Cortical magnification has been measured with different techniques in many primates, including humans. The most popular models assume a value reciprocal to eccentricity, and are therefore rotation symmetric. To simulate the location of a projected stimulus, a real mapping function is needed. We use the complex logarithm log(z+a)—introduced for this purpose by Schwartz (1977 Biological Cybernetics 25 181 – 194), which is close to recent brain imaging results in humans and macaque monkeys. The model contradicts the idea of symmetric magnification and the linear model implicitly used by most anatomists. Our model gives a quantitative correspondence from visual field to striate cortex and vice versa, which we use to relate topology and geometry of cortical structures such as ocular dominance stripes, orientation fields, and cytochrome oxidase blobs in V1 to the visual field. This model may serve to relate empirical knowledge about spatial properties of these brain structures to psychophysical stimulus arrangements. Together with the description of cell densities, the point-to-point (and thus simplified) model may be used as a basis for formalising convergence and divergence properties of connections in neural maps.
