At the Helm of the Burning Ship

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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Claude Heiland-Allen

Conference

Publication date: July 2019

Publication date (Print): July 2019

Pages: 402-408

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[0001]unaffiliated

London, UK

Article

DOI: 10.14236/ewic/EVA2019.74

SO-VID: 85a2a60c-54ee-47e8-87ea-2d220614e3bc

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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

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Conference location: London, UK

Conference date: 8 - 11 July 2019

Conference sponsor: Electronic Workshops in Computing (eWiC)

Conference theme: Electronic Visualisation and the Arts

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1477-9358 BCS 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/

REFERENCES

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Comments

Comment on this article

[1] “gerrit” 2017 Re: burning ship distance estimation https://fractalforums.Org/f/18/t/647/msg3207#msg3207 retrieved 14 February 2019 )

[2] B. R. HuntE. Ott 1997 Structure in the Parameter Dependence of Order and Chaos for the Quadratic Map J. Phys. A 30 7067 7076

[3] W. Jung 2018 Renormalization and embedded Julia sets in the Mandelbrot set Preprint of December 2018 http://mndynamics.com/papers/embed.pdf retrieved 14 February 2019 )

[4] “knighty” 2017 A little note about Ball arithmetic https://fractalforums.org/f/28/t/481/msg2800#msg2800 retrieved 14 February 2019 )

[5] “laser blaster” 2014 Perturbation Formula for Burning Ship http://www.fractalforums.com/index.php?topic=19165.msg74089#msg74089 retrieved 14 February 2019 )

[6] K. I. Martin 2013 SuperFractalThing Maths http://www.superfractalthing.co.nf/sft_maths.pdf retrieved 14 February 2019 )

[7] M. MichelitschO. E. Rössler The “Burning Ship” and its Quasi-Julia sets Comput. & Graphics 16 4 1992 435 438

[8] R. Munafo 2008 Finding the Period of a mu-Atom https://www.mrob.com/pub/muency/period.html retrieved 14 February 2019 )

[9] “Pauldelbrot” 2014 Perturbation Theory Glitches Improvement http://www.fractalforums.com/index.php?topic=18908.msg73027#msg73027 retrieved 14 February 2019 )

[10] H. G. PeitgenP. H. Richter 1986 The Beauty of Fractals: Images of Complex Dynamical Systems Springer-Verlag Berlin Heidelberg

[11] K. Runmo 2017 Re: compiling Kalles Fraktaler with mingw http://www.fractalforums.com/index.php?topic=25458.msg103177#msg103177 retrieved 14 February 2019 )

[12] F. Uhlig 1981 Explicit polar decomposition and a near-characteristic polynomial: The 2×2 case Linear Algebra and its Applications 38 June 1981 239 249

[13] L. Vepstas 1997 Renormalizing the Mandelbrot Escape https://linas.org/art-gallery/escape/escape.html retrieved 14 February 2019 )

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