Running Corolla

The current section of the gallery features Julia sets given by the Mandelbrot equation zn+1 = zn2 + p, and the above picture comes from p = (-1.1128, 0.23076). The interior of the gold Julia set comprises the initial values of orbits that are attracted to a cycle of period 54. It is in fact painted by the General Convergence Scheme (4.2) with k = 54.

With experience, it gets easier to figure out the period of the cycle involved by looking at the shape of the Julia set and/or the location of p in the Mandelbrot set. Both will tell us that 54 comes from 2 x 3 x 9 and we can clearly see the effect of 2, 3, and 9 in the shape of the Julia set. See Stories about Fractal Plotting for the technical terms.