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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 135637, 14 pages
Research Article

Coupling Patterns of External Arguments in the Multiple-Spiral Medallions of the Mandelbrot Set

Instituto de Física Aplicada, CSIC, Serrano 144, 28006 Madrid, Spain

Received 8 March 2009; Revised 2 July 2009; Accepted 16 November 2009

Academic Editor: B. Sagar

Copyright © 2009 M. Romera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The multiple-spiral medallions are beautiful decorations situated in the proximity of the small copies of the Mandelbrot set. They are composed by an infinity of babies Mandelbrot sets that have external arguments with known structure. In this paper we study the coupling patterns of the external arguments of the baby Mandelbrot sets in multiple-spiral medallions, that is, how these external arguments are grouped in pairs. Based on our experimental data, we obtain that the canonical nonspiral medallions have a nested pairs pattern, the canonical single-spiral medallions have an adjacent pairs pattern, and we conjecture that the canonical double, triple, quadruple-spiral medallions have a 1-nested/adjacent pairs pattern.