Sierpiński gasket

Let S0 be a triangular area, and define Sn+1 to be obtained from Sn by replacing each triangular area in Sn with three similar and similarly oriented triangular areas each intersecting with each of the other two at exactly one vertex, each one half the linear scale of the original in size. The limiting set as n (alternately the intersectionMathworldPlanetmath of all these sets) is a Sierpiński gasket, also known as a Sierpiński triangleMathworldPlanetmath.

Figure 1: Sierpiński gasket stage 0, a single triangle, and at stage 1, three triangles
Figure 2: Stage 2, nine triangles, and stage n, 3n triangles
Title Sierpiński gasket
Canonical name SierpinskiGasket
Date of creation 2013-05-18 22:53:46
Last modified on 2013-05-18 22:53:46
Owner mathwizard (128)
Last modified by unlord (1)
Numerical id 41
Author mathwizard (1)
Entry type Definition
Classification msc 28A80
Synonym Sierpinski triangle
Synonym Sierpinski gasket
Synonym Sierpiński triangle
Related topic MengerSponge