The fixed scale transformation approach to spatiotemporal intermittency in coupled map lattices

A one dimensional array of nonlinear maps with Laplacian couplings is studied at the phase transition between the asymptotically “turbulent” and “laminar” phases. Along the critical boundary, where spatiotemporal intermittency is observed, turbulent sites form a fractal set. The fixed scale transformation approach allows us to simultaneously determine the fractal dimension of the turbulent sites and the invariant asymptotic measure. Defining scale invariant conditional probabilities, and taking into account the nearest neighbour correlations exactly, we determine an asymptotic distribution function for the variables pertaining to sites on or neighbouring the turbulent clusters at any given level of coarse graining and obtain the fractal dimension analytically.