|Depending on the connectivity recurrent networks of simple computational units canshow very different types of dynamics ranging from totally ordered to chaotic. We analyze how thetype of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gatesdriven by a time varying input signal depends on the parameters describing the distribution of theconnectivity matrix. In particular we calculate the critical boundary in parameter space where thetransition from ordered to chaotic dynamics takes places. Employing a recently developed frameworkfor analyzing real-time computations we show that only near the critical boundary such networks canperform complex computations on time series. Hence, this result strongly supports conjectures thatdynamical systems which are capable of doing complex computational tasks should operate near theedge of chaos, i.e. the transition from ordered to chaotic dynamics.