On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson

Christian, JM ORCID: https://orcid.org/0000-0003-2742-0569 and Middleton-Spencer, HAJ 2020, 'On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson' , The College Mathematics Journal, 51 (2) , pp. 95-114.

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Abstract

We consider a systematic generalization of the well-known cube roots of -1 problem to include the Nth roots. The associated fractal basin boundaries are computed, and we also explore how sensitive this class of systems is to fluctuations at its input by estimating the “uncertainty” fractal dimension. Other curious results are uncovered along the way.

Item Type: Article
Schools: Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre
Journal or Publication Title: The College Mathematics Journal
Publisher: Taylor & Francis
ISSN: 0746-8342
Related URLs:
Depositing User: JM Christian
Date Deposited: 03 Mar 2020 10:22
Last Modified: 14 Jul 2020 14:46
URI: http://usir.salford.ac.uk/id/eprint/56536

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