The sets for other values of d also show fractal images[7] when they are plotted on the complex plane.
There is interesting complex behaviour in the contours between the set and the origin, in a star-shaped area with (1 − d)-fold rotational symmetry.
The resulting set rises vertically from the origin in a narrow column to infinity.
The first prominent bump or spike is seen at an exponent of 2, the location of the traditional Mandelbrot set at its cross-section.
[8] All the above images are rendered using an Escape Time algorithm that identifies points outside the set in a simple way.
Much greater fractal detail is revealed by plotting the Lyapunov exponent,[9] as shown by the example below.