"Burning Ship" fractal

The images described here are generated by analysing the following series for each point (c_x,c_y) on the plane.

The grey level assigned to each point (c_x,c_y) is determined by how fast the series tends to infinity. For example, the points shown in black in the center of the form don't ever diverge to infinity, they either oscillate or converge to a singe value. The points shown in light grey diverge very quickly. This is exactly the same technique used to create the Mandelbrot image. In all cases the starting point (x₀,y₀) is (0,0).

This fractal gets its name from the images obtained by zooming into regions along y=0 (x axis) an example is shown below for the largest "ship".

Source code

This C source code gives the basic idea of how the images on this page were created. As it stands it is run given a centre coordinate, a image width in world coordinates, and the name of the output file. It writes a raw RGB or greyscale image, this can be opened with most image editors or you can modify the code to save the image in your favorite format.

Buddhabrot style "fingerprint"

Exploring the tail (Click to enlarge)