In this assignment we will construct an example of a fractal called the Sierpinski Triangle. Fractals are shapes for which smaller parts are similar in shape to larger parts when magnified to the same size.
To construct a Sierpinski Triangle, first draw an equilateral triangle. For convenience, draw it with one side parallel to the bottom of your paper, so the top is a vertex.
To get the next step, connect the midpoints of the three sides to obtain four smaller triangles, three in the same orientation as the original and one upside down.
You can then repeat this process on each right side up triangle for as many times as you like. Each time you obtain four triangles from each right side up triangle.
To see this process carried out several times and in color, click here, or click here to get the negatives of the first set.