The crawling locomotion and shape of eukaryotic cells have been associated with the stochastic molecular dynamics of actin and its protein regulators, chiefly Arp2/3 and Rho family GTPases, in making a cytoskeleton meshwork within cell extensions. However, the cell's actin-dependent oscillatory shape and extension dynamics may also yield insights into locomotory mechanisms. Confocal observations of live Dictyostelium cells, expressing a green fluorescent protein^actin fusion protein, demonstrate oscillating supramolecular patterns of filamentous actin throughout the cell, which generate pseudopodia at the cell edge. The distinctively dissipative spatio-temporal behavior of these structures provides strong evidence that reversible actin filament assembly propagates as a self-organized, chemical reaction^diffusion wave. ß