Abstract

Abstract The first fractal constructions appeared in mathematics in the second half of the 19th century. Their history is divided into two periods. The first period lasted 100 years and is a good example of the method of proofs and refutations discovered by Lakatos. The modern history of these objects started 20 years ago, when Mandelbrot decided to create fractal geometry, a general theory concentrated on specific properties of fractals. His approach has been surprisingly effective. The aim of this paper is to examine the reasons for Mandelbrot's success and for the present popularity of fractals. They are now known not only in mathematics but also in many fields of natural, social and applied sciences, and even in the arts