The inhibition that is exerted mutually among receptor units (ommatidia) of the compound eye of Limulus is less for units widely separated than for those close together. This diminution of inhibition with distance is the resultant of two factors: (1) the threshold of inhibitory action increases with increasing distance between the units involved; and (2) the coefficient of inhibitory action decreases with increasing distance.
The discharge of nerve impulses from ommatidia at various distances from one another may be described quantitatively by a set of simultaneous linear equations which express the excitatory effects of the illumination on each ommatidium and the inhibitory interactions between each ommatidium and its neighbors. The values of the thresholds and coefficients of inhibitory action, which appear as parameters in these equations, must be determined empirically: their dependence on distance is somewhat irregular and cannot yet be expressed in an exact general law. Nevertheless the diminution of inhibitory influences with distance is sufficiently uniform that patterns of neural response generated by various patterns of illumination on the receptor mosaic can be predicted qualitatively. Such predictions have been verified experimentally for two simple patterns of illumination: an abrupt step in intensity, and a simple gradient between two levels of intensity (the so-called Mach pattern). In each case, transitions in the pattern of illumination are accentuated in the corresponding pattern of neural response.