Complex Function Visualizer - Domain Coloring & Transformation

Back to Portfolio Switch to Plane-Plane Mapping Mode

Riemann Surface Mode

Function

Function to Visualize

f(z) - Function f'(z) - Derivative

Component Selection

Riemann Surface: Re Riemann Surface: Im Magnitude: |f| Argument: arg(f)

Surface Display

Colorized Plane Surface in 3D (height = value)

Multi-Valued Functions

Show All Branches

Distortion Field Settings

Show Direction Arrows Show Stretch Ellipses Grid Density: 12

Riemann Surface Settings

Height Scale: 1.5

Curve Settings

Curved (vs Straight) Thick Tubes (vs Thin Lines) Opacity: 0.7

Arrow Grid Settings

Grid Density: 10

Highlight Settings

Show Highlight (Hover) Region Shape: Region Size: 0.3 Pipe Density: 24

Display

Show From Plane Show To Plane Show Grid

Singularity Analysis

f(z) Poles (Bright Red) f(z) Zeros (Bright Blue) f'(z) Poles (Dark Red) f'(z) Zeros (Dark Blue) Search Radius: 2.0

Camera

Interaction: Hover over the domain plane to see transformations in action: which region gets mapped where

About Color Noise: The chaotic/noisy color regions you may see (especially near the origin for 1/z, or at poles) are singularities — points where the function blows up to infinity or is undefined. Near these points, values change extremely rapidly, causing the "color explosion" effect. This is mathematically correct behavior, not a rendering artifact!

Two-Mode Complex Function Visualizer