Fractal measures

P. Meakin, Fractal Aggregates and Their Fractal Measure, in Phase Transitions arul Critical Phenomerui, Vol. 12, C. Domb and J. L. Lebowitz, eds.. Academic, New York, 1988. 

Linear a number of entropies, dimensions, Renyi measures, multi-fractal and fractal measures, and surrogate based quantities, iii. Prediction... 

P. Meakin, The growth of fractal aggregates and their fractal measures, Phase Transitions Crit. Phenomena 12 335 (1988). 

Halsey, T. C. Jensen, M. H. Kadanoff, L. P Procaccia, L Shraiman, B. L Fractal measures and their singularities the characterization of strange sets. Phys. Rev. A,... 

Samko, S. G. Kilbas, A. A. Marichev, O. I. Integrals and Derivatives of Fractional Order and their some Applications. Minsk, Science and Engineering, 1987, 688. Halsey, T. C. Jensen, M. H. Kadanoff, L. R Procaccia, I. Shraiman, B. I. Fractal measures and their singularities the characterization of strange sets. Phys. Rev. A, 1986,33(2), 1141-1151. 

Fractal analysis cannot be applied indiscriminately. For the values that are obtained to be mechanistically valid, comparisons must be made among similar measurements of fractal dimensions (e.g. mass, surface or pore fractal dimensions) that are made using a single given analytical technique or techniques based upon similar analytical principles. Future research is required to better relate measurements that are performed in different manners and indeed to better understand the limitations of the fractal measurements. Nonetheless, the majority of future research in the field will necessarily be focused upon applying established determinations of fractal dimensions to understanding the physicochemistry of complex (i.e. natural) systems better (e.g. Chapters 4-9 [32-35, 39, 40]). 

Meakin, P. and Deutch, J.M. (1987). Properties of the fractal measure describing the hydrodynamic force distributions for fractal aggregates moving in a quiescent fluid. J. Chem. Phys., 86, 4648-4656. 

E. Ott, J. Antonsen, Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows, Phys. 

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