Bravais mark BRAVAIS
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Pentapole Star
Newton & Halley

Pentapole Star

Newton Fractal

Newton's method applied to the rational function f(z) = z^5 - 1 + 0.1/(z^5 + 0.25). The poles are repelling points of the map, so no basin can settle around them and each one punches a vortex hole through the star. Colour shows the captured root and the smoothed count of steps.