This ugly fractal is the Mandelbrot set equivalent for the Phoenix set. It is here only so you can look at the more beautiful Julia set equilalents, or Phoenix Sets. (Hint: try c = (0.56667, -0.5))

The formula for the Phoenix Sets and its Mandelbrot equivalent is

z_{n + 1} =
z_{n}^{2} + Re(c) + Im(c) * z_{n - 1}

The sugested value of c to use to get a Phoenix Set gives the same image as the phoenix curve originally discovered by Shigehiro Ushiki. Unfortunately this set doesn't have the same Mandelbrot/Julia Set properties as the classic Mandelbrot Set. That is values of c inside the black area will not nesessarily give a connected set and vice versa.