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Exact Computation and Approximation of Stochastic and Analytic Parameters of Generalized Sierpinski Gaskets

Author

Listed:
  • Uta Freiberg

    (University of Siegen)

  • Christoph Thäle

    (University of Fribourg)

Abstract

The interplay of fractal geometry, analysis and stochastics on the one-parameter sequence of self-similar generalized Sierpinski gaskets is studied. An improved algorithm for the exact computation of mean crossing times through the generating graphs SG(m) of generalized Sierpinski gaskets sg(m) for m up to 37 is presented and numerical approximations up to m = 100 are shown. Moreover, an alternative method for the approximation of the mean crossing times, the walk and the spectral dimensions of these fractal sets based on quasi-random so-called rotor walks is developed, confidence bounds are calculated and numerical results are shown and compared with exact values (if available) and with known asymptotic formulas.

Suggested Citation

  • Uta Freiberg & Christoph Thäle, 2013. "Exact Computation and Approximation of Stochastic and Analytic Parameters of Generalized Sierpinski Gaskets," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 485-509, September.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9254-7
    DOI: 10.1007/s11009-011-9254-7
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