A general fractal distribution function for rough surface profiles

Denis Blackmore, Jack G. Zhou

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Starting with a very general functional description, involving fractal parameters, of the height along a given line on a rough surface, a distribution function for the corresponding surface profile is derived. This distribution is found to differ from Gaussian form by a convergent power series and to be directly dependent on two fractal parameters: the fractal dimension and topothesy. It is shown how the distribution function can be used to determine the effects of varying the fractal parameters on the height of the bearing-area curve (a standard measure of surface roughness). By truncating the series representation for the distribution function for the surface profiles, two approximate models for the height distribution are obtained. These models are shown to compare favorably with experimentally obtained distributions.

Original languageEnglish (US)
Pages (from-to)1694-1719
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number6
StatePublished - Dec 1996

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Bearing-area curve
  • Box dimension
  • Distribution
  • Fractals
  • Hausdorff dimension
  • Method of moments
  • Surface profiles
  • Topothesy


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