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Aurora Pentad
Newton & Halley

Aurora Pentad

Relaxed Newton Fractal

Newton's method with complex relaxation a = 0.72 - 0.60i applied to f(z) = z^5 - 1. The multiplier at every root is 1 - a, so convergence is linear and rotating and each of the five basins drains as a logarithmic spiral. Brightness follows the smooth iteration count and the arms follow the Koenigs phase alpha = arg(u) - n arg(lambda), which is constant along an orbit.