How domain coloring renders complex functions as vivid images in a browser

Domain coloring is a mathematical visualization technique that maps complex functions onto a 2D plane by encoding each output's angle as hue and its magnitude as brightness, making zeros, poles, and growth rates instantly readable. A developer has implemented this method inside LK Forge, a free browser-based graphing calculator, without using WebGL or 3D rendering. The tool relies on a custom shunting-yard expression parser that handles complex arithmetic using paired real-imaginary values, correctly computing identities such as i² = −1 and e^(iπ) = −1. To maintain interactivity, the renderer samples at half resolution during idle states and drops to quarter resolution while dragging, achieving roughly 3.4 million evaluations per second on a single thread. The result is a fully interactive complex function plotter that loads any expression safely via a URL parameter and repaints the canvas within milliseconds of user input.