170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 229 10. 2 A NEW MATHEMATICAL FORMULATION OF V1 CIRCUITRY 229 (a) (b) Figure 10. 11 Lateralconnectionsmadeby V1cellsin Owl Monkey(a)and Tree Shrew(b)V1. A radioactive tracer is used to show the locations of all terminating axons from cells in a central injection site, superimposed on an orientation map obtained by optical imaging. Source: Repro-duced with permission of Nature Publishing Group. ( Seeinsertforcolourrepresentationofthis figure. ) 1992). Figure 10. 11b shows a similar arrangement in the Tree Shrew, where the anisotropy of the longer-ranged connections is more striking. We can conclude from this data that local connectivity in V1 is isotropic, and is predominantly inhibitory, whereas lateral connectivity is anisotropic, and from Gilbert's data that it is predominantly excitatory. Thus there is an anisotropy in the inverted Mexican Hat, representing the intrinsic connectivity of V1, so that iso-orientation preference patches connect mainly to other iso-orientation patches with the same preference. [Note that Mitchison and Crick (1982) conjectured that such was the case, based on (then) unpublished data collected by Rockland and Lund (1982, 1983). ] Figure 10. 12 shows a diagram of such a connectivity pattern between Hubel-Wiesel hypercolumns (Hubel and Wiesel, 1974b). Hypercolumn was the term introduced by Hubel and Wiesel to denote a patch of V1 containing two completesetsofiso-orientationpreferencepatchesrunningfrom0∘to180∘,oneset driven by images from the right eye, the other by images from the left eye. It turns out that the diameter of such a hyper column corresponds precisely to the 2-point resolutionlimitoftheeyes,thatis,the visualacuity ateachpointinthevisualfield. This limit increases with r, the radial component of the retinal coordinate system, and translates to the (constant) diameter of any hypercolum in V1. In the human cortex this diameter is approximately 1. 5mm. Thus the direction of the lateral connections between neighbouring hypercolumns is determined by the common orientation preference of the patches they connect. Interestingly,thissameanisotropywasintroducedby Zweckand Williams(2000, 2004)intwopaperson Computer Visionasamethodofpreserving Euclideansym-metry in transforming from a continuous planar sheet to a discrete lattice or array, which is precisely what we do inour analysis of hallucinations.