Burning Ship fractal

High-quality overview image of the Burning Ship fractal
High-quality image of the large ship in the left antenna

The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:

z_{n+1} = (|\operatorname{Re} \left(z_n\right)|+i|\operatorname{Im} \left(z_n\right)|)^2 + c, \quad z_0=0

in the complex plane \mathbb{C} which will either escape or remain bounded. 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 equations.[1]

Burning Ship fractal renderings
High-quality deep-zoom image of a small ship in the armada in the left Western antenna of the main ship structure 
Burning Ship deep zoom to 2.3·10−50 
The Burning Ship fractal 
A zoom-in to the lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal 
A zoom-in to line on the left of the fractal, showing nested repetition (a different colour scheme is used here) 
High-quality image of the Burning Ship fractal 
The Burning Ship fractal featured in the 1K intro "JenterErForetrukket" by Youth Uprising; a demoscene production 
A corresponding Julia set of Burning Ship fractal 
A corresponding Julia set of Burning Ship fractal 

References

  1. ↑ 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

External links

Wikimedia Commons has media related to Burning Ship fractal.
This article is issued from Wikipedia - version of the Monday, February 15, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.