FRACTALS AND GROWTH-PROCESSES

The physics of far-from-equilibrium growth phenomena represents one of the important applications of fractal geometry. Fractals are objects having a special kind of geometrical complexity and are characterised by a non-integer (fractal) dimensionality. These objects have a self-s imilar structure. A part of the object looks like the whole under appr opriate scaling. Examples of growth processes leading to objects with fractal structures include dendritic solidification, viscous fingering , aggregation, electrodeposition, etc. These objects have a self-simil ar or scale invariant structure in a statistical sense. The volume of the object bounded by its surface is related to its linear size in a p owerlaw fashion and the scaling exponent is the fractal dimension. Sev eral theoretical models have been proposed to explain the observed gro wth processes. Some important models are diffusion limited aggregation , ballistic aggregation, cluster-cluster aggregation, etc. The compute r simulations of these models are able to reproduce the growth process es and resulting structures reasonably well. Multifractal scaling, whi ch is a generalisation of simple fractal scaling, is also important in analysing fractal growth processes. Multifractals allow us to probe d ifferent scaling relations and physical and geometrical properties dep endent on scaling relations.