I saw this featured in the University of Minnesota Brief today:
Artists' statement: "The goal of our art is to create aesthetically pleasing fractal patterns,” stated Dunham. “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 butterfly - to overlap another butterfly. For the randomly placed butterflies to exactly fill the rectangular region in the limit, their areas must decrease in size according to a precise formula: the area of the n-th butterfly is given by A/(zeta(c,N)(N+n)^c), where A is the area of the rectangle, and zeta(c,N) is the Hurwitz zeta function. For this pattern c = 1.26, N = 1.5, and 150 butterflies fill 72% of the rectangle."
The algorithm is completely mystifying to me, but the pattern is really cool. I was drawing shapes like these just the other day and feel inspired to draw from this image to extend my own sketching.
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| Douglas Dunham and John Shier, "Fractal Monarchs" 30 x 40 cm digital print |
Artists' statement: "The goal of our art is to create aesthetically pleasing fractal patterns,” stated Dunham. “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 butterfly - to overlap another butterfly. For the randomly placed butterflies to exactly fill the rectangular region in the limit, their areas must decrease in size according to a precise formula: the area of the n-th butterfly is given by A/(zeta(c,N)(N+n)^c), where A is the area of the rectangle, and zeta(c,N) is the Hurwitz zeta function. For this pattern c = 1.26, N = 1.5, and 150 butterflies fill 72% of the rectangle."
The algorithm is completely mystifying to me, but the pattern is really cool. I was drawing shapes like these just the other day and feel inspired to draw from this image to extend my own sketching.
