A breath pacer drives a sine wave at your chosen rate. Sustained, on-pace attention builds a focus streak F (seconds since the last distraction), which saturates into HRV coherence C:
C_target = min(cap, F / (F + 8))
cap = 1 - 0.05 · |rate − 6|
Coherence chases that target smoothly. Stress S then decays faster the higher C is:
dS/dt = −(0.03 + 0.4·C) · S
- Breath pace — near 6 breaths/min the achievable coherence cap is highest, matching the resonance-frequency breathing findings in HRV biofeedback research; pacing far from it caps how coherent you can get even with a long streak.
- Mind-wandering — at random intervals set by this rate, attention slips: the focus streak snaps to zero and coherence drops sharply, so stress reduction stalls until focus rebuilds. This is the attentional cost the article's "gently redirect your attention" FAQ answer is describing.
- Pause / Reset — pause freezes the model to inspect it; reset returns stress to a baseline-stressed 70% and clears the streak, as if starting a fresh sitting.
The green ring of particles orbits in sync with the breath only while coherence is high; a mind-wandering event scatters a burst of amber particles outward, visualising attention breaking away from the breath.