# Sierpinski Christmas tree

- Author:
- Mrs Riddle

The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a 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.e., it is a mathematically generated pattern that can be reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński but appeared as a decorative pattern many centuries prior to the work of Sierpiński.
The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets:
Start with an equilateral triangle.
Construct the three midsegments to subdivide it into four smaller congruent equilateral triangles and remove the central one.
Repeat step 2 with each of the remaining smaller triangles
(From https://en.wikipedia.org/wiki/Sierpinski_triangle)