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Burning Ship fractal

Complex plane fractal

$Burning Ship fractal$

Complex plane fractal

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.

Virtually all images of the Burning Ship fractal are reflected vertically for aesthetic purposes, and some are also reflected horizontally.

Implementation

The below pseudocode implementation hardcodes the complex operations for Z. Consider implementing complex number operations to allow for more dynamic and reusable code.

for each pixel (x, y) on the screen, do: x := scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.5, 1)) y := scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1, 1))

zx := x // zx represents the real part of z zy := y // zy represents the imaginary part of z

iteration := 0 max_iteration := 100

while (zxzx + zyzy xtemp := zxzx - zyzy + x zy := abs(2zxzy) + y // abs returns the absolute value zx := xtemp iteration := iteration + 1

if iteration = max_iteration then // Belongs to the set return INSIDE_COLOR

return (max_iteration / iteration) × color // Assign color to pixel outside the set

Gallery

|File:Burning Ship 3e-9.jpg|High-quality deep-zoom image of a small ship in the armada in the left Western antenna of the main ship structure |File:Burning Ship Deep Zoom 2e-50.jpg|Burning Ship deep zoom to 2.3·10−50 |File:Burning Ship Fractal.png|The Burning Ship fractal |File:Burning Ship Fractal Zoom.png|A zoom-in to the lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal |File:Burning Ship Fractal Zoom 2.png|A zoom-in to line on the left of the fractal, showing nested repetition (a different colour scheme is used here) |File:Burning Ship 144x.jpg|High-quality image of the Burning Ship fractal |File:Jentererforetrukket.jpg|The Burning Ship fractal featured in the 1K intro "JenterErForetrukket" by Youth Uprising; a demoscene production |File:Ghost Ship fractal.png|Ghost Ship - The Burning Ship fractal rendered using the Nebulabrot technique |File:A Corresponding Julia Set of Burning Ship Fractal 2.PNG|A corresponding Julia set of Burning Ship fractal |File:A Corresponding Julia Set of Burning Ship Fractal.PNG|A corresponding Julia set of Burning Ship fractal |File:Burning Ship Fractal 4800x3600.png|High resolution image of the burning ship fractal |File:High quality rendering of the structure of the Burning Ship fractal's pattern.png|The structure of the Burning Ship fractal |File:Burning Ship 20210818.png|High-quality overview image of the Burning Ship fractal |File:Burning Ships.jpg|Chain of burning ships |File:Burning Ship 0002 20210818.png|High-quality image of the large ship in the left antenna |File:BurningShip full.jpg|Full fractal

References

(2013). "Inventive Burning Ship". International Journal of Advances in Engineering & Technology.
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
"HPDZ.NET - Still Images - Burning Ship".

Info: Wikipedia Source

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