Two perpendicular sinusoidal oscillations draw harmonic figures. The frequency ratio determines the topology — from a line to an infinite knot.
// Lissajous — harmoniques visuelles let t = 0; function draw() { const x = cx + amp * Math.sin(freqX * t + phase); const y = cy + amp * Math.sin(freqY * t); ctx.lineTo(x, y); ctx.strokeStyle = 'rgba(200, 241, 53, 0.7)'; ctx.stroke(); t += 0.005; requestAnimationFrame(draw); }
Which freqX/freqY ratio produces a perfect circle? Try 3:2 vs 5:4 — which produces the more complex pattern? Push the trail to maximum to reveal the full figure.
Mathematics in the service of generative art
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