Burning Ship fractal

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

${\displaystyle z_{n+1}=(|\operatorname {Re} \left(z_{n}\right)|+i|\operatorname {Im} \left(z_{n}\right)|)^{2}+c,\quad z_{0}=0}$

in the complex plane ${\displaystyle \mathbb {C} }$ 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.^[1] The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy–Riemann equations.^[2]

Virtually all images of the Burning Ship fractal are reflected vertically for aesthetic purposes, and some are also reflected horizontally.^[3]