Burning Ship fractal
in the complex plane 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.
- Burning Ship fractal renderings
The below pseudocode implementation hardcodes the complex operations for Z. Consider implementing complex number operations to allow for more dynamic and reusable code. Note that the typical images of the Burning Ship fractal display the ship upright: the actual fractal, and that produced by the below pseudocode, is inverted along the x-axis.
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 := 1000 while (zx*zx + zy*zy < 4 and iteration < max_iteration) do xtemp := zx*zx - zy*zy + x zy := abs(2*zx*zy) + y // abs returns the absolute value zx := xtemp iteration := iteration + 1 if iteration = max_iteration then // Belongs to the set return insideColor return iteration × color
- 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
|Wikimedia Commons has media related to Burning Ship fractal.|
- About properties and symmetries of the Burning Ship fractal, featured by Theory.org
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- Fractal webpage includes the first representations and the original paper cited above on the Burning Ship fractal.
- 3D representations of the Burning Ship fractal
- FractalTS Mandelbrot, Burning ship and corresponding Julia set generator.