Joel C. Langer and David A. Singer, The lemniscatic chessboard,
Forum Geometricorum, 11 (2011) 183--199.

Abstract.   Unit speed parametrization of the lemniscate of Bernoulli is given by a simple rational expression in the lemniscatic sine function. The beautiful structure of this parametrization becomes fully visible only when complex values of the arclength parameter are allowed and the lemniscate is viewed as a complex curve. To visualize such hidden structure, we will show squares turned to spheres, chessboards to lemniscatic chessboards.

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