Torus Knots: Mathematical Beauty in Motion скачать в хорошем качестве

Torus Knots: Mathematical Beauty in Motion

Torus Knots: Mathematical Beauty in Motion A visual meditation on torus knots — curves that wind around a donut-shaped surface, creating intricate patterns that have fascinated mathematicians for centuries. Featured Knots (p,q parameters): 0:00 - Trefoil Knot (2,3) — The simplest nontrivial knot 0:08 - Solomon's Seal (2,5) — Ancient symbol, mathematical elegance 0:16 - Cinquefoil (3,5) — Five-pointed star topology 0:24 - Septafoil (3,7) — Seven-fold symmetry 0:32 - Seven Twist (2,7) — Extended winding pattern 0:40 - Complex (4,5) — Higher-order interweaving 0:48 - High Order (5,7) — Dense orbital structure 0:56 - Three-Four (3,4) — Classic harmonic ratio Each knot is traced by 8 particles following the parametric equations: x = cos(p·t) · (3 + cos(q·t)) y = sin(p·t) · (3 + cos(q·t)) z = sin(q·t) Rendered in real-time ASCII using Python terminal graphics. Part of the Lissajous Curves educational series exploring the intersection of mathematics, art, and code. #mathematics #torusknot #generativeart #ascii #coding #visualization #topology #3dmath #pythonart #procedural