Fractals are mathematically fascinating and immensely useful

Fractals are complex structures or patterns that looks similar at any level of magnification. Fractals are found everywhere from snowflakes and plants to the distribution of galaxies in the universe.

The coastline of Great Britain is said to be fractal.

But how can we confirm this?

All we only need to do is examine how the measured length of the coast changes as a function of the length of the measuring stick. When we use a long ruler we get a rough estimate. As the ruler length (r) shrinks, the length of the coastline (N) increases. The more twists and turns the coast has, the more its length will grow as we use smaller rulers.

We are interested in the rate at which the coastline changes as a function of the ruler length. By plotting the coast length against the ruler length on log scales, we can see the relationship.

If the coastline is fractal, this relationship will be a straight line. For Great Britain's coast, this is true, with a fractal dimension "D".