Complexity of the Fibonacci snowflake

Abstract

The object under study is a particular closed curve on the square lattice ${\mathbb{Z}}^2$ 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.

6 pages, 1 figure