At the Helm of the Burning Ship

Abstract

The Burning Ship fractal is a non-analytic variation of the Mandelbrot set, formed by taking absolute values in the recurrence. Iterating its Jacobian can identify the period of attracting orbits; Newton’s root-finding method locates their mini-ships. Size estimates tell how deep to zoom to find the mini-ship or its embedded quasi-Julia set. Pre-periodic Misiurewicz points with repelling dynamics are located by Newton’s method. Stretched regions are automatically unskewed by the Jacobian, which is also good for colouring images using distance estimation. Perturbation techniques cheapen deep zooming. The mathematics can be generalised to other fractal formulas. Some artistic zooming techniques and domain colouring methods are also described.

Contributors

Claude Heiland-Allen

Conference

Publication date: July 2019

Publication date (Print): July 2019

Pages: 402-408

Affiliations

unaffiliated

London, UK

Article

DOI: 10.14236/ewic/EVA2019.74

Copyright statement: © Heiland-Allen. Published by BCS Learning and Development Ltd. Proceedings of EVA London 2019, UK

License:

This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Conference name: Proceedings of EVA London 2019

Conference acronym: EVA 2019

Conference number:

Conference location: London, UK

Conference date: 8 - 11 July 2019

Conference sponsor: Electronic Workshops in Computing (eWiC)

Conference theme: Electronic Visualisation and the Arts

Product

Product Information: 1477-9358BCS Learning & Development

Self URI (article page): https://www.scienceopen.com/hosted-document?doi=10.14236/ewic/EVA2019.74

Self URI (journal page): https://ewic.bcs.org/

Categories

Series title: Electronic Workshops in Computing