Complexity of the Fibonacci snowflake

Details Complexity of the Fibonacci snowflake Complexity of the Fibonacci snowflake

2011-03-29

arxiv.org/abs/1103.6171v1

Mathematics

Metric Geometry

6 pages, 1 figure

Scientific paper

The object under study is a particular closed curve on the square lattice $\Z^2$ related with the Fibonacci sequence $F_n$. It belongs to a class of curves whose length is $4F_{3n+1}$, 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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