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.

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 FILE 11/27

# "Mandelbrot's Chandelier," by Jeffrey Stewart Ely (Lewis and Clark College, Portland, OR)

## 24" x 18", Digital print on archival paper, 2012 The spherical chandelier is composed of squarish lenses. Inside the chandelier is a cubical object that has been painted with the Mandelbrot set. Each of the lenses gives us a different view of this object. This interior object and the individual lenses are all variations of the quartic surface, x^4 + y^4 + z^4 = 1. The image was constructed using the ray tracing technique and required the solution of over a billion quartic equations, At^4 + Bt^3 + Ct^2 + Dt + E = 0, as the individual rays through each pixel were followed into this mathematical world of quartic surfaces. Snell's law was used to correctly model the refraction of the rays as they passed through the lenses. Finally, the background also shows a portion of the Mandelbrot set. -- Jeffrey Stewart Ely

 Art & Music, MathArchives Geometry in Art & Architecture, by Paul Calter (Dartmouth College) Harmony and Proportion, by John Boyd-Brent International Society of the Arts, Mathematics and Architecture Journal of Mathematics and the Arts Mathematics and Art, the April 2003 Feature Column by Joe Malkevitch Maths and Art: the whistlestop tour, by Lewis Dartnell Mathematics and Art, (The theme for Mathematics Awareness Month in 2003) MoSAIC - Mathematics of Science, Art, Industry, Culture Viewpoints: Mathematics and Art, by Annalisa Crannell (Franklin & Marshall College) and Marc Frantz (Indiana University) Visual Insight, blog by John Baez