Domain coloring a complex function

For \(f(z)=\dfrac{z^3-1}{z^2+1}\), hue records the argument of the output while lightness records its magnitude.

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Domain-coloring implementation by Raj Raizada (@rajraizada.bsky.social); function and presentation adapted for this demo.

What you’re seeing

Black regions mark zeros, bright regions approach poles, and the repeating bands make changes in magnitude and argument easier to follow.