Symmetrology of art: coloured and generalized symmetries

AbstractThe paper describes general features and analyses a number of examples of various categories of colored and generalized symmetries used in visual arts. After a thorough discussion of the problems of symmetry analysis and construction of dichroic and colored patterns, examples of South American. Mexican, Egyptian, Celtic, New Guinean, Australian Aboriginal and Moorish, as well as 20th century ornamental art are analysed. It is shown that with the exception of the modern creations by Hinterreiter and Escher, colored symmetry has been used much less than dichroic symmetry and has remained largely limited to unidirectional color modulation of uncolored or originally dichroic patterns.From among the categories of generalized symmetry, similarity, affine- and perspective-projective transformations are discussed and illustrated as well as catamorphy and the plane groups in non-Euclidean planes. Finally, the notions of submotif, submesh, supermesh, twinning, pseudosymmetry, noncommensurability of patterns, positional and “occupational” order-disorder phenomena, local high symmetry, dissymetry, enhancement of symmetry, dichotomy, modulation, antiphase boundaries and the hierarchy and superposition of symmetries are applied to the world of visual arts