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Home > 2016 Mathematical Art Exhibition
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"A Radin-Conway Pinwheel Lace Sampler," by Douglas G. Burkholder (Lenoir-Rhyne University Hickory, NC)

Digital Print, 50 x 50 cm, 2015

This artwork evolved from a search for beauty and patterns within Conway and Radin’s non-periodic Pinwheel Tiling of the plane by 1x2 right triangles. The Pinwheel tiling can be created by repeatedly subdividing every triangle into five smaller triangles. This lace resulted from alternately subdividing triangles and removing triangles. Triangles are removed based upon their location in the next larger triangle. First, on the macro level, the five distinctive removal rules are applied one to each row. This removal rule is especially easy to see in the bottom row. These same five rules are then applied, on the micro level, to the columns. The remaining triangles form a sampling of twenty-five styles of lace generated by the Pinwheel tiling. --- Douglas G. Burkholder

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American Mathematical Society