A generalized entropy characterization of N -dimensional fractal control   systems
  It is presented the general properties of N-dimensional multi-component or many-particle systems exhibiting self-similar hierarchical structure. Assuming there exists an optimal coarse-graining scale at which the quality and diversity of the (box-counting) fractal dimensions exhibited by a given system are optimized, it is computed the generalized entropy of each hypercube of the partitioned system and shown that its shape is universal, as it also exhibits self-similarity and hence does not depend on the dimensionality N . For certain systems this shape may also be associated with the large time stationary profile of the fractal density distribution in the absence of external fields (or control). 
Marcos E. Gaudiano
nlin.AO