The market dynamics produced by simple interactions among rational investors can generate complex phenomena such as bubbles, crashes, and business cycles. One powerful tool to understand those phenomena might be the use of Cellular Automata (CA) models. In this contribution we investigate spatial aggregations effects associated to the propagation of information contagion waves across a network of non-equivalent adjustable agents. The contagion dynamics is modeled by an inhomogeneous cellular automaton (InCA) as proposed by Weisbuch and Stauffer[Physica A, 1(323), 651-662 (2003)]. In this system, a tatonnement process emerges as the individual agents try to adjust their reservation price to follow the externality produced by the state of the neighborhood. Using rescale range analysis we show that the periodic oscillations of InCA average state (that resembles business cycles) have long memory effects (for a determined interval of time). The presence of long memory effects is a usual feature present in many real markets. Our results are obtained after the development of an efficient algorithm to count the cluster of agents with the same state. The application of this algorithm revealed that the number and the size of the agent's cluster increase as adjustment amplitude (the parameter that controls the velocity of the tatonnement process) increases. We then show that there is a value of this amplitude that maximizes the system's tendency to form large and synchronized clusters. By associating this adjustment parameter with the liquidity, we demonstrate that the dynamics of the inhomogeneous cellular automata can mimic liquidity externalities found in real markets.

理性投资者之间的简单互动所产生的市场动态可能会产生复杂的现象，例如泡沫、崩盘和商业周期。理解这些现象的一种强大工具可能是使用元胞自动机 (CA) 模型。在这个贡献中，我们研究了与信息传染波在非等效可调代理网络中的传播相关的空间聚合效应。传染动力学由 Weisbuch 和 Stauffer 提出的非均匀元胞自动机 (InCA) 建模[ Physica A, 1(323), 651-662 (2003)]。在这个系统中，当个体代理试图调整他们的保留价格以跟随邻域状态产生的外部性时，就会出现一个 tatonnement 过程。使用重新调整范围分析，我们表明 InCA 平均状态的周期性振荡（类似于商业周期）具有长记忆效应（在确定的时间间隔内）。长记忆效应的存在是许多真实市场中常见的特征。我们的结果是在开发了一种有效的算法来计算具有相同状态的代理集群之后获得的。该算法的应用表明，随着调整幅度（控制咬合过程速度的参数）的增加，智能体集群的数量和大小也随之增加。然后，我们证明了这个幅度的值可以最大化系统形成大型同步集群的趋势。通过将此调整参数与流动性相关联，我们证明了非齐次元胞自动机的动态可以模拟真实市场中发现的流动性外部性。