Neurones are characterized by a sigmoid nonlinearity comprising a threshold, followed by a regime of monotonically increasing spike rates, and finally a region where very high input leads to saturation. Given this commonality, the unique capabilities of the brain are determined by the topology of connections among groups of excitatory and inhibitory neurones. I will explore the roles of distinct neuronal connectivity in modelling two visual phenomena. The first is the transition (via hysteresis) from depth perception (stereopsis) to the default oscillation of binocular rivalry when the two stimuli are too disparate for fusion. This requires two spatially distributed populations of monocular excitatory neurones interacting via two inhibitory populations with quite distinct connectivities. Then I shall briefly consider requirements on the connectivity of distributed excitatory and inhibitory neural populations to generate the hyperchaos observed in a visuomotor task and in the resting electroencephalogram. Results show that both the spatial pattern of connections and the connection strengths are critical to our understanding.