For some years now, ‘fractals’ have provided spectacular displays (which have seemingly hypnotised both the popular technical press and the ‘media’) on computer workstations equipped with high-power graphics processors, and also provoked much controversy with regard to their potential for mimicking real-world imagery. In this paper the authors briefly describe the theoretical background of fractal representations and investigate in more detail the validity of such an approach for applications in natural scene portrayal and coding.