On the Edge: Statistics & Computing
The most captivating aspect of a fractal is that, at first sight, it may appear to have a highlyirregular geometric shape, but with a closer look one will find that it is in fact exccedingly regular in the sense that at any detailed level the same pattern repeats.
Abstract
The name fractal, coined in \975 by the mathematician Benoit Mandclbrot, known as the godfather of fractals, comes from the Latin adjectivefractus. The corresponding Latin verb frangere means "to break" or "to create irregular fragments:' as Mandelbrot put it. To the best of our knowledge, there is no unitary mathematical definition of a fractal, although many attempts have been made. In layman's terms, a fractal is a "picture" with an incredible level of detail. No matter how deep one zooms in to it, one will find irregular details as well as miniatures of parts of the original picture. Since \975, the subject has received a great deal of research as well as public attention. Many articles and books have been written, forexperts as wellas for the general public, among which Mandelbrot's \977 book, The Fractal Geometryof Nature, is a must for anyone who is interested in the subject. A selection of further reading is given at the end of the article. For general audiences, fractals arc often presented as a kind of "computerart" because they are computer-generated and colorful, with fascinating geometric shapes. The most captivating aspect of a fractal is that, at first sight, it may appear to have a highlyirregular geometric shape, but with a closer look one will find that it is in fact exccedingly regular in the sense that at any detailed level the same pattern repeats. Perhaps this is best summarized by the title of Lauwerier's 199\ book, Fractals: Endlessly Repeated Geometrical Figures.