Symmetry breaking of three self-organization rules:A general theory for the origin of complexity

TL;DR

This paper proposes a unified theory that explains the emergence of complex patterns in nature through symmetry breaking of three fundamental self-organization rules, linking physics principles to complexity.

Contribution

It introduces a novel framework showing how breaking symmetry in simple rules leads to diverse natural patterns, unifying complexity origins across disciplines.

Findings

Reproduces various natural patterns like Turing patterns, fractals, and waves.

Discovers phenomena such as pattern percolation and phase transitions.

Establishes a deep connection between physics principles and complexity emergence.

Abstract

Complex spatiotemporal patterns in nature significantly challenge reductionism-based modern science. The lack of a paradigm beyond reductionism hinders our understanding of the emergence of complexity. The diversity of countless patterns undermines any notion of universal mechanisms. Here, however, we show that breaking the symmetry of three simple and self-organization rules give rise to nearly all patterns in nature, such as a wide variety of Turing patterns, fractals, spiral, target and plane waves, as well as chaotic patterns. The symmetry breaking is rooted in basic physical quantities, such as positive and negative forces, space, time and bounds. Besides reproducing the hallmarks of complexity, we discover some novel phenomena, such as abrupt percolation of Turing patterns, phase transition between fractals and chaos, chaotic edge in travelling waves, etc. Our asymmetric self-organization theory established a simple and unified framework for the origin of complexity in all fields, and unveiled a deep relationship between the first principles of physics and the complex world