The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Winter," by Veronika Irvine (University of Victoria, British Columbia, Canada)
White cotton, DMC Cebelia No 20, 2014
Periodic bobbin lace patterns can be described by a mathematical model. Key elements of the model are 1) a toroidal embedding of a directed graph describing the movement of pairs of threads and 2) a function that maps each vertex of the digraph to a braid word. Using an intelligent combinatorial search, over 100,000 patterns matching the fundamental properties of this model were found. Of these, three closely related patterns were chosen (see inset). The three patterns can be transformed into one another by a small number of changes. The submitted piece was designed to show a gradual transition from one pattern to the next resembling the transformation from perfect, large snowflakes to the slanted, driving snow of a blizzard. When I first learned to make bobbin lace, some 20 years ago, I was struck by its mathematical nature. The patterns are diagrams, not a linear set of instructions. The order in which braids are worked and most of the decisions about how threads should move so that they arrive in the correct position as needed, are left up to the lacemaker. Over the past 4 years, I have been developing a mathematical model for bobbin lace and discovering the joy of designing my own pieces. More information: http://arxiv.org/abs/1406.1532. --- Veronika Irvine (http://web.uvic.ca/~vmi/)