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5)) in regards to rank-2 tensors Rank-2 Minkowski tensors 2D V0 E2 V1 E2 V2 E2 – V10;2 – V02;0 V12;0 V22;0 – Rank-2 Minkowski tensors 3D V0 E2 V1 E2 V2 E2 V3 E2 V10;2 V20;2 V02;0 V12;0 V22;0 V32;0 44 P. Schönhöfer and K. F // WD d X d ! F ; / is well defined. 0 that it cannot be applied to the physical structures shown above and that one looses important information on the shape of the fractal structures found in Nature. Both is related to the existence of a smallest length scale l which regularises the fractal but does not exist for F , where can be chosen arbitrarily small.

Trans. Am. Math. Soc. 347, 967–983 (1995) 76. M. Rams, K. Simon, Projections of fractal percolations. Ergod. Theory Dyn. Syst. 35, 530–545 (2015) 77. M. Rams, K. Simon, The dimension of projections of fractal percolations. J. Stat. Phys. 154, 633–655 (2014) 78. M. Rams, K. Simon, The geometry of fractal percolation, in Geometry and Analysis of Fractals, ed. -J. -S. Lau. Springer Proceedings in Mathematics & Statistics, vol. 88 (Springer, Berlin/Heidelberg, 2014), pp 303–324 79. C. Robinson, Dimensions, Embeddings, and Attractors (Cambridge University Press, Cambridge, 2010) 80.

D; k; ˛/ we can reason similarly. References 1. T. M. Fisher, On the magnification of Cantor sets and their limit models. Monatsh. Math. 121(1–2), 11–40 (1996) 2. T. M. Fisher, Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets. Ergod. Theory Dyn. Syst. 17(3), 531–564 (1997) 38 A. Käenmäki 3. T. M. Fisher, M. Urba´nski, The scenery flow for hyperbolic Julia sets. Proc. Lond. Math. Soc. (3) 85(2), 467–492 (2002) 4. S. Besicovitch, On the fundamental geometrical properties of linearly measurable plane sets of points.

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