Summary: Large scale spatiotemporal organization and enhanced periodicity are seen when a population of chaotic Rössler attractors is coupled through one or more of the variables. The resulting periodicity has been analyzed by means of return maps and by the projection of these maps as state variable dispersion histograms. Self-mapping of cells in the array, within dispersion criteria, yielded evidence of reverse bifurcation sequences, \(F^{\dots 8,4,2,1}\), expressed in the behavior of most of the 900 to 25 600 individual cells. Self-mapping is seen in spiral and periodic banded fields, but not in turbulent fields or in synchronous chaos. Coupling of arrays of periodic attractors leads to dispersion in self-mapping similar to that seen in the coupled chaotic arrays. Fixed patterns representing the bifurcation sequences that occur in these arrays were overlaid on the spiral field portraits.