divide it in 4 new line segments according to a fixed pattern:
repeat this as often as you like:
Relatively simple formulas may create the most spectacular figures. For example:
Apart from artistic applications fractals are very useful in the area of mathematics that is called chaos theory (see also backgrounds). The characterisation of apparently disorderly structures (e.g. small parts with a very rough surface, coastlines, the structure of branches and leaves) makes grateful use of fractal mathematics as well.