Fractals are complicated geometrical objects which can be described in terms of non-integer (fractal) dimensions. For the last decade fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry and earth sciences.

Using fractal geometry as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Through the application of such concepts as scale invariance, self-affinity and multifractality a better understanding of such phenomena as aggregation, turbulence, percolation, biological pattern formation and granular flows has emerged.

For the last couple of years our research has been focussed on the dynamic scaling behaviour of growing self-affine surfaces and on self-organized criticality (SOC). Using experiments, computer simulations and theoretical methods we have investigated various physical phenomena ranging from wetting in porous media to erosion processes. We have introduced the concept of multiaffine surfaces and, among other topics, we have studied continuous models of SOC and the reasons and consequences of anomalous roughening in disordered media.