Burning Ship fractal
4264157
224421425
2008-07-08T19:46:50Z
Mdd
113850
Wikification
[[Image:Burning Ship Fractal.png|thumb|240px|The Burning Ship fractal]]
[[Image:Burning Ship Fractal Zoom.png|thumb|240px|A zoom-in to the lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal.]]
[[Image:Burning Ship Fractal Zoom 2.png|thumb|240px|A zoom-in to line on the left of the fractal, showing nested repetition (a different colour scheme is used here).]]
The '''Burning Ship fractal''', first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:
:<math>Z_{n+1} = (|\Re \left(Z_n\right)|+i|\Im \left(Z_n\right)|)^2 + c, \quad Z_0=0</math>
in the complex c-plane which will either converge or escape. The difference between this calculation and that for the [[Mandelbrot set]] is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The mapping is non-analytic because its real and imaginary parts do not obey the [[Cauchy-Riemann conditions]].<ref>Michael Michelitsch and Otto E. Rössler (1992). "The "Burning Ship" and Its Quasi-Julia Sets". In: ''Computers & Graphics'' Vol. 16, No. 4, pp. 435-438, 1992. Reprinted in [[Clifford A. Pickover]] Ed. (1998). ''Chaos and Fractals: A Computer Graphical Journey - A 10 Year Compilation of Advanced Research''. Amsterdam, Netherlands: Elsevier. ISBN 0-444-50002-2</ref>
==References==
{{reflist}}
==External links==
*[http://www.theory.org/fracdyn/burningship/ About properties and symmetries of the Burning Ship fractal], featured by Theory.org,
*[http://ozviz.wasp.uwa.edu.au/~pbourke/fractals/burnship/ Burning Ship Fractal], Description generated by a C source code.
*[http://www.graphicandfractalworld.com/Me.html Burning Ship with its Mset of higher powers and Julia Sets]
*[http://clanspk.hostingposts.com/burningship.htm Burning Ship fractal] Some features.
*[http://jet.ro/effects Burning Ship fractal zoomer by Jetro Lauha]
*[http://jet.ro/video_burningship Burningship], Video,
*[http://www.geocities.com/tmichelitsch/Michelitsch_Fractals.html Fractal webpage] includes the first representations and the original paper cited above on the Burning Ship fractal.
[[Category:Fractals]]
{{geometry-stub}}
[[hr:Gorući brod (fraktal)]]
[[ja:バーニングシップ・フラクタル]]
[[pl:Płonący statek]]