Jump to content

Burning Ship fractal

From Wikipedia, the free encyclopedia
Detail of the Burning Ship fractal

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

in the complex plane Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \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.[1] The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy–Riemann equations.[2]

Virtually all images of the Burning Ship fractal are reflected vertically for aesthetic purposes, and some are also reflected horizontally.[3]

Implementation

[edit]
Animation of a continuous zoom-out to show the amount of detail for an implementation with 64 maximum iterations

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 (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 (max_iteration / iteration) × color
[edit]

References

[edit]
  1. ^ Agarwal, Shafali; Negi, Ashish (2013). "Inventive Burning Ship". International Journal of Advances in Engineering & Technology.
  2. ^ 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
  3. ^ "HPDZ.NET - Still Images - Burning Ship".
[edit]