Every board square is tracked in an 8×8 occupancy grid. On a timer (the move interval, jittered ±25% like the 3D version), a random occupied piece is chosen and sent to a random empty square. The hop itself is a simple parametric arc: horizontal position is linearly interpolated from start to target over the hop duration, while the vertical "lift" follows height·sin(π·progress) so the piece rises and falls smoothly and lands exactly on the target square at progress = 1.
- Lower the density slider to start with fewer pieces — more empty squares means more possible hop targets.
- A longer hop duration with a taller arc reads as a slow lob; a short duration with a low arc reads as a quick shuffle.
- "Hop now" forces an immediate move without waiting for the timer (does nothing while a hop is already in flight).