Fractals are characterised by their property of self-similarity, they are both similar to themselves in all regions and similar to themselves on
different length scales, so that an enlargement of a fractal looks the same as the original.
The Polish mathematician Waclaw Sierpinski discovered a famous fractal structure now known as the Sierpinski gasket. Sierpinski's method of
construction was to start with an equilateral triangle, then remove the central triangle to leave three smaller triangles.
Each of these triangles is a smaller version of the original triangle. The central triangle is then removed from each of the smaller triangles to leave
even smaller equilateral triangles. This process can be continued indefinitely. The end result is the Sierpinski Gasket, which is composed of a dust of disconnected points.