Topological Characterization of Spiral Defect Chaos

Computational Homology is used as a measure of the complexity of geometric structures in the weakly turbulent state of spiral defect chaos in experiments on Rayleigh-Bénard convection. Different attractors of spiral defect chaos are distinguished by their homology. This technique reveals asymmetric patterns. In addition global stochastic ergodicity is observed for system parameter values where locally chaotic dynamics has been previously reported.