The burning ship fractal is the set of complex parameters 
for which the sequence beginning with 
and defined by
![z_(n+1)=[|Rez_n|+i|Imz_n|]^2+c.](/images/equations/BurningShipFractal/NumberedEquation1.svg) |
remains bounded. It differs from the Mandelbrot set by taking the absolute values of the real and imaginary parts before squaring at every iteration.
The defining map is not complex analytic because of the absolute values. Escape-time images color parameters outside the set according to how rapidly their iterates escape. The name comes from the ship-like appearance of the main component when displayed with the conventional orientation.
