This fractal, known as the Sierpinski Triangle, can be generated with a very interesting procedure. Starting with the
three points of a triangle, place a fourth point anywhere inside. Then repeat the process of selecting one of the outer
three points at random, then drawing a new point halfway between that point and the one you drew most recently. Despite
seeming like they would produce a random pattern, the points arrange themselves neatly into this triangular fractal.

To prove that this shape is really a fractal, you can reduce the point size. Try finding the smallest visible triangle before and after the decrease.

To prove that this shape is really a fractal, you can reduce the point size. Try finding the smallest visible triangle before and after the decrease.