Visualizing the beauty in physics and mathematics
You are looking at a 3D visualization of complex-valued functions
\[\psi(z) = F(z), \quad z \in \mathbb{C}.\]↔️ Horizontal plane represents the complex input $z = x + iy$
↕️ Height shows the magnitude $\text{height} = \log\left( |F(z)|\right)$
🎨 Color encodes the complex phase (argument) of $F(z)$: colors rotate continuously as the phase winds around zero points
✂️ Branch cuts appear as sudden color jumps — places where the phase cannot be made continuous
🔴↔🔵 Full color cycles indicate a complete $2\pi$ phase rotation
Height & color reveal how the function stretches, twists, and folds the complex plane.
🛠️ The images are generated with complex_surfaces.html.
Share on: