Fractals Everywhere Author:Michael Fielding Barnsley FRACTALS EVERYWHERE: THE FIRST COURSE IN DETERMINISTIC FRACTAL GEOMETRY — "The observation by Mandelbrot of the existence of a 'Geometry of Nature' has led us to think in a new scientific way about the edges of clouds, the profiles of the tops of forests on a horizon, and the intricate moving arrangement of the feathers on the wings ... more »of a bird as it flies. Geometry is concerned with making our spatial intuitions objective. Classical geometry provides a first approximation to the structure of physical objects; it is the language which we use to communicate the designs of technological products, and, very approximately, the forms of natural creations. Fractal geometry is an extension of classical geometry. It can be used to make precise models of physical structures from ferns to galaxies. Fractal geometry is a new language. Once you understand fractal geometry, you will be able to describe the shape of a cloud as precisely as an architect describes a house. " From the Preface
The focus of this text is how fractal geometry can be used to model real objects in the physical world. Rather than considering only fractal images that have been generated randomly, the approach here is to start with a natural object and find a specific fractal to fit it. Applications of fractal geometry extend to biological modeling, physiological modeling, geography, coastlines, turbulence, images, computer graphics, feathers, and ocean spray. The applications to computer graphics and, in particular, image compression for data transmission and reconstruction are exciting new developments.
Cover illustration:
Andes Indian Girl(Michael Barnsley, Arnaud Jacquin, Francois Malassenet, Laurie Reuter, Alan Sloan). This illustration (color plate 9.8.7), encoded from a color photograph, is an example of the application of fractal geometry to computer graphics.
Fractals Everywhere may be supplemented by Michael F. Barnsley's Desktop Fractal Design System (version 2.0) with IBM for Macintosh software. The Desktop Fractal Design System 2.0 is a tool for designing Iterated Function Systems codes and fractal images, and makes an excellent supplement to a course on fractal geometry.« less