A view of the Burning Ship fractal. This is a fractal generated by iterating the following equation for each point with coordinates c in the complex plane:
Z_{n+1}=\left( |\Re \left( {Z_n} \right)|- i|\Im\left( {Z_n} \right)| \right)^2 + c, \quad Z_0=0
This image is in the complex plane with lower left corner (-1.67, -0.002i) and upper right corner (-1.65, 0.013i). Some descriptions of this fractal give the equation with an addition rather than a subtraction. This produces a reflection in the real-axis, which means that it is hard to see the “burning ship”.
If the iteration “escapes” to large numbers, it is coloured according to how long it took to reach a cutoff point (here, 40). If it does not escape after 100 iteration, the point is coloured black.
This image was made in Ultrafractal 4.
