How Long is the Coastline of Britain?
“Beautiful, damn hard, increasingly useful. That’s fractals.” Benoit Mandlebrot
The idea of fractals began when Benoit Mandlebrot asked, “How long is the coastline of Britain?” It sounds simple enough, measuring things has never been the top complaint of young students, but think about the physical process of measuring. If you drove around the coasts of England taking the distance you travelled to be your length your answer would be smaller than if you measured every cm of the coast with a ruler. You can keep increasing your accuracy till your measuring each stone, each grain of sand, each atom…
Mandlebrot simplified this issue using fractals. Fractals are infinitely complex self-similar patterns. The self-similarity means that if you zoom into the shape you will see the same complex pattern. By applying the idea of fractals to natural objects like a coastline that would show a similar pattern at different magnifications Mandlebrot achieved much more accurate approximations.
Fractals have many uses from understanding and modelling landscapes and clouds to creating and storing incredible computer graphics.
Finally, it is very important to not forget the main success of fractal geometry. The pictures look so pretty!!!