视界

见、不可见

interactive

Harmonic Motion

Lissajous Curves

The visible trace of two oscillating frequencies. When the ratio is rational, the loop closes—chaos becomes order.

TrigonometryOscillationParametric
Shuyu
animation
4:32

Complex Function Transformations

Visualizing Möbius Transformations

Watch how the complex plane bends and twists under the influence of Möbius transformations.

Complex AnalysisTransformations
Shuyu
simulation
3:15

Vector Flow Fields

Fluid Dynamics Simulation

Observe the elegant patterns that emerge from differential equations governing fluid motion.

Differential EquationsFluid Dynamics
Shuyu