Sierpinski triangle in logic: The first 16 conjunctions of lexicographically ordered arguments. Sierpinski gasket or the Sierpinski Sieve, is construction of triangles pdf fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
Originally constructed as a curve, this is one of the basic examples of self-similar sets, i. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries prior to the work of Sierpiński. There are many different ways of constructing the Sierpinski triangle.
Start with an equilateral triangle. Subdivide it into four smaller congruent equilateral triangles and remove the central one.
This process of recursively removing triangles is an example of a finite subdivision rule. Holes are an important feature of Sierpinski’s triangle. Note that this infinite process is not dependent upon the starting shape being a triangle—it is just clearer that way. The first few steps starting, for example, from a square also tend towards a Sierpinski triangle.