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

Christian, JM; Middleton-Spencer, HAJ

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.

Citation

Christian, J., & Middleton-Spencer, H. (2020). On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson. College Mathematics Journal, 51(2), 95-114. https://doi.org/10.1080/07468342.2020.1703452

• Journal Article Type: Article
• Acceptance Date: Dec 9, 2019
• Online Publication Date: Feb 25, 2020
• Publication Date: Feb 25, 2020
• Deposit Date: Mar 3, 2020
• Publicly Available Date: Feb 25, 2021
• Journal: The College Mathematics Journal
• Print ISSN: 0746-8342
• Electronic ISSN: 1931-1346
• Publisher: Mathematical Association of America
• Volume: 51
• Issue: 2
• Pages: 95-114
• DOI: https://doi.org/10.1080/07468342.2020.1703452
• Publisher URL: https://doi.org/10.1080/07468342.2020.1703452
• Related Public URLs: https://www.tandfonline.com/toc/ucmj20/current