Fractal structures derivable from the generalisations of the Pascal triangle

A. Lakhtakia; R. Messier; V. K. Varadan; V. V. Varadan

doi:10.1088/0305-4470/20/11/011

Fractal structures derivable from the generalisations of the Pascal triangle

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

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4 Scopus citations

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 language	English (US)
Article number	011
Pages (from-to)	L735-L738
Journal	Journal of Physics A: General Physics
Volume	20
Issue number	11
DOIs	https://doi.org/10.1088/0305-4470/20/11/011
State	Published - 1987

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
General Physics and Astronomy
Mathematical Physics

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10.1088/0305-4470/20/11/011

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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.",

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year = "1987",

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AU - Lakhtakia, A.

AU - Messier, R.

AU - Varadan, V. K.

AU - Varadan, V. V.

PY - 1987

Y1 - 1987

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AB - 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.

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Fractal structures derivable from the generalisations of the Pascal triangle

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