Loxodromic Spirals in M. C. Escher's Sphere Surface

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Loxodromic spirals are the analogues in spherical geometry of logarithmic spirals on the plane. M.C. Escher's 1958 woodcut Sphere Surface is an image of black and white fish arranged along eight spiral paths on the surface of a sphere. By connecting the plane and spherical models of the complex numbers, we show that Sphere Surface is the conformal image on the sphere of a tessellation of fish on the plane, and that the spirals running through the fish are indeed loxodromic spirals to a high degree of accuracy.

Original Citation

Marcotte, J. & Salomone, M. (2014). Loxodromic Spirals in M. C. Escher's Sphere Surface. Journal of Humanistic Mathematics: 4(2), 25-46. https://doi.org/10.5642/jhummath.201402.04