1. Pick a Gait
Walk: 4-beat gait. Feet hit the ground in sequence: LH → LF → RH → RF.
2. Watch the Horse
Top view. Hooves light up when touching the ground. When you switch gaits, the horse takes a moment to transition — how fast depends on the coupling strength K in section 4 (higher K = faster lock-in).
3. Footfall Pattern
Each row is one limb. Colored bars show when the hoof is on the ground (stance); gaps are airborne (swing). The pattern scrolls in sync with the horse above, and the vertical line marks right now.
4. The Math Behind It
dθᵢ/dt = ω + (K/3) Σⱼ≠ᵢ sin((θⱼ−θᵢ) − (φⱼ*−φᵢ*))
Each leg is a hand on its own clock ring — all four spin at the same rate. A solid dot in the shaded slice means that hoof is on the ground; a hollow dot is in the air. Coupling pulls the four clocks into a stable pattern.
Lower duty = more time airborne. Try a low duty with trot or pace to see suspension.
Target phase offsets (fraction of stride) — drag to invent your own gait:
5. Real Horse Data
80 strides from an actual horse. Each dot = one hoof hitting the ground. Dashed lines = ideal walk.