FRACTAL STRUCTURES

Fractal geometry is a rapidly growing but already quite extensive area. As with all such areas much of our knowledge and many techniques will be superceded during the coming years. However, substantial progress has been made and both the basic concepts of fractal geometry and many of its applications will have lasting value. In this review I have described the ideas and approaches that I have found to be of most value in applying fractal geometry to the results of computer experiments. The same methods have been applied successfully by other to a wide variety of experiments on real systems. The development and eventual popularization of fractals by B. B. Mandelbrot has stimulated a renewed interest in the science of complex and random systems. This background and the introduction of the diffusion-limited aggregation model by Witten and Sander21 has led to a broad interest in non-equilibrium growth models. Here I have attempted to illustrate some of the progress that has been made in this area and use it to show how fractal geometry can be applied to problems in the physical sciences. There has also been a large quantity of concommitent experimental work. The examples of experiments and simulations have been selected to illustrate how fractal geometry can be applied in solid state chemistry. Consequently, I have neglected, for the most part, the quite extensive experimental work on fractal colloidal aggregates. A description of multifractals has been included. Interest in this aspect of fractal geometry is quite recent (though its origins are much older). There are, as yet, few applications in areas relevant to solid state chemistry. However, there are strong indications that this approach will eventually prove to be of value in understanding phenomena such as diffusion-limited reactions at rough interfaces, mechanical and dielectric breakdown phenomena, catalysis and other phenomena of importance in solid state chemistry. Despite the substantial progress that has been made in recent years, much work remains to be done. Our basic understanding of even very simple processes leading to the formation of fractal structures is still, in most cases, quite inadequate. In many areas there is still an urgent need for high quality experimental studies that will help to determine the scope of applications of fractal geometry to real systems and assess the quality of understanding what can be achieved in this manner. A comprehensive survey of fractal geometry and its applications is no longer a practical undertaking. There are now a substantial number of books, reviews and conference proceedings devoted to fractal geometry and its applications. The Mandelbrot classics (particularly The Fractal Geometry of Nature, W. H. Freeman and Company, New York (1982)) are still the major sources of information. In addition, there are two excellent intermediate level books that I would strongly recommend to anyone interested in applying fractal geometry to solid state chemistry. These are Fractals by J. Feder (Plenum, New York (1989)) and Fractal Growth Phenomena by T. Vicsek (World Scientific, Singapore (1989)). Of the many multiauthor books and conference proceedings, The Fractal Approach to Heterogeneous Chemistry: Surfaces, Colloids, Polymers (D. Avnir, ed., Wiley, Chichester (1989)) and Fractals in Physics: Essays in Honor of Benoit B. Mandelbrot (A. Aharony and J. Feder, eds., North Holland, Amsterdam (1989)) would be of particular interest to readers of Progress in Solid State Chemistry. © 1990.