Lissajous Web

Three-dimensional Bowditch-Lissajous knot curves projected into 2D space with rotating perspective depth attenuation.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Frequency A 3

Harmonic X ratio

Frequency B 4

Harmonic Y ratio

Rotation Speed 0.6

3D perspective rotation rate

Mathematical Formulation

72 chars medium

Analytical Equation

x(t) = \sin(a t + \delta), \quad y(t) = \sin(b t), \quad z(t) = \cos(c t)

Compact Formula

x = sin(3φ + δ), y = sin(4φ), z = cos(5φ + t), px = cx + rotX * depth

Renderer Logic

const lx = Math.sin(a * phi + delta);
const ly = Math.sin(b * phi);
const lz = Math.cos(c * phi + t);
const rotY = lx * Math.cos(t * 0.3) - lz * Math.sin(t * 0.3);
const px = cx + rotY * rx * depth;
const py = cy + ly * ry * depth;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#lissajous #harmonics #knot #3d #geometry #trigonometry

Author: Math Art Core Target: 60 FPS

Lissajous Web

Live Parameters

Mathematical Formulation

Mathematical Tags

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