What Is the Recursive Formula for a Sierpinski Triangle?

The recursive formula for Sierpinski triangle is An=An-1*3. The procedure of constructing the triangle with this formula is called recursion. Alternatively, the Sierpinski triangle can be created using the explicit formula An=1*3(n-1), where (n-1) is the exponent.

The Sierpinski triangle is also known as a Sierpinski gasket or Sierpinski Sieve. This large triangle is recursively subdivided in to a series of smaller equilateral triangles. The pattern of the triangles displays a uniform image of smaller triangles that are aesthetically arranged. This arrangement of triangles is an example of a mathematical concept known as similar-sets, which are patterns that are created using mathematical formulae and can effectively be reduced without limit.