It is chiefly within the superficial layers of 1 - 3 of the cerebral cortex that new properties are developed from relayed afferent information. The intrinsic circuitry of these layers is uniquely structured compared to the deeper layers; each pyramidal neuron connects laterally to other pyramids at a series of offset points spaced at regular intervals around it. As seen in tangential sections of layers 1 - 3, the pyramidal neuron axon terminal fields are roughly circular in cross section, forming a `polka dot' overall pattern of terminal distribution. In regions of peak density, the diameter of the circular fields matches the width of the uninnervated regions between the terminal fields. This dimension is also that of the average lateral spread of the dendrites of single pyramidal neurons making up the connections in each visual cortical area, a dimension which varies considerably between different cortical regions. Since every point across each cortical area shows similar laterally spreading patterns of connectivity, the overall array is believed to be a continuum of offset connectional lattices. It is also presumed that each pyramidal neuron, as well as projecting to separate points, receives convergent inputs from similar arrays of offset neurons. The geometry of local circuit inhibitory neurons matches elements of these lattices; basket neuron axons in these layers spread three times the diameter of the local pyramidal neuron dendritic fields while the basket neuron dendritic field matches that of the pyramidal cell. If both basket cell and pyramidal neuron at single points are coactivated by afferent relays, the basket axon might create a surround zone of inhibition preventing other pyramidal cells in the surrounding region being active simultaneously. As the pyramid develops its connections in this inhibitory field may fore each pyramidal neuron to send its axon out beyond the local inhibitory zone to find other pyramidal cells activated by the same stimulus. Since the basket neuron also contacts other basket neurons, by disinhibition through offset basket neurons, it will simultaneously encourage activity in pyramidal cells in a zone outside the limit of its axon field. This scaling of basket neuron axons is present in early postnatal cortex and it could lead to the punctate patterns of pyramidal neuron connectivity which also appear to develop postnatally. This anatomy might also produce the regular spacing of different functional attributes that is typical of visual cortical organization. Models that explore spatial geometries of excitation and inhibition resembling those described above are urgently needed to test current biological hypotheses underlying investigations of cerebral cortex.