Mach bands in the lateral eye of Limulus

Patterns of optic nerve activity were computed for stationary step patterns of illumination from theoretical models of lateral inhibiton based on revised Hartlin-Ratliff equations. The computed response patterns contain well-defined Mach bands which match closely in amplitude and shape those recorded from single optic nerve fibers of the Limulus lateral eye. Theory and experiment show that the amplitude of the Mach bands is reduced by in inhibitory nonlinearity, the width of the Mach bands is approximately equal to the lateral dimension of the inhibitory field, but the shapes of the Mach bands are poor indices of the precise configuration of the inhibitory field. Theorems are proved establishing the equivalence of Mach-band patterns for models of different dimensions and a uniqueness condition for solutions of the piecewise linear model.