The empirical data of this manuscript are predominantly derived from previous studies [3] (link),[15] (link),[27] (link). The modeling and results presented here were implemented in Matlab 7.6 (Mathworks, MA). We provide the code in the Protocol S1 of Supplementary Materials, enabling concrete and unambiguous specification of the computing methods employed, and the possibility to further explore the parameter space. This computation was chosen to closely mimic procedures from empirical work [3] (link),[15] (link),[27] (link).
To test local and meridional anisotropy a finely meshed grid in the visual field was projected through the models. Squares of the grid were oriented in such a way that one side was orthogonal to eccentricity, while the other side was orthogonal to polar direction. In principle, anisotropies can be derived analytically [15] (link), however the computational approach implemented for this manuscript allows flexible and comparable testing of model variations. Since we provide the code, the reader can easily implement alternative model functions within the code and test these using the methods provided.
Local anisotropy for a given position in the projection was then calculated as the length ratio of the side oriented parallel to isoeccentricity lines (i.e. Me) divided by the length of the side parallel to isopolar lines (Mp). Meridional anisotropy is calculated based on the surface area of a set of squares with the same eccentricity, but varying polar position. Meridional anisotropy for a given position in the projection was then calculated as the surface of a square at this position (Ma(P,E′)) divided by the surface of a square at the horizontal meridian in V1 (Ma(0,E′)). Predicted areal magnification M (Figure 6c , Figure 9c ) was estimated by projecting isoeccentricity bands. Areal magnification is then the square root of the projected surface divided by the surface in visual space. Analytical considerations [15] (link), have shown that this estimate of M is the most informative.
To test local and meridional anisotropy a finely meshed grid in the visual field was projected through the models. Squares of the grid were oriented in such a way that one side was orthogonal to eccentricity, while the other side was orthogonal to polar direction. In principle, anisotropies can be derived analytically [15] (link), however the computational approach implemented for this manuscript allows flexible and comparable testing of model variations. Since we provide the code, the reader can easily implement alternative model functions within the code and test these using the methods provided.
Local anisotropy for a given position in the projection was then calculated as the length ratio of the side oriented parallel to isoeccentricity lines (i.e. Me) divided by the length of the side parallel to isopolar lines (Mp). Meridional anisotropy is calculated based on the surface area of a set of squares with the same eccentricity, but varying polar position. Meridional anisotropy for a given position in the projection was then calculated as the surface of a square at this position (Ma(P,E′)) divided by the surface of a square at the horizontal meridian in V1 (Ma(0,E′)). Predicted areal magnification M (
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