Three-Fold Development

This sculpture is based on the first five generations of a fractal curve. The starting point is a circle, and the first iteration produces a three-lobed form. With each iteration, the number of lobes is tripled. The spacing between features is essentially constant throughout a layer, while the three-fold symmetric boundary of the curve becomes increasingly complex. A hexagonal version of this curve is found in Benoit Mandelbrot's book "The Fractal Geometry of Nature". This hyperbolic surface is reminiscent of naturally-occurring corals. The sculpture measures 13" in both diameter and height. It was inspired in part by a 3D-printed model created by Henry Segerman. The sculpture won the 2014 Joint Mathematics Meetings Art Exhibition Prize for Best Textile, Sculpture, or Other Medium.

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Copyright 2013 Robert Fathauer