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.
"Ribbon weaving no. 1," by Christine Liu, Ergun Akleman, Qing Xing (Texas A&M University, College Station, TX)
Digital print, 13” x 9”, 2009. This plain-weaving model is automatically generated from the algorithm in the paper Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems. Cycles of the plain-woven object are created from any manifold-mesh surface by twisting every edge of the manifold mesh and convert the plain-weaving cycles to 3D thread structures. Users interactively control the shape of the threads and the size of gaps with a set of parameters creating a wide variety of unique plain- weaving patterns. This generated weaving model has 16 identical closed cycles with user control over the width, displacement, and curvature of the weaving yarns. "Inspired by the detail of that which is supple, Christine Liu continually updates her mathematical techniques with a self-driven craft refinement in classical training. Paint, sculpture and architectural drafting have all formulated a longstanding basis for an appropriate representation in her personal form of rational digital expression. Here, a timeless balance of scale, form and simulated vernacular methods are evident in the otherwise conventional mathematical art expression. Inspiration for the selected style and palette come from classic vibrant colored ribbon fabric and various types of ribbon weaving crafts. This piece is rendered and produced through Maya and Photoshop." --- Christine Liu, Ergun Akleman, Qing Xing (Texas A&M University, College Station, TX)