Sierpiński Triangle

The Sierpiński triangle, also called the Sierpiński gasket, is a fractal built by recursively subdividing an equilateral triangle into four smaller triangles and removing the central one, repeated infinitely on each remaining triangle. Wacław Sierpiński described the fractal in 1915, though similar patterns appear in 13th-century Cosmatesque stone inlay. The figure is self-similar at every scale and has a Hausdorff dimension of log 3 divided by log 2, approximately 1.585, between that of a line and a plane. Coloring Pascal's triangle by marking its odd entries and leaving its even entries blank produces an approximation of the Sierpiński triangle that becomes exact as the number of rows tends to infinity, linking the fractal directly to binomial coefficients.