Interactive three-dimensional simulations & visualizations

Visualizing the beauty in physics and mathematics


Project maintained by zhendrikse Hosted on GitHub Pages — Theme by mattgraham

Complex functions $\phi: \mathbb{C} \rightarrow \mathbb{C}$


What are you looking at?

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.


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