# Conan Chadbourne

My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the frequently mystical or cosmological significance that is often attributed to such imagery. Mathematical themes both subtle and overt appear in a broad range of traditional art, from Medieval illuminated manuscripts to Buddhist mandalas, intricate tilings in Islamic architecture to restrained temple geometry paintings in Japan, complex patterns in African textiles to geometric ornament in archaic Greek ceramics. Often this imagery is deeply connected with how these cultures interpret and relate to the cosmos, in much the same way that modern scientific diagrams express the scientific worldview. I am especially interested in symmetry as a mechanism for finding order in the universe, from its intuitive appearance in ancient cosmological diagrams to its important role in modern theoretical physics, and my recent works explore various forms of symmetry.

This work is part of a series of visual meditations on the symmetry groups of the two-dimensional Euclidean plane. This print focuses on the symmetry group p4 (orbifold signature 442) and its presentation by a particular set of two generators (generators {a,b} with relations aaaa = bb = abababab = 1). In the main section of the image, a network of connected dots forms a stylized Cayley diagram for this presentation of p4, while the small motifs at the bottom describe the local features of the orbifold for the symmetry group (in this case, one 2-fold and two 4-fold gyration or "cone" points). The image is constructed from multiple hand-drawn elements and natural textures which are scanned and digitally manipulated to form a composite image and subsequently output as an archival digital print.

This work is part of a series of visual meditations on the symmetry groups of the two-dimensional Euclidean plane. This print focuses on the symmetry group p4 (orbifold signature 442) and its presentation by a particular set of three generators (generators {a,b,c}, with the relations aaaa = bbbb = cc = abc = 1). In the main section of the image, a network of connected dots forms a stylized Cayley diagram for this presentation of p4, while the small motifs at the bottom describe the local features of the orbifold for the symmetry group (in this case, one 2-fold and two 4-fold gyration or "cone" points). The image is constructed from multiple hand-drawn elements and natural textures which are scanned and digitally manipulated to form a composite image and subsequently output as an archival digital print.