Authors: Patricia Alonso-Ruiz; Uta R. Freiberg
Addresses: Departement Mathematik, Emmy-Noether Campus, Walter-Flex Straße 3, 57072 Siegen, Germany. ' Departement Mathematik, Emmy-Noether Campus, Walter-Flex Straße 3, 57072 Siegen, Germany
Abstract: The famous game Towers of Hanoi is related with a family of so-called Hanoi-graphs. We regard these non-self-similar graphs as geometrical objects and obtain a sequence of fractals (HGa)a converging to the Sierpinski gasket which is one of the best studied fractals. It is shown that this convergence holds not only with respect to the Hausdorff distance, but that also Hausdorff dimension does converge. Moreover, it is shown that each of the approximating sets has non-trivial Hausdorff measure.
Keywords: fractals; Hausdorff dimension; iterated function systems; attractors; Hausdorff measure; Hanoi graph; Sierpinski gasket; self-similar set; non-self-similar set; Hausdorff distance; Hanoi attractor; Towers of Hanoi.
International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.4, pp.251 - 265
Published online: 30 Aug 2014 *Full-text access for editors Access for subscribers Purchase this article Comment on this article