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Math ImageryThe 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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Home > Mike Field :: Realizations

"UncertainEnd," by Mike Field (University of Houston)

"UncertainEnd" is a section of a planar repeating pattern of type p'_{c}gg (or, in Coxeter notation, cmm/pgg). Ignoring the colors, the underlying pattern is of type cmm and is the superposition of two colored patterns, each of type pgg. The pattern was generated using an iterated function system defined on the two-dimensional torus. The resulting pattern on the torus was lifted to the plane to obtain a repeating pattern. The coloring reflects invariant measures on each of the underlying patterns of type pgg and takes account of overlap, as well as symmetry, using algorithms designed for revealing detail hidden in the dynamics. The original image was created in 2001. --- Mike Field

InHotPursuitAMS.jpg ThornsAMS.jpg UncertainEndAMS.jpg DNA_QuiltAMS.jpg saw.gif