the numerator is the logarithm of the number of copies of the shape formed from each copy of the previous iteration, and the denominator is the logarithm of the factor by which these copies are scaled down from the previous iteration. If all points are projected onto a plane that is parallel to two of the outer edges, they exactly fill a square of side length without overlap. History Wacław Sierpiński described the Sierpiński triangle in 1915. However, similar patterns appear already as a common motif of 13th-century Cosmatesque inlay stonework. The Apollonian gasket was first described by Apollonius of Perga (3rd century BC) and further analyzed by Gottfried Leibniz (17th century), and is a curved precursor of the 20th-century Sierpiński triangle. Etymology The usage of the word "gasket" to refer to the Sierpiński triangle refers to gaskets such as are found in motors, and which sometimes feature a series of holes of decreasing size, similar to the fractal; this usage was coined by Benoit Mandelbrot, who thought the fractal looked similar to "the part that prevents leaks in motors". See also Apollonian gasket, a set of mutually tangent circles with the same combinatorial structure as the Sierpinski triangle List of fractals by Hausdorff dimension Sierpiński carpet, another fractal named after Sierpiński and formed by repeatedly removing squares from a larger square Triforce, a relic in the Legend of Zelda series References External links Sierpinski Gasket by Trema Removal at cut-the-knot Sierpinski Gasket and Tower of Hanoi at cut-the-knot Real-time GPU generated Sierpinski Triangle in 3D Pythagorean triangles, Waclaw Sierpinski, Courier Corporation, 2003 A067771 Number of vertices in Sierpiński triangle of order n. at OEIS Interactive version of the chaos game Factorial and binomial topics Curves Topological spaces Types of triangles Cellular automaton patterns Science and technology in Poland L-systems