The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals

  • Philipp Schönhöfer
  • Klaus MeckeEmail author
Conference paper
Part of the Progress in Probability book series (PRPR, volume 70)


The shape of fractals can be characterized by intrinsic volumes, so-called Minkowski functionals, which share with the common d-dimensional volume of spatial structures the property of being additive. Here, we study the effects of anisotropy on the scaling behavior beyond the fractal dimension by applying tensorial functionals. It can be shown that Minkowski tensors of anisotropic pre-fractals scale with additional subdimensions. In addition, for anisotropic pre-fractals even scalar Minkowski functionals exhibit multiple edge subterms which merge for the isotropic case.


Integral geometry Fractals Anisotropy Minkowski functionals DLA 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Friedrich Alexander University Erlangen-NürnbergErlangenGermany

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