
complexnewton and complexbasin

    Newton fractal types extended to complex degrees. Complexnewton
    colors pixels according to the number of iterations required to
    escape to a root. Complexbasin colors pixels according to which
    root captures the orbit. The equation is based on the newton
    formula for solving the equation z^p = r

      z(0) = pixel
      z(n+1) = ((p - 1) * z(n)^p + r)/(p * z(n)^(p - 1)).

    Four parameters: real & imaginary parts of degree p and root r


Well, hey, "Z^n - 1" is so boring when you can use "Z^a - b" where "a" and
"b" are complex numbers!  The new "complexnewton" and "complexbasin"
fractal types are just the old "newton" and "newtbasin" fractal types with
this little added twist. When you select these fractal types, you are
prompted for four values (the real and imaginary portions of "a" and "b").
If "a" has a complex portion, the fractal has a discontinuity along the
negative axis - relax, we finally figured out that it's *supposed* to be
there!

