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      At the Helm of the Burning Ship

      Proceedings of EVA London 2019 (EVA 2019)

      Electronic Visualisation and the Arts

      8 - 11 July 2019

      Burning Ship, Dynamical systems, Fractal art, Numerical algorithms, Perturbation theory

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          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.

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          Most cited references 6

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          The “burning ship” and its quasi-Julia sets

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            Renormalization and embedded Julia sets in the Mandelbrot set

             W. JUNG (2018)
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              SuperFractalThing Maths

               K. P. MARTIN (2013)
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                Author and article information

                Contributors
                Conference
                July 2019
                July 2019
                : 402-408
                Affiliations
                unaffiliated

                London, UK
                Article
                10.14236/ewic/EVA2019.74
                © Heiland-Allen. Published by BCS Learning and Development Ltd. Proceedings of EVA London 2019, UK

                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/

                Proceedings of EVA London 2019
                EVA 2019
                London, UK
                8 - 11 July 2019
                Electronic Workshops in Computing (eWiC)
                Electronic Visualisation and the Arts
                Product
                Product Information: 1477-9358BCS Learning & Development
                Self URI (journal page): https://ewic.bcs.org/
                Categories
                Electronic Workshops in Computing

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