Pascal's triangle mod 2 | Sierpiński gasket | Sierpiński pattern | Sierpiński triangle

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century. It is also called the Sierpiński gasket or Sierpiński triangle. The curve can be written as a Lindenmayer system with initial string FXF--FF--FF, string rewriting rules F" -> "FF, X" -> "--FXF++FXF++FXF--, and angle 60°. The n th iteration of the Sierpiński sieve is implemented in the Wolfram Language as SierpinskiMesh[n]. Let N_n be the number of black triangles after iteration n, L_n the length of a side of a triangle, and A_n the fractional area which is black after the n th iteration.

chaos game | Lindenmayer system | Lucas correspondence theorem | Pascal's triangle | rule 102 | rule 90 | Sierpiński arrowhead curve | Sierpiński carpet | Sierpiński gasket graph | tetrix

SierpinskiMesh

Wacław Sierpiński