Spatiotemporal clustering and temporal order in the excitable BZ reaction

The prototype experimental example of "spontaneous" pattern formation in an unstirred chemical medium is the oscillatory Belousov-Zhabotinsky (BZ) reaction: target patterns of outward-moving concentric rings are readily observed when the reaction is run in a thin layer in a Petri dish. In many experimental runs, new target centers appeared to form closer to pre-existing target centers than expected in a randomized model. Here we describe a simple direct test for the presence of temporal order in the spatiotemporal dynamics of target nucleation, and apply this test to detect significant temporal order in target formation in the ferroin-catalyzed BZ reaction. We also describe how mixing heterogeneity can generate temporal order, even in the absence of heterogeneous physical nucleating centers.