AI 中文总结
本文以元胞自动机建模活性介质，分析其临界演化的分形维数与涨落统计，发现临界区间内动力学由雪崩主导，涨落分布连接活动衰减与全填充活动波两种状态。
AI 中文摘要
本文研究了元胞自动机建模的活性介质中临界演化的特征。该系统遵循随机规则演化，呈现两种性质不同的动力学状态：活动衰减态与全填充活动波态。每种状态都有其自身的分形维数和涨落统计特征，两者均得到详细分析。在临界区间内，系统表现出非平凡的分形维数和连接两种状态的涨落分布，这种连接行为源于临界区间内动力学由雪崩主导。
英文摘要
The paper examines the features of critical evolution in an active medium modeled by a cellular automaton. The system evolves according to stochastic rules, exhibiting two qualitatively distinct dynamical regimes: one of fading activity and another of all-filling activity waves. Each regime is characterized by its own fractal dimension and fluctuation statistics, both of which are analyzed in detail. Within the critical interval, the system displays a nontrivial fractal dimension and a fluctuation distribution that bridges the two regimes. This bridging behavior arises because, in the critical interval, the dynamics are governed by avalanches.
Comments9 pages, 21 figures
