The Phoenix set was discovered by Shigehiro Ushiki in 1988. The fractal is generated by iterating the equation:

    Zn+1 = Zn2 + Re(C) + Im(C) * Zn-1

Where the Zs and C are complex numbers, C is a constant, and for a point (X, Y):

    Z0 = 0
    Z1 = 0
    C  = X + Yi

The program iterates this equation until the magnitude of Z_n is at least 2 or the program performs a maximum number of iterations.

See the code for details.