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Persistence intervals of fractals

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  • Máté, Gabriell
  • Heermann, Dieter W.

Abstract

Objects and structures presenting fractal like behavior are abundant in the world surrounding us. Fractal theory provides a great deal of tools for the analysis of the scaling properties of these objects. We would like to contribute to the field by analyzing and applying a particular case of the theory behind the P.H. dimension, a concept introduced by MacPherson and Schweinhart, to seek an intuitive explanation for the relation of this dimension and the fractality of certain objects. The approach is based on recently elaborated computational topology methods and it proves to be very useful for investigating scaling hidden in dimensions lower than the “native” dimension in which the investigated object is embedded. We demonstrate the applicability of the method with two examples: the Sierpinski gasket–a traditional fractal–and a two dimensional object composed of short segments arranged according to a circular structure.

Suggested Citation

  • Máté, Gabriell & Heermann, Dieter W., 2014. "Persistence intervals of fractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 252-259.
    • Handle: RePEc:eee:phsmap:v:405:y:2014:i:c:p:252-259
    DOI: 10.1016/j.physa.2014.03.037
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    References listed on IDEAS

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    1. Yongmei Lu & Junmei Tang, 2004. "Fractal Dimension of a Transportation Network and its Relationship with Urban Growth: A Study of the Dallas-Fort Worth Area," Environment and Planning B, , vol. 31(6), pages 895-911, December.
    2. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
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