The word geometry might conjure up images or circles, squares, cylinders, and cubes, but many phenomena in Nature and science are anything but regular or smooth. Think coastlines, mountain ranges, clouds, and trees. Fractals allow these complex and irregular objects to be described in simple terms.

This book outlines how fractals may be constructed and analysed as geometrical objects and how mathematical fractals relate to fractals out there in nature.

Fractals became ‘popular’ in the 1980s thanks to Benoit Mandelbrot who died in 2010 and is referred to as ‘the Father of Fractals’. Fractals are increasingly used in sophisticated scientific research.

Brownian Motion was first noticed by the Scottish botanist Robert Brown in 1827 when he observed that particles of pollen moved on irregular paths in water. This motion is a very good example of a natural fractal phenomenon.