Fractal Surfaces

Abstract

Much of the broad interest in fractals has probably been generated by the striking computer-generated pictures of landscapes. The beautiful color pictures in Mandelbrot’s last book (Mandelbrot, 1982) of valleys and of a rising ‘earth’ seen from a ‘moon’ have captured the imagination of scientists and laymen alike. An early popular discussion by Gardner (1976) of Mandelbrot’s work probably helped much in building interest — at least it was my first contact with these ideas. Even more spectacular pictures with haze in the valleys, also generated by R. F. Voss, have been published in a popular account in a widely circulated microcomputer journal (Sørensen, 1984). Indeed the irregularity of the earth’s topography over a large range of length scales indicates that useful models of landscapes may be obtained using fractals.