The Burning Ship fractal is a variation of the Mandelbrot set. The iteration formula is very similar, but with a key difference:

 z_{n+1} = (|\Re(z_n)| + i|\Im(z_n)|)^2 + c
    

where $z_0 = 0$ and $c$ is the point on the complex plane being tested. Before squaring the complex number $z_n$ in each iteration, the absolute values of its real and imaginary parts are taken. This simple change creates a dramatically different fractal shape, which often resembles a ship on fire.

For more information on the general principles of this type of fractal, see the description of the Mandelbrot set.

Parameters

GUI Parameters

• Iterations: This integer value determines the maximum number of times the formula is applied for each point.

Complex Parameters

This fractal does not have any complex parameters that can be controlled directly as control points. The complex number $c$ corresponds to each point on the plane being tested.