Fractal structures derivable from the generalisations of the Pascal triangle

Akhlesh Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan

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Abstract

Generalisations, of order K>or=2, of the Pascal triangle are used to construct generalised Pascal-Sierpinski gaskets of orders (K, L>or=2). It is shown that all such gaskets are self-affine fractals, but when K=2 and L is ′ then the gasket is rigorously self-similar and possesses a similarity dimension. The evolutionary morphology of the gaskets of orders (K, L ′) bears a resemblance to the growth of pyrolitic graphite films and other material structures.

Original languageEnglish (US)
Article number011
JournalJournal of Physics A: General Physics
Volume20
Issue number11
DOIs
StatePublished - Dec 1 1987

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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