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

Engineering Science and Mechanics

Research output: Contribution to journal › Article › peer-review

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: Mathematical and General
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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T1 - Fractal structures derivable from the generalisations of the Pascal triangle

AU - Lakhtakia, A.

AU - Messier, R.

AU - Varadan, V. K.

AU - Varadan, V. V.

PY - 1987

Y1 - 1987

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/36149028980

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 11

M1 - 011

ER -

Fractal structures derivable from the generalisations of the Pascal triangle

Abstract

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