Abstract
The spectra of generalized dimensions Dq and of local exponents f() for fractal measures are evaluated by using the uniform partitions to compute the free energy. The numerical results obtained from optimal algorithms are compared with the analytical results obtained from the free energy evaluated with dynamical partitions, in the case of IFS measures. It is proved that the spectra Dq obtained from correlation integrals and dynamical partitions are the same even for q 1 and for q<1 only if the support of the measure is not fractal or if the dynamical partitions are a subset of the uniform partitions. The spectra obtained from a numerical approximation of the correlation integrals provide the correct result for any value of q. The algorithms based on the uniform partitions are fast and can be used for real-time analysis of digitized images.
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