Fig. 1: The Coastline illustration of the concept of fractal scaling.

(A) Breakdown of Great Britain’s self-similar features in the coastline. (B) Measured length of the fractal coast increases as the scale of measurement, or compass setting, decreases. By contrast, the length of a non-fractal circle’s circumference has a converging value. (C) The scaling of a fractal structure follows a power law from which the fractal dimension may be approximated. Measurement precision is defined as the inverse of the compass setting where for a small setting s the precision 1/s is large. Figure reproduced with permission from [²].