  We use a quantitative topological characterization of complex dynamics to
measure geometric structures. This approach is used to analyze the weakly
turbulent state of spiral defect chaos in experiments on Rayleigh-Benard
convection. Different attractors of spiral defect chaos are distinguished by
their homology. The technique reveals pattern asymmetries that are not revealed
using statistical measures. In addition we observe global stochastic ergodicity
for system parameter values where locally chaotic dynamics has been observed
previously.
