Burning Ship

The Burning Ship fractal process is similar to the Mandelbrot Set process, but now the real and imaginary components of z are replaced by their absolute values (i.e. replace – with +):

zn+1 = (|Re(zn)| + i * |Im(zn)|)2 + c

Wikiepdia: 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} = (|\operatorname{Re} \left(z_n\right)|+i|\operatorname{Im} \left(z_n\right)|)^2 + c, \quad z_0=0

in the complex plane \mathbb{C} which will either escape or remain bounded. The difference between this calculation and that for theMandelbrot 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.

Burning Ship Fractal renderings
High-quality deep-zoom image of a small ship in the armada in the left Western antenna of the main ship structure
Burning Ship Deep Zoom to 2.3e-50
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 line on the left of the fractal, showing nested repetition (a different colour scheme is used here).
High quality image of the Burning Ship fractal.
The Burning Ship Fractal featured in the 1K intro “JenterErForetrukket” by Youth Uprising; a demoscene production.
A Corresponding Julia Set of Burning Ship Fractal
A Corresponding Julia Set of Burning Ship Fractal.

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