THE REMARKABLE KALEIDOSCOPIC DECOMPOSITIONS OF THE BIVARIATE GAUSSIANDISTRIBUTION

The construction of bivariate Gaussian distributions by Puente and Kle banoff,(1) as transformations of diffuse probability distributions via space-filling fractal interpolating functions is reviewed. It is show n that the ergodic theorem,(2) which allows a simple computer implemen tation of the construction for some diffuse measures, leads in a great many instances, to unexpected kaleidoscopic patterns of exotic nature , which, when added, yield the bivariate Gaussian distribution. Exampl es of such patterns, some resembling natural shapes, are presented.