Do you know what a fractal is? Its called SMART, science+math+art. There are natural fractals and artificial fractals. The most well known fractal is the Sierpinski triangle. The rule for the Sierpinski triangle is, each triangle decreases by 1/2 height and 1/2 width. The interesting thing about the Sierpinski Triangle is that you can keep making smaller and smaller triangles forever and it is self-similar. Which means you can take any segment of the triangle and expand it and it will look exactly the same as the original. Unless you only take part of a triangle.
Here is a computer generated fractal from this site.
There are also natural fractals, like ferns. Ferns are fractals because each segment has another little segment on it and that little segment has another, smaller segment on it.