Original Articles

A geometric property of the Sierpiński carpet

Published in: Quaestiones Mathematicae
Volume 28 , issue 2 , 2005 , pages: 251–262

DOI: 10.2989/16073600509486126

Author(s): LigiaL. Cristea

Keywords: FRACTAL , SIERPINSKI 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 Sierpí nski carpet. This is accomplished by introducing carpet coordinates. Subsequently we show the equivalence of the Euclidean and the geodesic metric on this fractal.

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