Sierpinski triangle source:

Sierpinski triangle 1 iteration:

Sierpinski triangle 2 iterations:

Sierpinski triangle 3 iterations:

# Fractal Explorer

## Sierpinski triangle

The Sierpinski triangle fractal was first introduced in 1915 by Wacław Sierpiński. But similar patterns already appeard in the 13th-century in some cathedrals.

The concept of the Sierpinski triangle is very simple:

• Take a triangle
• Create four triangles out of that one by connecting the centers of each side
• Cut out the middle triangle
• Repeat the process with the remaining triangles

Mathematical aspects:

The area of the Sierpinski Triangle approaches 0. This is because with every iteration 1/4 of the area is taken away. After an infinit number of iterations the remaining area is 0.

The number of triangles in the Sierpinski triangle can be calculated with the formula:

Where n is the number of triangles and k is the number of iterations.

Besides the two dimensional Spierpinski triangle exists the three dimensional Spierpinski pyramid fractal.