Fractals, self-organized-criticality and the fixed scale transformation

DLA Fractal growth models and the sand pile models are both characterized by a non linear irreversible dynamics that evolves spontaneously in a critical state. These phenomena pose questions of new type for which novel theoretical concepts are necessary. We argue that the approach of the Fixed Scale Transformation contains some of the essential theoretical elements to treat these problems and to compute their properties analytically. Its original application to DLA-like problems has been made more systematic by the analysis of the scale invariant growth dynamics. Recently these concepts have been also developed for an analytical study of the critical properties of sandpile models.