A Survey of Mathematics Related Topics: Pg. 482, Figure 9.69

This activity allows the user to step through the process of building the Sierpinski's Triangle.

Turn of the century mathematician Waclaw Sierpinski's name was given to several fractal objects, the most famous being his Triangle or Gasket. This surface is idiosyncratic in that it has no area.

To build the Sierpinski's Gasket, start with an equilateral triangle with side length 1 unit, completely shaded (Iteration 0, or the initiator).

Cut out of each triangle the smaller triangle formed by connecting the midpoints of each of the sides (the generator).

Repeat this process on all shaded triangles. Stages 0, 1 and 2 are shown below.

The limiting figure for this process is called the Sierpinski's Gasket. It is one of the classic regular fractals.