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Dimension of hyperfractals

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  • Andres, Jan
  • Rypka, Miroslav

Abstract

It is shown that multivalued fractals have the same address structure as the associated hyperfractals. Hyperfractals may be used to model self-similar diffusion limited aggregations, structure of urban settlements, and clusters of nanoparticles. We establish that the Hausdorff dimensions of a particular class of hyperfractals can be calculated by means of the Moran–Hutchinson formula.

Suggested Citation

  • Andres, Jan & Rypka, Miroslav, 2013. "Dimension of hyperfractals," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 146-154.
    • Handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:146-154
    DOI: 10.1016/j.chaos.2013.10.003
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    1. Chifu, Cristian & Petruşel, Adrian, 2008. "Multivalued fractals and generalized multivalued contractions," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 203-210.
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    5. Cinzia Colapinto & Davide Torre, 2008. "Iterated Function Systems, Iterated Multifunction Systems, and Applications," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 83-90, Springer.
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