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