The book "The Beauty of Fractals", from which the article published below is taken, is, in fact, an expanded scientific catalog for three exhibitions of paintings organized by a group of Bremen mathematicians and physicists back in 1984. The exhibits of these exhibitions were computer images of fractal objects of various natures, mainly Julia and Mandelbrot sets. In 1993, a Russian translation of this book, done by our colleagues from Kyiv, was finally published in Moscow.