The same sequence of shapes, converging to the Sierpiński triangle, can alternatively be generated by the following steps: This process of recursively removing triangles is an example of a finite subdivision rule. Repeat step 2 with each of the remaining smaller triangles infinitely.Įach removed triangle (a trema) is topologically an open set.Subdivide it into four smaller congruent equilateral triangles and remove the central triangle.The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets: Removing triangles The evolution of the Sierpinski triangle There are many different ways of constructing the Sierpinski triangle. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński. Originally constructed as a curve, this is one of the basic examples of self-similar sets-that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. The Sierpiński triangle (sometimes spelled Sierpinski), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
(sequence A001317 in the OEIS) Sierpiński pyramid as light installation fractal on the Tetrahedron in Bottrop, Germany The columns interpreted as binary numbers give 1, 3, 5, 15, 17, 51. Fractal composed of triangles Sierpiński triangle Generated using a random algorithm Sierpiński triangle in logic: The first 16 conjunctions of lexicographically ordered arguments.
0 kommentar(er)
