Type of fractals : Halley.

Basic function used : F = z (z ^ a - 1) = 0

z(0) = pixel;
z(n+1) = z(n) - R * F / [F' - (F'' * F / 2 * F')]
bailout when abs(mod(z(n + 1))- mod(z(n)) < epsilon.

4 parameters :
. 2 real numbers : order a (integer > 1) and epsilon,
. Real and imaginary parts of R (relaxation coefficient).

Parameters used here : a = 2, epsilon = 2.5 e ^ -9, real(R) = 2, imag(R) = 0.

With the same parameters but with another palette of colors, the new fractal looks like this :



If epsilon = 0.01, the fractal is the folowing (with the palette used for fractal HALL001) :



With epsilon = 0.05, epsilon = 0.001 and epsilon = 0.0001, the three fractals below are displayed :
1) epsilon = 0.05 :



2) epsilon = 0.001 :



3) epsilon = 0.0001 :