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 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 CauchyâÂÂRiemann equations.
Virtually all images of the Burning Ship fractal are reflected vertically for aesthetic purposes, and some are also reflected horizontally.
The below pseudocode implementation hardcodes the complex operations for Z. Direct complex number operations may optionally be implemented instead.
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 INSIDE_COLOR
return (max_iteration / iteration) ÃÂ color // Assign color to pixel outside the set