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Lanterns on the Logarithmic SeaZeros and poles of a complex rational function R(z,t) drift across a 3D landscape carved from the logarithmic potential U(z,t)=log|R(z,t)|. Every ridge, valley, and glowing thread comes from the moving R(z,t), while the particles follow the tangent field of its level curves. The golden lantern ovals mark the singularities directly. So, the whole scene becomes a living map of where the function vanishes, where it blows up, and how the surrounding geometry bends in r
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Lanterns on the Logarithmic SeaZeros and poles of a complex rational function R(z,t) drift across a 3D landscape carved from the logarithmic potential U(z,t)=log|R(z,t)|. Every ridge, valley, and glowing thread comes from the moving R(z,t), while the particles follow the tangent field of its level curves. The golden lantern ovals mark the singularities directly. So, the whole scene becomes a living map of where the function vanishes, where it blows up, and how the surrounding geometry bends in r
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The Cosmic Cartography of Zeros and PolesYou are looking at a moving map of a rational function.The golden wells are zeros.The dark singular crowns are poles.Between them, the glowing threads trace the invisible geography of a complex function as it bends, folds, and reorganizes the plane.The object driving the scene isR(z,t) = ∏ⱼ₌₁ᵐ(z - aⱼ(t)) / ∏ₖ₌₁ⁿ(z - bₖ(t))The zeros aⱼ(t) act like downward wells in the logarithmic landscape.The poles bₖ(t) act like upward singular peaks.That landscape isU(
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The Cosmic Cartography of Zeros and PolesYou are looking at a moving map of a rational function.The golden wells are zeros.The dark singular crowns are poles.Between them, the glowing threads trace the invisible geography of a complex function as it bends, folds, and reorganizes the plane.The object driving the scene isR(z,t) = ∏ⱼ₌₁ᵐ(z - aⱼ(t)) / ∏ₖ₌₁ⁿ(z - bₖ(t))The zeros aⱼ(t) act like downward wells in the logarithmic landscape.The poles bₖ(t) act like upward singular peaks.That landscape isU(
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