2.1.0.5

The cortex is often called the iso-cortex because of the repeated structures of which it is comprised (Douglas & Martin, 1991). The smallest scale of structure is the minicolumn which, in the monkey, consists of 30 adjacent pyramidal cell shafts in layers 2/3 packed within a diameter of 23 *μ*m (Peters & Sethares, 1996). There are approximately 20 cell bodies within a minicolumn in layers 2/3. The next largest physical scale in V1 at which repeated structures occur is the cortical column (Lund et al., 2003). The cortical column is 200 *μ*m in diameter and is the scale at which long-range patchy connections terminate. A number of anatomical and functional markers repeat at a larger scale of 400 *μ*m. These include the distance between CO blobs, the approximate periodicity of the orientation preference map, and the spatial scale of a single ocular dominance band (Lund et al., 2003). Orientation pinwheels are also of approximately this spatial scale. Each of these functional markers has been shown to be closely related to the system of patchy connections, in which like response preference connects to like, and the inter-patch distance in V1 has this same periodicity of 400 *μ*m (Bartfeld & Grinvald, 1992); (Malach et al., 1993); (Bosking et al., 1997). The largest spatial scale is V1 itself, which is some 4 cm wide in the monkey. There are of the order of 10,000 CO blobs in layers 2/3 of V1 (Murphy et al., 1998), and ocular dominance bands of 120 in number (Horton & Hocking, 1998), suggesting that the multiple response property maps with periodicity of 400 *μ*m repeat around 10,000 times over layers 2/3 of V1. The input connections from the LGN arborize at a range of scales within layer 4C of V1. These inputs are arranged in block-like structures at the approximate scale of an ocular dominance band in layer 4C, but at a finer scale of approximately one column in layer 4C (Fitzpatrick et al., 1985). Further fine scale arborizations occur at approximately the scale of one minicolumn in layer 4A. At the global scale of the cortex, inputs from the LGN are organized into a retinotopic mapping of the visual field (Rolls and Cowey 1970; (Tootell et al., 1988). Connectivity into the layers 2/3

self-similar super-hexagons tile the plane in a recursively modular manner. As an example, a super-hexagon of size 7<sup>2</sup> = 49 and its concomitant addressing scheme is displayed in Fig. 1 (a).

<sup>185</sup> Cortical Specification of a Fast Fourier

Transform Supports a Convolution Model of Visual Perception

(a) Hexagonal SHIA

(b) Rectangular SHIA

Fig. 1. Displays the two-level addressing scheme of SHIA: (a) Hexagonal and (b) Rectangular. In the latter case, each rectangle has a designated positive integer address expressed in base

five. An example of this addressing scheme is displayed in Fig. 1 (b).

of V1 occurs via a number of anatomical routes, apart from the well described feedforward connections from layer 4 (Fitzpatrick et al., 1985). Other routes of information transfer include extra-striate feedback (Rockland et al., 1994); (Rockland & Vanhoesen, 1994); (Angelucci et al., 2002), long-range intrinsic fibres within V1 (Blasdel et al., 1985), as well as feedback from V1 to the lateral geniculate nucleus (Marrocco et al., 1982); (Briggs & Usrey, 2007), and diffusion of visual signal in the retina (Kruger et al., 1975); (Berry et al., 1999).
