170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 237 10. 3 CONDITIONS FOR THE LOSS OF STABILITY OF THE HOMOGENEOUS STATE 237 (a) (b) Figure 10. 18 (a) Contoured square pattern on the square lattice. (b) Contoured hexagonal pat-ternon thehexagonal lattice. [Therearesomeotherdetailsthathavetobeworkedouttoobtaintheseplanforms withthecorrectscalings. See Bressloff etal. (2001)forsuchdetails. ]Thedetailslead to about 30-40 repetitions of the roll pattern around a circumference of the visual fieldcorrespondingtolength-scalesofabout2. 4-3. 2mm,sothecriticalwavelength 2𝜋∕qcat which patterns form is in this range. [This length-scale is consistent with a lattice spacing Lof some 0. 4-0. 5mm. ] The striking feature of these images is that each is an example of one of the four classes of form constants used by Klüver to classify hallucinatory images. Thus the above model has provided an answer as to why there are four, and only four, classes of form constants, that is, they correspond to only those V1 planforms with thesymmetries oftheaxialsubgroups 𝔻nofthe Euclidean group 𝔼(2)intheplane. 10. 3. 3 Some comments There are several aspects of this work that require further comment. 1. The analysis indicates that under certain conditions the planforms are either contoured or else non-contoured, depending on the strength of inhibition between neighbouring isoorientation patches. Ifsuchinhibitionisweak,individualhypercolumnsdonotexhibitanytendency to amplify any particular orientation. In normal circumstances such a prefer-ence would have to be supplied by inputs from the LGN. In this case, V1 can besaidtooperateinthe Hubel-Wieselmode. Ifthehorizontalinteractionsare stilleffective,thenplanewavesofcorticalactivitycanemerge,withnolabelfor