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A survey on fractal dimension for fractal structures

  
08. Sept. 2016

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The table above summarizes all the theoretical properties satisfied by each definition of fractal dimension explored throughout this paper_ We set 1 to denote that the corresponding property is satisfied by each fractal dimension and 0 otherwise (c_f_ [42])_

Theoretical propertiesdimBdimΓ1$\begin{array}{} {\rm{dim}}_{\bf{\Gamma }}^1 \end{array}$dimΓ2$\begin{array}{} {\rm{dim}}_{\bf{\Gamma }}^2 \end{array}$dimΓ3$\begin{array}{} {\rm{dim}}_{\bf{\Gamma }}^3 \end{array}$dimΓ4$\begin{array}{} {\rm{dim}}_{\bf{\Gamma }}^4 \end{array}$dimΓ5$\begin{array}{} {\rm{dim}}_{\bf{\Gamma }}^5 \end{array}$dimΓ6$\begin{array}{} {\rm{dim}}_{\bf{\Gamma }}^6 \end{array}$dimH
Monotonicity11111111
Finite stability11011111
Countable stability00000111
Countable sets00000111
Closure dimension01110111
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Englisch
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Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere