COMPLEXITY OF THE FIBONACCI SNOWFLAKE
Abstract
The object under study is a particular closed and simple 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 tile the plane by translation. The limit object, when conveniently normalized, is a fractal line for which we compute first the fractal dimension, and then give a complexity measure.
References
- Ann. Sci. Math. Québec 35(2), 141 (2011). Google Scholar
- A. Monnerot-Dumaine, The Fibonacci word fractal (2009), Available at http://hal.archives-ouvertes.fr/hal-00367972/fr/ . Google Scholar
- Mém. Acad. Sci. 22, 3 (1850). Google Scholar
- Philos. Trans. Roy. Soc. Lond. 158, 181 (1868). Crossref, Google Scholar
- Colloq. Math. 3, 1 (1954). Crossref, Google Scholar
- Fractal Geometry and Analysis,
NATO ASI series 346, eds.J. Bélair and S. Dubuc (Kluwer Academic Publishers, 1991) pp. 325–366. Crossref, Google Scholar ,