COLLECTIVE PATTERNS ARISING OUT OF SPATIOTEMPORAL CHAOS

We present a simple mathematical model in which a time averaged patter n emerges out of spatio-temporal chaos as a result of the collective a ction of chaotic fluctuations. Our evolution equation possesses spatia l translational symmetry under periodic boundary conditions. Thus the spatial inhomogeneity of the statistical state arises through spontane ous symmetry breaking. The transition from a state of homogeneous spat io-temporal chaos to one exhibiting spatial order is explained by intr oducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.