Irreducible fractal structures for Moran's theorems

[EN] In this paper, we deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of IFS-attractors. The open set condition allows to easily calculate their similarity dimension though it depends on an external open set. We contribute a necessary condition to reach the equality among some fractal dimensions for the natural fractal structure for IFS-attractors and the similarity dimension. That condition, weaker than the SOSC, becomes more representative of the attractor’s self-similar structure.