I stumbled across this fractal while trying to draw the Phoenix set. The vortex fractal (a name I picked because some versions of the fractal look like whirling vortices) 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 = X + Yi
    Z1 = 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.