Estevez-Rams E, Estevez-Moya D, Garcia-Medina K, Lora-Serrano R
Facultad de Física, Instituto de Ciencias y Tecnología de Materiales (IMRE), University of Havana, San Lazaro y L, La Habana CP 10400, Cuba.
Facultad de Física, University of Havana, San Lazaro y L, La Habana CP 10400, Cuba.
Chaos. 2019 Apr;29(4):043105. doi: 10.1063/1.5062364.
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular automata, there is an enhancement of computation capabilities as the system moves towards cellular automata with chaotic spatiotemporal behavior. The computation capabilities are followed by looking into the Shannon entropy rate and the excess entropy, which allow identifying the balance between unpredictability and complexity. Enhanced computation power shows an increase of excess entropy, while the system entropy density has a sudden jump to values near one. The analysis is extended to a system of non-linear locally coupled oscillators that have been reported to exhibit spatiotemporal diagrams similar to cellular automata.
虽然对于经历相变的动力系统，在混沌边缘研究计算一直有着浓厚的兴趣，但对于细胞自动机来说，这一点受到了质疑。我们表明，对于连续变形的细胞自动机，随着系统向具有混沌时空行为的细胞自动机转变，计算能力会增强。通过研究香农熵率和过剩熵来跟踪计算能力，这有助于确定不可预测性和复杂性之间的平衡。增强的计算能力表现为过剩熵的增加，而系统熵密度会突然跃升至接近1的值。该分析扩展到了一个非线性局部耦合振荡器系统，据报道该系统表现出与细胞自动机相似的时空图。
