Calculation of the structure of a shrub in the Mandelbrot set
type: Item
instance of: scholarly article
title: Calculation of the structure of a shrub in the Mandelbrot set
zbMATH Open document ID: 1267.37050
DOI: 10.1155/2011/837262
author: A. B. Orue
author: G. Pastor
author: M. Romera
author: A. Martin
author: M.-F. Danca
author: Fausto Montoya
published in: Discrete Dynamics in Nature and Society
publication date: 2012-01-23T00:00:00Z
review text: Summary: We calculate the external arguments of the structure of any shrub in the Mandelbrot set. Before calculating, we revise, expand, and clarify some tools useful for this paper: harmonics, pseudoharmonics, the concept of structure, the structure of a shrub, and the ancestral route. Finally we present the main contribution of this paper, a three-step algorithm which allows us to calculate the structure of the shrub. In the first step, we use pseudoharmonics that were previously introduced by us, in order to calculate the first and last external arguments of a structural node. In the second step, starting from two general properties of the Misiurewicz points external arguments introduced here by us, we present a new method to calculate the intermediate external arguments. In the last step we introduce a third property that allows us to calculate the external arguments of the representatives of the branches emerging from the structural nodes.
Mathematics Subject Classification ID: 37F45
zbMATH DE Number: 5999662
zbMATH Keywords: shrub
zbMATH Keywords: Mandelbrot set
Wikidata QID: Q58655550
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/837262
OpenAlex ID: W2021587188
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description: scientific article; zbMATH DE number 5999662