Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under periodic boundary conditions. Thus the spatial inhomogeneity of the statistical state arises through spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations. (c) 1996 American Institute of Physics.