Self-similarity versus self-affinity: The Sierpinski gasket revisited

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

doi:10.1088/0305-4470/19/16/007

Self-similarity versus self-affinity: The Sierpinski gasket revisited

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

Engineering Science and Mechanics

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

11 Scopus citations

Abstract

A Hilbert curve is constructed on the Sierpinski gasket. It is shown that despite the fact that the Sierpinski gasket is rigorously self-similar, the Hilbert curve is merely self-affine.

Original language	English (US)
Article number	007
Pages (from-to)	L985-L989
Journal	Journal of Physics A: Mathematical and General
Volume	19
Issue number	16
DOIs	https://doi.org/10.1088/0305-4470/19/16/007
State	Published - Dec 1 1986

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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title = "Self-similarity versus self-affinity: The Sierpinski gasket revisited",

abstract = "A Hilbert curve is constructed on the Sierpinski gasket. It is shown that despite the fact that the Sierpinski gasket is rigorously self-similar, the Hilbert curve is merely self-affine.",

author = "A. Lakhtakia and R. Messier and Varadan, \{V. V.\} and Varadan, \{V. K.\}",

year = "1986",

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T1 - Self-similarity versus self-affinity

T2 - The Sierpinski gasket revisited

AU - Lakhtakia, A.

AU - Messier, R.

AU - Varadan, V. V.

AU - Varadan, V. K.

PY - 1986/12/1

Y1 - 1986/12/1

N2 - A Hilbert curve is constructed on the Sierpinski gasket. It is shown that despite the fact that the Sierpinski gasket is rigorously self-similar, the Hilbert curve is merely self-affine.

AB - A Hilbert curve is constructed on the Sierpinski gasket. It is shown that despite the fact that the Sierpinski gasket is rigorously self-similar, the Hilbert curve is merely self-affine.

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U2 - 10.1088/0305-4470/19/16/007

DO - 10.1088/0305-4470/19/16/007

M3 - Article

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

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M1 - 007

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Self-similarity versus self-affinity: The Sierpinski gasket revisited

Abstract

All Science Journal Classification (ASJC) codes

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