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:

:$z_ = (, \operatorname \left(z_n\right), +i, \operatorname \left(z_n\right), )^2 + c, \quad z_0=0$

in the complex plane $\mathbb$ 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.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.

Implementation

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'' := 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 ''iteration'' × ''color''

References

External links

About properties and symmetries of the Burning Ship fractal
featured by Theory.org
Burning Ship Fractal
Description and C source code.
Burningship
Video,

includes the first representations and the original paper cited above on the Burning Ship fractal.
3D representations of the Burning Ship fractalFractalTS
Mandelbrot, Burning ship and corresponding Julia set generator.

{{Mathematics and art

Fractals
Articles with example pseudocode