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Home > 2017 Mathematical Art Exhibition

"Fractal Monarchs," by Doug Dunham and John Shier (University of Minnesota, Duluth)

Best photograph, painting, or print - 2017 Mathematical Art Exhibition

30 x 40 cm, color printer, 2016

This is a fractal pattern whose motifs are monarch butterflies. We modify our usual rule that motifs cannot overlap by allowing the antennas - but not the rest of the motif - to overlap another motif. Expanding on the area rule of the Goals statement, the area of the n-th motif is given by A/(zeta(c,N)(N+n)^c), where A is the area of the region, and zeta(c,N) is the Hurwitz zeta function, a generalization of the Riemann zeta function (for which N = 1; our algorithm starts with n = 0). For this pattern c = 1.26, N = 1.5, and 150 butterflies fill 72% of the bounding rectangle. --- Doug Dunham

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American Mathematical Society