Скачать или смотреть Mathematical Beauty: A Visual Journey Through Lissajous Curves & Torus Knots

A 2:38 meditation on mathematical beauty.

Particles trace patterns discovered by Jules Lissajous in 1857 — curves that appear when two perpendicular oscillations
combine. These same forms appear in oscilloscopes, laser shows, and the fabric of harmonics itself.

The Journey:
0:00 - Neon Emergence (trefoil, cinquefoil, Solomon's seal)
0:48 - The Torus Gallery (8 mathematical knots with earthy palettes)
1:38 - Chaos & Order (particle swarms, breathing spheres)
2:26 - Return to Light

Featured Torus Knots:
• Trefoil (2,3) - The simplest nontrivial knot
• Solomon's Seal (2,5) - Ancient symbol, mathematical elegance
• Cinquefoil (3,5) - Five-pointed star topology
• Septafoil (3,7) - Seven-fold symmetry
• Complex (4,5) - Higher-order interweaving

All visuals generated with Python using parametric equations:
• Lissajous: x=sin(at), y=sin(bt+δ)
• Torus Knots: x=(R+r·cos(qt))·cos(pt), y=(R+r·cos(qt))·sin(pt), z=r·sin(qt)

No AI image generation — pure mathematics rendered as ASCII art in a terminal.

#mathematics #generativeart #lissajous #torusknot #visualization #coding #pythonart #procedural #ambient #ascii