170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 225 10. 1 INTRODUCTION 225 π/2 y π/2 ππ/2 3π/23π/2 π/2 π/2 π 3π/2 3π/23π/20 0 Visual field (a)Striate cortexx (b) Striate cortex transfor med (c)y x0π Figure 10. 7 The retino-cortical map. (a) Visual field, (b) the actual cortical map, comprising rightandlefthemispheretransforms,(c)atransformedversionofthecorticalmap. Thetwotrans-formsare realigned sothat both foveal regions correspondto x=0. It should now be clear that the logarithmic map from retina to V1 provides a constant area or number of cortical neurons for the analysis of retinal stimuli independent of their retinal location, that is, V1 is optimized for the analysis of retinal images. Similar properties arefound inall other sensory cortices. 10. 1. 3 Form constants in cortical coordinates We now apply the retino-cortical map to the form constants. Figure 10. 8 shows, for example, the funnel and spiral images of figure 10. 3 mapped into cortical coor-dinates. It will be seen that both images are mapped into noisy stripes in cortical coordinates. These correspond to the plane waves discussed earlier and reflect the symmetries of the Euclidean group 𝔼(2). This analysis and the resulting images in cortical coordinates were first worked out by Ermentrout and Cowan (1979). 10. 1. 4 The Turing mechanism Thestartingpointofthe Ermentrout-Cowanworkwastherecognitionthattheform constants were stripe patterns or combinations of stripe patterns that generated