Estudo de criticalidade auto organizada

Abstract

In this study, we investigate the Self-Organized Criticality (SOC), an intriguing phenomenon where complex systems spontaneously evolve towards a phase transition state. This concept unveils a compelling connection between ordinary daily occurrences and large-scale catastrophic events, both arising from the underlying principles of self-organization. To illustrate SOC, we employ the analogy of a continuously growing sandpile, which maintains a specific inclination angle, emblematic of a constant state of near-collapse, or a critical state. In this work, we implement three computational models, known as Cellular Automata (CA), where pixels in a grid interact and change state following specific rules. The first model, called ”Sandpile Model", was proposed by Per Bak. The second is a modification of the traditional sand pile model where energy dissipation is taken into account. In the third, the traditional model is modified to consider a fixed global slope of the sandpile. In these self-organizing environments, we observed the occurrence of abrupt structural changes, termed "avalanches", spanning all feasible spatial dimensions within the confines of the system’s size. Intriguingly, these avalanches exhibit a frequency distribution that aligns with a power law, marked by an exponent close to −1. This pattern indicates a remarkable consistency in the manifestation of critical events, irrespective of their scale. Furthermore, we engage in a detailed discussion on the specific parameters that may trigger the onset of the critical state in each CA model, as well as the essential conditions conducive to the development of SOC characteristics in a system. This research not only sheds light on the complexities inherent in various systems but also provides valuable insights into the interconnected nature of phenomena that, at first glance, appear to be isolated. It enhances our understanding of the intricate ways simple patterns can evolve into complex and unpredictable dynamics.