The Artful Kaleidoscopes of the Circular and Spherical Bells

Carlos Puente
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 283–290 Regular Papers


The Gaussian bell, over one or more dimensions, is one of the most ubiquitous mathematical objects in science. This work explains, essentially summarizing previously published research, how the iteration of simple maps leads to universal constructions of bells, over two and three dimensions, which surprisingly define vast assortments of exotic kaleidoscopic decompositions of the circular and spherical bells in terms of crystalline patterns that include, among others, the geometric structure of ice crystals and that of the DNA rosette.