FRACTALS, SELF-ORGANIZED-CRITICALITY AND THE FIXED SCALE TRANSFORMATION

DLA Fractal growth models and the sand pile models are both characteri zed by a non linear irreversible dynamics that evolves spontaneously i n a critical state. These phenomena pose questions of new type for whi ch novel theoretical concepts are necessary. We argue that the approac h of the Fixed Scale Transformation contains some of the essential the oretical elements to treat these problems and to compute their propert ies analytically. Its original application to DLA-like problems has be en made more systematic by the analysis of the scale invariant growth dynamics. Recently these concepts have been also developed for an anal ytical study of the critical properties of sandpile models.