103.38 Four hundred years of the fractal coastline of Scotland

摘要

Fractals are a relatively new area of study in mathematics and science. Indeed the word fractal was only coined in 1975 by pioneer and energetic promoter of the subject, Benoit Mandelbrot (1924-2010). The simplest way to define a fractal is that it is an object which is self-similar across all scales of magnification. Thus, no matter how closely we ‘zoom in’ a fractal it will look the same, or at least similar, to the whole object. Examples of fractals are common in nature. For example, a tree is a fractal-like object. If we take a branch of a tree it looks similar to the whole tree, as does a branch of the branch and so on down to the level of a twig, at which point the selfsimilarity breaks down. An important consequence of self-similarity is that without being given a reference scale for a fractal object it is not possible to determine its actual size. This can be observed with isolated trees in areas where there are no man-made objects to provide a visual cue to give a suggestion of size. For example, in mountainous regions it may be difficult determine whether a tree in the distance is 10 feet, or 30 feet, tall.