Geodesic
Chromatic Plane Compositions
In this article we are studying the general problem of coloring a periodical plane mosaic, carried out by the action of a crystallographic group. In the first epigraph, we discover the color stains for a plane tiling by means of the conceptualization of plane chromatic composition. The symmetries of a chromatic composition are studied and, in Theorem 1, the plane periodical chromatic compositions are characterized. The second epigraph is dedicated to establishing a method of obtaining the chromatic plane compositions without being necessary that all the colors intervene in equal proportion. The main theorem of the article is the Theorem 2 which by means of the color equation characterizes the successions of subgroups of a crystallographic group which may be the isotropy color groups of a chromatic plane periodic composition. The article is illustrated with multiple examples, extracted fundamentally from the Alhambra of Granada (Spain).
Classification : 20H15
Keywords: Mosaic, Symmetry, Group, Tiling, Crystallographic Groups 
@article{VM_2000_2_1_a2,
     author = {R. P\'erez-G\'omez and Ceferino Ruiz},
     title = {Chromatic {Plane} {Compositions}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2000_2_1_a2/}
}
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R. Pérez-Gómez; Ceferino Ruiz. Chromatic Plane Compositions. Visual Mathematics, Tome 2 (2000) no. 1. http://geodesic.mathdoc.fr/item/VM_2000_2_1_a2/