单模型对于复杂自适应系统的研究非常重要，因为现实世界系统的复杂性往往掩盖了一般的潜在原理。

Cellular automata and iterated systems are discrete dynamical systems that can be used to model many processes of interest in a variety of sciences. They have been used, for example, to construct models of crystal growth, chemical reactions, spiral galaxies, social interactions, and vehicle traffic. They are used in applications in computer chip design, cryptography, and as pseudo-random number generators. The program set forth in this proposal involves both analytic studies of the mathematical properties of cellular automata and iterated systems and their application in construction of simple models that illustrate general principles of complex systems. For example, recent work has considered the trade-off between stability and flexibility and shown that in environments where random fluctuations occur that preferentially select for one or another of two stable types, an unstable type (that is, one which through self-monitoring and adaptive control remains "balanced" between distinct behavioral responses) can come to dominate, even if it pays a cost in terms of increased mortality. Another study proposed for continued work will consider the trade-off between quickness of response and accuracy in perception of threat situations: a quick response increases the likelihood of escaping danger, but also increases the likelihood of missing opportunity that might be perceived with more careful consideration. Simple models of cases like these are important for research on complex adaptive systems since the complexity of real world systems often masks general underlying principles.