A GEOMETRIC PROPERTY OF THE SIERPIŃSKI CARPET

  • Ligia L Cristea Johannes Kepler University, Institute for Mathematical Analysis, Altenbergerstrasse 69, 4040-Linz, Austria and Department of Mathematics, Politehnica University of Timi&#351oara, Romania.
Keywords: Fractal, Sierpi&#324ski carpet, geodesic metric, equivalent metrics.

Abstract

The main aim of this paper is to find formulae for the computation of the geodesic metric on the Sierpiński carpet. This is accomplished by introducing carpet coordinates. Subsequently we show the equivalence of the Euclidean and the geodesic metric on this fractal.

Mathematics Subject Classification (2000): 28A80, 54E35.
Published
2005-06-17
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606