FRACTALS. ORIGINS AND HISTORY

Abstract

Fractal shapes can be found everywhere around us in Nature, at small scale microscopic level, at normal scale observable with the naked human eye, but also at very large scale level, when looking at very far distant galaxies. As it will be presented in this paper, there is an inherent relationship between fractal structures in Nature and the harmony perceived by human eye in the structures of Nature. Although not explicitly formulated until late XII century by Fibonacci, the very same Golden Proportion had been already approached by the ancient Greeks. This Divine Proportion which can be found around us in Nature, represents the base for the latter concept of fractal and is also the link between early mathematics and advanced fractal mathematics. Some of the first ideas about harmony and proportions are dating back in Antiquity and they were promoted by the ancient Greeks in their philosophical schools, by scholars like Euclid, Thales and Pitagora. Although the concept of fractal it is a rather young one, being introduced by Mandelbrot in the ‘70s of the XX th century, the origins of the concept of fractal seem to be found, much earlier, in the aforementioned philosophical schools. In their philosophical schools, the antics, as far as we know, beginning with the Greeks, had discovered and used the concepts of proportion and harmony, in certain proportions they worked with. One such proportion is represented by the Golden Ratio.