Brennendes Schiff.jpg|thumb|Main body of the Burning Ship fractal; window-coodinates: -1.25< cx < 2.25; -0.75 < cy <1.75; initial condition: x0 = y0 = 0]]

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

$z\; \backslash rightarrow\; (|\backslash Re\; \backslash \{z\backslash \}|+i|\backslash Im\; \backslash \{z\backslash \}|)^2\; +\; c$ in the complex c-plane (initial condition z = 0) which will either converge or escape. 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 conditions ^*.

References

• Michael Michelitsch and Otto E. Rössler, The "Burning Ship" and Its Quasi-Julia Sets, Computers & Graphics Vol. 16, No. 4, pp. 435-438, 1992, reprinted in [2
• ^* Clifford A. Pickover Ed., Chaos and Fractals: A Computer Graphical Journey - A 10 Year Compilation of Advanced Research. Amsterdam, Netherlands: Elsevier 1998. ISBN 0-444-50002-2

External links

• Michelitsch Fractals -- A collection of fractals created by Michael Michelitsch
• Representation of the Burning Ship fractal by Paul Burke
• About properties and symmetries of the Burning Ship fractal, featured by Theory.org
• Burning Ship with its Mset of higher powers and Julia Sets
• Burning Ship fractal zoomer by Jetro Lauha, Video
• Burning Ship Fractal zoomer by tAAt

Fractals

Płonący statek