The Sierpinski Sieve

Also known as the Sierpinski Gasket or the Sierpinski Triangle



Right-click here to download this page and the Java Class File.

The Java applet above draws the Sierpinski Sieve of order n = 0 to 8.
Each order of the Sierpinski Sieve is formed by dividing each black triangle into 4 congruent triangles and removing the central triangle.

OrderArea of the Sierpinski Sieve
011
11 - 1/4 = 3/40.75
21 - 1/4 - 3(1/4)2 = (3/4)20.5625
31 - 1/4 - 3(1/4)2 - 32(1/4)3 = (3/4)30.422
41 - 1/4 - 3(1/4)2 - 32(1/4)3 - 33(1/4)4 = (3/4)40.316
:::
n(3/4)n:

The area of Sierpinski Sieve of order n approaches zero as n approaches infinity.
1