Mathematical Beauty: A Visual Journey Through Lissajous Curves & Torus Knots скачать в хорошем качестве

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