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Christiane’s Hair

by Jaques Lévy Véhel and Franklin Mendivil

Year of Award: 2014

Publication Information: The American Mathematical Monthly, vol. 120, no. 9, November 2013, pp. 771-786.

Summary (adapted from the MAA Prizes and Awards booklet for MathFest 2014): Beginning with a striking visualization of stacked Cantor sets that reminded the first author of his wife Christiane’s braided hair, Lévy Véhel and Mendivil guide the reader through an exploration of the geometric and measure-theoretic properties of these fractal sets. The authors describe the constructions from different perspectives, using iterated function systems as well as ternary (and more general) expansions. While the horizontal cross-sections of their constructions are Cantor sets generated from the interval [0,1] with continuously changing gap parameters, the vertical view consists of many smooth strands, thus producing an appearance of a woman’s hair.

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About the Authors: (From the MathFest 2014 MAA Prizes and Awards Booklet)

Jacques Lévy Véhel is a Research Director at Inria, France. He studied at Ecole Polytechnique and received his Ph.D. in Applied Mathematics at Orsay University. His research interests lie in probability theory, statistics, harmonic analysis, and fractal geometry. He is also working in various applied areas, such as signal processing and financial modelling.

Franklin Mendivil is a Professor in the Department of Mathematics and Statistics at Acadia University in Nova Scotia, Canada. He started his studies by obtaining a BS in Civil Engineering but then switched to mathematics for his PhD (both at Georgia Tech). His research interests include general topology, applied probability, evolutionary optimization algorithms, and fractal geometry.

 

Subject classification(s): Geometry and Topology | Fractal Geometry
Publication Date: 
Wednesday, August 13, 2014

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