We assume that the mammalian neocortex is built up out of some six layers which differ in their morphology and their external connections. Intrinsic connectivity is largely excitatory, leading to a considerable amount of positive feedback. The majority of cortical neurons can be divided into two main classes: the pyramidal cells, which are said to be excitatory, and local cells (most notably the non-spiny stellate cells), which are said to be inhibitory. The form of the dendritic and axonal arborizations of both groups is discussed in detail. This results in a simplified model of the cortex as a stack of six layers with mutual connections determined by the principles of fibre anatomy. This stack can be treated as a multi-input-multi-output system by means of the linear systems theory of homogeneous layers. The detailed equations for the simulation are derived in the Appendix. The results of the simulations show that the temporal and spatial behaviour of an excitation distribution cannot be treated separately. Further, they indicate specific processing in the different layers and some independence from details of wiring. Finally, the simulation results are applied to the theory of visual receptive fields. This yields some insight into the mechanisms possibly underlying hypercomplexity, putative nonlinearities, lateral inhibition, oscillating cell responses, and velocity-dependent tuning curves.