Sierpinski Gasket

Introduction to Fractal Geometry

Get out a ruler and prepare to use it.

Recursion Rule: Find the midpoint of each side of the triangle below. Connect those three midpoints with straight lines. Now you see four new, smaller triangles inside of your original triangle. The middle triangle is upside down. Write your name in that triangle and then leave that one alone. It will remain white for the rest of the process. In the other three triangles, find the midpoint of each side. Connect the three midpoints with straight lines. Now you see a bunch of new even smaller triangles. You always get three right-side-up triangles, with one upside-down triangle in the middle. You should always leave the middle triangle blank, while you take the other three triangles and find their midpoints. Continue this process until you have at least six different sizes of triangles (the original big triangle counts as one size). You may find this tedious and/or mesmerizing, but this is how fractals are made. Then, in class, we will be putting all of our triangles together to make one huge triangle on the bulletin board.