COMPLEXITY AND FRACTALS IN PHYSICS

The study of complex systems and Fractal Geometry is having a profound impact on the physical sciences. These concepts change the way we look at nature and permit to include in the scientific domain new phenomena characterized by strong irregularities and self-similarity. Experiments and observations indeed suggest that many physical systems develop spontaneously self-similar behavior both in space and time. Pattern formation, aggregation phenomena, biological and geological systems, disordered materials, clustering of matter in the universe are just some of the fields in which scale invariance has been observed as a common basic feature. The value and impact of these concepts, however, is still rather controversial. In this paper we discuss the main advancements as well as the present limitations of these ideas by discussing some (representative) examples. We also outline the main open problems and the possible developments of the field.