Self Organized Critical Dynamic on the Sierpinski Carpet

TL;DR

This paper investigates self-organized criticality on the fractal Sierpinski carpet using an Ising-BCP model, revealing how topology influences critical dynamics and demonstrating improved efficiency over traditional lattices.

Contribution

It introduces a novel model and algorithm for self-organized criticality on fractal structures, highlighting the role of topology in critical dynamics.

Findings

Enhanced efficiency in reaching criticality on the Sierpinski carpet

Dependence of self-organized criticality on lattice topology

Potential applications in information transmission fields

Abstract

Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power-law with a non-integer exponent, i.e. a fractal. To achieve this, we proposed an Ising-BCP (bond-correlated percolation) model as the foundation for investigating critical dynamics. Within this framework, we outlined a feedback mechanism for critical self-organization and followed an algorithm for its numerical implementation. The results obtained from the algorithm demonstrated enhanced efficiency when driving the Sierpinski carpet towards critical self-organization compared to a two-dimensional lattice. This efficiency was attributed to the iterative construction of the lattice and the distribution of spins within it. The key outcome of our findings is a novel dependence of self-organized criticality on topology for this particular model, which may have several applications in fields regarding information transmission.