Coastlines are fractal curves. When you zoom in, you will see similar shaped curves on every scale. The same is true for market data. On a naked chart you can hardly tell if it is a daily or hourly chart. This article will explore this feature of crinkly curves and show how much markets and coastlines have in common.

## The coastline paradox

When trying to measure the length of the British coastline you will quickly notice, that the length measured depends on the length of the ruler you use. The shorter the ruler, the longer the measured length of the coastline.

When measuring a straight line, the length of the ruler has no influence. You can measure 1 meter with a 1cm ruler applied 100 times or with a 50cm ruler applied 2 times. Both methods will give you the same result. Not so when measuring a crinkly line like a coast.

British coastline length paradox (c) wikipedia

In 1967 Benoit Mandelbrot wrote a famous article in Science magazine about this problem. This was the birth of fractal geometry. The basic assumption was, that if a curve is self similar, this self similarity can be described by the fractal dimension of a curve. Self similarity means, that if you zoom into a curve, it looks similar on all zoom levels.