On the symmetries of the Julia sets for the process zzp+c

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

doi:10.1088/0305-4470/20/11/051

On the symmetries of the Julia sets for the process zz^p+c

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

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84 Scopus citations

Abstract

The self-replicating properties of the Julia sets J_c(p) for the iterative processes z implies z^p+c are examined for integers p)1. It is shown that the corresponding Mandelbrot sets M(p) contain (p-1)-fold symmetries, which results in J_c(p) having p-fold symmetries.

Original language	English (US)
Article number	051
Pages (from-to)	3533-3535
Number of pages	3
Journal	Journal of Physics A: General Physics
Volume	20
Issue number	11
DOIs	https://doi.org/10.1088/0305-4470/20/11/051
State	Published - 1987

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
General Physics and Astronomy
Mathematical Physics

Access to Document

10.1088/0305-4470/20/11/051

Cite this

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title = "On the symmetries of the Julia sets for the process zzp+c",

abstract = "The self-replicating properties of the Julia sets Jc(p) for the iterative processes z implies zp+c are examined for integers p)1. It is shown that the corresponding Mandelbrot sets M(p) contain (p-1)-fold symmetries, which results in Jc(p) having p-fold symmetries.",

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AU - Messier, R.

AU - Varadan, V. K.

PY - 1987

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AB - The self-replicating properties of the Julia sets Jc(p) for the iterative processes z implies zp+c are examined for integers p)1. It is shown that the corresponding Mandelbrot sets M(p) contain (p-1)-fold symmetries, which results in Jc(p) having p-fold symmetries.

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