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The Limit

Riemann sums approaching the integral

Chaos Theory

Double pendulum — coupled nonlinear oscillators

Self Similarity

Apollonian gasket — Descartes recursion

Synchronization

Kuramoto model — coupled phase oscillators

Position · Navigation · Timing

Clock drift on the sphere — a Kuramoto 'standing truce'

The Torus

Two coupled angles on a donut — a winding flow to a locking state on the surface

The Torus +

An Apollonian gasket revolved into a torus — a curvature change ripples around as a wave

soon<br>Resonance

The hidden frequency — coupled oscillators pulling voices out of noise