Ice Crystals Inside the Bell


Carlos E. Puente, Marta G. Puente




A recent universal construction of bivariate Gaussian distributions, leading to unforeseen kaleidoscopic decompositions of circular bells in terms of a host of elegant patterns having arbitrary n-fold symmetries, is reviewed. It is shown, via a variety of examples, that such patterns, revealed by iterating simple affine mappings yielding space-filling fractal interpolating functions in three dimensions, encompass the common 6-fold geometric structure encountered in natural ice crystals. It is illustrated how both stellar and sectored crystals may be "grown'' in the "fullness of dimension'' via a variety of iteration schemes, leading to the conclusion that such sets are mathematical designs concealed inside the bell.