Each midsole cell is a nanoactuator swarm that senses compression and retunes its local stiffness in real time — a semi-active spring-damper, not a fixed piece of foam. Contact physics follow a one-sided spring-damper impact model, the same class used in running-biomechanics research to model leg stiffness:
m·x″ = m·g − k(x)·x − c·x′, x ≥ 0
F(t) = k(x)·x + c·x′ (ground reaction force)
where x is compression depth (0 at first touch, growing as the foot sinks in), m the effective limb mass (~6% of body mass) and c a fixed viscous damping constant. The two midsoles differ only in k(x):
Static foam: k = k_static (constant)
Nanobot swarm: k(x) = k_min(v0) + (k_max−k_min)·(x/x_cap)²
k_min(v0) rises with sensed impact speed v0
The adaptive law stays soft on first contact (low k near x=0, cutting the initial force spike) then progressively stiffens as compression deepens, preventing the midsole from bottoming out against the cap x_cap — and it pre-tensions its floor stiffness k_min from the sensed impact velocity of the incoming strike. Note on this build: the original 3D source shipped with the contact-triggering velocity given the wrong sign (initialized as −v0 instead of +v0), which made the compression coordinate x go briefly negative on every strike and the contact-end test never fire on a genuine rebound — the peak-force and reduction% readouts were silently stuck at zero on every impact. That sign was flipped here (verified with a standalone Node script against both versions) so x actually integrates forward into compression and the stats read real numbers. The ceiling/floor/pre-tension/static sliders below are exposed so you can find the sign's other implication for yourself: pre-tensioning the floor stiffness too aggressively for a given ceiling can make the adaptive sole read a higher peak force than plain foam at hard impacts — a genuine design trade-off (anticipatory stiffening vs. bottom-out risk), not a bug, and the reduction box turns red when it happens.
- Impact velocity — vertical foot-strike speed; harder landings raise both the adaptive floor stiffness and the peak force on both midsoles.
- Body mass — sets the effective limb mass in the equation of motion.
- Cadence — steps per minute; sets how often a new strike cycle begins.
- Ceiling / floor / pre-tension / static — retune the two midsoles live; watch the stiffness-curve panel and the reduction box respond instantly.