Fractal basin boundaries in coupled map lattices

It has been suggested that spatiotemporal dynamical systems cannot exhibit fractal basin boundaries, as interactions among chaotic elements at different spatial sites may destroy fine scale phase-space structures. We present evidence of an extreme type of fractal basin boundary in spatiotemporal chaotic systems modeled by globally coupled, two-dimensional maps. The existence of fractal basin boundaries for these systems indicates an extreme sensitive dependence of asymptotic attractors on both initial conditions and parameters.