Abstract
A simple model of diffusively coupled genetic networks on a 1d lattice is considered as a case study for characterizing complex unpredictable dynamics in Lyapunov-stable spatially extended systems. This dynamical regime, corresponding to transient evolution lasting over times that grow exponentially with the system size, is shown to be associated to the existence of a multifractal attractor in the thermodynamic limit. Space-time averages of proper observables exhibit robust statistical properties for finite, sufficiently large samples.