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.
"Jellyfish," by Kendra Lockman (Photographer, artist, and teacher, Oakland, CA)
Digital print, 20" x 24" , 2009. Two fractals are combined to mimic the shape of the jellyfish used to create this image. The "head" fractal uses the famous dragon curve iteration. Here, the first iteration maps the negative-sloped diagonal of the starting photograph to the lower edge, and also maps the same diagonal to the left edge. The "tail" fractal uses a double spiral iteration. The original photograph was taken at Monterey Bay Aquarium by the artist. "I began iterating photographs into fractals after watching a video on fractals, in which the point was made that whether you started with a single segment or a 2-dimensional photograph, the resulting fractal was the same. I explored this on my own and learned that it can be more visually interesting to expose each step of the iteration. Photographs interact with themselves at each iteration level to reveal new shape and structure. Fractals are appealing for their seemingly complex structures which bloom from often simple iteration rules. I find that using photographs in the iterations can make the fractals much more captivating than if they were created with abstract geometry. I work intensely between Photoshop and The Geometer's Sketchpad to create these images." --- Kendra Lockman (Photographer, artist, and teacher, Oakland, CA) kendralockmanphoto.com