Fractals

Abstract

Fractals are exotic sets that first appeared in the mathematical literature at the end of the 19th century. They were devised by Georg Ferdinand Ludwig Philipp Cantor (1845–1918), Giuseppe Peano (1858–1932), David Hilbert (1862–1943), Henri Léon Lebesgue (1875–1941), Arnaud Denjoy (1884–1974), George Pólya (1887–1985), Wacław Sierpiński (1882–1969), and many others. There is no precise definition but most authors agree to call fractals sets possessing certain characteristic properties such as self-similarity illustrated in the examples presented below. The idea of self-similarity originated implicitly in a paper of Niels Fabian Helge von Koch (1870–1924) (see the von Koch curve below), and was formulated explicitly by Ernesto Cesàro (1859–1906). The word fractal was coined by Benoît Mandelbrot (born 1924) who wrote a few books [34,35] and many articles on fractal geometry, drawing attention to its relevance in such diverse fields as fluid mechanics, geomorphology, economics, and linguistics.