On certain families of planar patterns and fractals

This survey article is dedicated to some families of fractals that were introduced and studied during the last decade, more precisely, families of Sierpi\'nski carpets: limit net sets, generalised Sierpi\'nski carpets and labyrinth fractals. We give a unifying approach of these fractals and several of their topological and geometrical properties, by using the framework of planar patterns.Comment: survey article, 10 pages, 7 figure

A GEOMETRIC PROPERTY OF THE SIERPI&#323SKI CARPET

The main aim of this paper is to find formulae for the computation of the geodesic metric on the Sierpi&#324ski 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