Spatial and temporal averages in chaotic patterns

We show that spatiotemporally complex patterns in the presence of a symmetry imposed by the container geometry can have ordered spatial and temporal averages. The system studied was the K\"uppers-Lortz unstable state in rotating thermal convection. As the control parameter {Δ}T was increased above onset, fluctuations about the ordered averaged state increased and the correlation of individual patterns with the averaged state decreased. The pattern fluctuations about the averaged state were highly correlated with the instantaneous heat transport fluctuations.