same equation, different discretization — symplectic preserves the structure (KAM tori, bounded energy); naive euler doesn't. this is the argument for Hamiltonian neural nets.
move to set your frequency · ride cyan · avoid magenta
You're a packet of energy in a kicked rotor — a rotor that gets a periodic shove. Steer your frequency (move up/down). Ride the cyan currents (stable tori, where the flow carries you for free) and gather energy. Stray into the magenta sea and you overheat.
stable torus · coldchaos · heatinggolden mean
move pointer / finger — or ↑ ↓ keys · ε rises as you go