12 research outputs found
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 SIERPIŃSKI CARPET
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