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Complexity of the Fibonacci snowflake

2011/03/29 by Alexandre Blondin Massé, Massé, Alexandre Blondin, Srečko Brlek +5
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #math.MG

paper · pdf · doi:10.48550/arxiv.1103.6171

6 pages, 1 figure

arxiv created 2011/03/29 · arxiv updated 2011/04/01

Abstract

The object under study is a particular closed curve on the square lattice \Z2 related with the Fibonacci sequence Fn. It belongs to a class of curves whose length is 4F3n+1, and whose interiors by translation tile the plane. The limit object, when conveniently normalized, is a fractal line for which we compute first the fractal dimension, and then give a complexity measure.

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