Network structure of chaotic patterns

Abstract

We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the state of spiral defect chaos state in experiments on Rayleigh Benard convection. These measure the role of boundary influence on the dynamics, and suggest an exponential distribution for the length of edges in the pattern. We also indicate a systematic method to study hierarchies of defect interactions based on the network structure.