England Annexes Neighbor ?

Fractal geometry is able to interpret irregular shapes like mountain ranges, coastlines and banks of clouds and describe them in mathematical terms. When this idea was first published in 1967 by Benoit Mandelbrot the term fractal had not yet been coined. The term fractal came from Mandelbrot in 1975 and has come to mean an object characterized by the repetition of similar patterns at ever diminishing scales. You will see why in a moment in this classic example. Imagine wanting to know the length of the coastline of Britain. Using Euclidean geometry a fairly straight outline of Britain would be used to find the perimeter of the island and it would be approximately 2400 km. Fractal geometry will measure the coastline using ever decreasing units of measure so that the resulting measurement will include all the nooks and crannies that make the true perimeter of the island and the coast is approximately 3400 km.  No, Britain did not annex a neighbor’s coast to generate the extra 1,000 km. Instead, all the little fractions, or fractals, of the coast are included in the measurement. These nooks and crannies are referred to as self-similar in fractal terms. This means the coastline repeats a pattern of nooks and crannies at ever diminishing scales. In the case of the coast, the small little bays are very similar to the next larger bay and that bay is shaped a lot like the bigger bay it is a part of and so on.

2400 km versus 3400 km