Brains and Projective Functions

Introduction: Analytic functions perform a conformal mapping of the complex plane or of the threedimensional space to itself. Examples are the classical fractal function of squaring complex numbers and its reversed function, which will project any point z to its two complex square roots at + and – sqrt(z). The projection of the receptive field of the retina to the area V1 is described quite well by the function of the complex logarithm(1). Each point z on the complex plane, or, in spatial functions, in 3D-space, is interpreted as a neural column. The trajectory of the projective function from z to w describes th…