  We present a universal view on diffusive behaviour in chaotic spatially
extended systems for anisotropic and isotropic media. For anisotropic systems,
strong chaos leads to diffusive behaviour (Brownian motion with drift) and weak
chaos leads to superdiffusive behaviour (L\'evy processes with drift). For
isotropic systems, the drift term vanishes and strong chaos again leads to
Brownian motion. We establish the existence of a nonlinear Huygens principle
for weakly chaotic systems in isotropic media whereby the dynamics behaves
diffusively in even space dimension and exhibits superdiffusive behaviour in
odd space dimensions.
