Golden Hexad

Newton's method with complex relaxation a = 0.60 - 0.70i applied to f(z) = z^6 + z^3 - 1, whose roots are the cube roots of the two golden-section values. The multiplier at every root is 1 - a, so convergence is linear and rotating and the basins smear into logarithmic spirals. Hue is set by the Koenigs phase alpha = arg(u) - n arg(lambda) and brightness by the smooth iteration count.