Fig. 4

Variance is a decreasing function of spectral thinness. This is a plot of the variance of the random variable recording the number of times a given orientation is present on a straight line segment of fixed length. We considered here Invariant Gaussian Random Fields with uniform power spectra, and plotted the variance as a function of spectral width. For each percentage of the mean wavenumber, we displayed two outputs to give an idea of the attained precision. A low value for variance, here expressed in the unit given by the square of the expectation, corresponds to a field whose hypercolumns have relatively constant size across the resulting orientation map; the results displayed here show that a very regular hypercolumnar organization is quite compatible with stochastic modeling, and is a direct consequence of the spectral thinness condition found in models. Moreover, the horizontal slope at zero shows that as regards the global properties of quasi-periodic maps, there is very little difference between a theoretically ideal monochromaticity and a more realistic (and more model-independent) spectral thinness