Beyond the Third Dimension
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Artist's Comments on the Necklaces

The subject of each Necklace is the graph of a function of a complex variable. First the complex squaring operation, then the cubing function. In each case there are five images, starting with a disc and ending with a doubly or triply covered disc, with intermediate steps possessing three- or fourfold symmetry. The first of these pictures appeared in rotated form as "Z-Squared Crescent" on the cover of the Notices of the American Mathematical Society issue of November 1996, with a technical explanation inside.