This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Kluver into four groups called form constants comprising (a) gratings, lattices, fretworks, filigrees, honeycombs and checkerboards (b) cobwebs (c) tunnels, funnels, alleys, cones and vessels and (d) spirals. This paper describes a mathematical investigation of their origin based on the assumption that the patterns of connection between retina and striate cortex, the retino-cortical map - and of neuronal circuits in V1, both local and lateral, determine their geometry.