Burning Ship fractal

From Wikipedia, the free encyclopedia

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

$Z_{n+1} = (|\Re \left(Z_n\right)|+i|\Im \left(Z_n\right)|)^2 + c, \quad Z_0=0$

in the complex c-plane 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.^[1]

$The Burning Ship fractal$

The Burning Ship fractal

$A zoom-in to the lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal.$

A zoom-in to the lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal.

$A zoom-in to line on the left of the fractal, showing nested repetion (a different colour scheme is used here).$

A zoom-in to line on the left of the fractal, showing nested repetion (a different colour scheme is used here).

[edit] 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
- 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