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Parhelion
Newton & Halley

Parhelion

Newton Fractal

A vibrant, symmetrical fractal with a dark circular void at its centre, surrounded by radiating arms. A repeating pattern of smaller circles and intricate curves transitions through green, orange, red, purple and blue, geometric and endlessly deep. Newton's method applied to f(z) = cos(z^3) - 1/2. The roots lie on six rays sixty degrees apart, which is where the frame gets its exact sixfold symmetry. Colour shows which ray each point falls to, and the boundary lace glows warm white.