This section packages interactive, real-time GLSL fragment shaders visualizing chaotic dynamical systems and complex functions.

Each interactive visualizer uses a dual-panel layout, split-sync state broadcasting across windows, and touch-responsive gesture support.

Interactive Visualizers

• Newton’s Fractal - Visualize the basins of attraction for Newton’s root-finding method on cubic polynomials. Drag the third root or step-by-step orbit path.
• Logistic Family - Explore fixed points, critical orbits, and chaotic regions under the complex logistic map $f_a(z) = a z (1 - z)$ with dual phase/parameter space navigation.
• Mandelbrot & Julia - The classic complex quadratic map $f_c(z) = z^2 + c$. Toggle between the parameter space (Mandelbrot set) and dynamical plane (Julia sets).

Architecture

All visualizers are designed with:

1. Dual-panel layout: Dynamical space vs Parameter space.
2. State sync: Web BroadcastChannel API syncs zoom, pan, parameters, and paths across popout/main window instances.
3. WebGL shaders: Rendered on the client’s GPU via glslCanvas libraries.