The word 'Fractal' was coined in 1975 by the mathematician BenoĂ®t Mandelbrot - but the study of self-repeating mathematical systems dates back several centuries.
Mandelbrot provided a definition of a fractal as : â€śA rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the wholeâ€ť.
There are many naturally-occurring examples e.g. crystals, tree structures, electrical discharges, frictional surfaces, bio-rhythms, mountain ranges, coastline shapes, sea-surface waves, etc etc.
The purely mathematical representations are often an infinite series, but the 'real-world' examples are bound by limits - even so, one of the key features of systems which have a fractal component is that they are hard (or sometimes impossible) to accurately quantify.
See, for example, this now-famous paper by B. B. Mandelbrot How long is the coast of Britain? Statistical self-similarity and fractional dimension Science: 156, 1967, 636-638
To specify the conditions for the existence of a similarity dimension is not a fully solved mathematical problem. In fact, a number of conceptual problems familiar in other uses of randomness in science are also raised by the idea that a geographical curve is random.â€ś
In other words :
Geographical curves are so involved in their detail that their lengths are often infinite or more accurately, undefinable.â€ť
The implications for any system with a fractal component (not just geographical ones) is that a completely accurate mathematical description is often impossible. The amount of 'fractal-ness' - called the 'Fractal Dimension' ( D ) - can however often be specified (or estimated).
Descriptions of fractal systems fall into the special category of Known Unknowables
Also see :and
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