When interaction among regularly firing neurons is simulated (using measured cortical response profiles as experimental input), besides complex network dominated behavior, embedded periodicity is observed. This is the starting point for our theoretical analysis of the potential of neocortical neuronal networks for synchronized firing. We start from the model that complex behavior, as observed in natural neural firing, is generated from such periodic behavior, lumped together in time. We address the question of whether, during periods of quasistatic activity, different local centers of such behavior could synchronize, as required, e.g., by binding theory. It is shown that for achieving this, methods of self-organization are insufficient - additional structure is needed. As a candidate for this task, thalamic input into layer IV is proposed, which, due to the layer's recurrent architecture, may trigger macroscopically synchronized bursting among intrinsically non-bursting neurons, leading in this way to a robust synchronization paradigm. This collective behavior in layer IV is hyperchaotic; its characteristic statistical descriptors agree well with the characterizations obtained from in vivo time series measurements of cortical response to visual stimuli. When we evaluate a novel, biological relevant measure of complexity, we find indications that the natural system has a tendency of tuning itself to the regions of highest complexity.