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 :