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The Map That Pulls The Plane Through Its ResiduesA meromorphic function can turn the complex plane into a living flow.Here we build a rational map from moving zeros and poles:R(z) = Π(z-aⱼ) / Π(z-bₖ).The field color comes fromU(z) = log|R(z)|,so one side of the image is dominated by zeros, the other by poles, and the pale lace appears where |R(z)| ≈ 1.The motion comes from the logarithmic derivative:S(z) = R′(z)/R(z)   = Σ 1/(z-aⱼ) - Σ 1/(z-bₖ).Instead of pushing particles through an arbitrary v
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