Complexity and criticality in Laplacian growth models

TL;DR

This paper investigates how simple growth laws in systems like diffusion limited aggregation lead to complex, scale-invariant patterns and intrinsic noise, indicating self-organized criticality driven by pattern complexity.

Contribution

It demonstrates that pattern complexity, rather than external randomness, causes scale-invariant noise spectra in Laplacian growth models, linking complexity to criticality.

Findings

Complex patterns generate scale-invariant noise spectra.

Intrinsic noise is independent of external stochastic factors.

Pattern complexity drives self-organized criticality.

Abstract

We analyze the dynamical evolution of systems which obey simple growth laws, like diffusion limited aggregation or dielectric breakdown. We show that, if the developing patterns is sufficiently complex, a scale invariant noise spectrum is generated, in agreement with the hypothesis that the system is in a self organized critical state. The intrinsic noise generated in the evolution is shown to be independent of the (extrinsic) stochastic aspects of the growth. Instead, it is related to the complexity of the generated pattern.