The normal of a fractal surface

Wayne O. Cochran, Robert R. Lewis, John C. Hart

Research output: Contribution to journalArticlepeer-review


We have discovered a class of fractal functions that are differentiable. Fractal interpolation functions have been used for over a decade to generate rough functions passing through a set of given points. The integral of a fractal interpolation function remains a fractal interpolation function, and this new fractal interpolation function is differentiable. Tensor products of pairs of these fractal functions form fractal surfaces with a well-defined tangent plane. We use this surface normal to shade fractal surfaces, and demonstrate its use with renderings of fractal mirror.

Original languageEnglish (US)
Pages (from-to)209-218
Number of pages10
JournalVisual Computer
Issue number4
StatePublished - Jun 2001


  • Fractal
  • Fractal function
  • Fractal terrain
  • Iterated function system
  • Recurrent modeling

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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