Geodesic
Ice Crystals Inside the Bell
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.
Classification : 20H15 
@article{VM_2004_6_1_a1,
     author = {Carlos E. Puente and Marta G. Puente},
     title = {Ice {Crystals} {Inside} the {Bell}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2004_6_1_a1/}
}
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UR  - http://geodesic.mathdoc.fr/item/VM_2004_6_1_a1/
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%A Marta G. Puente
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Carlos E. Puente; Marta G. Puente. Ice Crystals Inside the Bell. Visual Mathematics, Tome 6 (2004) no. 1. http://geodesic.mathdoc.fr/item/VM_2004_6_1_a1/