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.