The Fractal dropdown menu in the ChaosExplorer program contains 4 menu items:
- z^p + c
- c*e^z, and
Each of these menu items displays the fractal (z0 = 0.0 + 0.0i, varying c over the complex plane). Selecting the first menu item displays the Mandelbrot Set; selecting any of the others displays the fractal for the indicated formula. This post specifically shows the fractal and Julia Sets for the second menu item, whose formula is:
zn+1 = (zn3 + 1) / (1 + czn2)
Here is the fractal display. This is for the region -10.0 ≤ x ≤ 10.0, -10.0 ≤ y ≤ 10.0:
And here are 4 Julia Set displays for points in this fractal:
As you can see, the fractal and Julia Sets are very different from the Mandelbrot/Multibrot fractals and Julia Sets.