Phase, Synchrony, and the Rotating Arrow

Phase, Synchrony & the Rotating Arrow — BrainSegrity Interactive
BrainSegrity · Live Teaching Tool

Phase, Synchrony, and the Rotating Arrow

Companion to slide 17. Every oscillation is a rotating arrow: length r = amplitude, angle θ = phase. Drag the controls live — this is built to run alongside the talk, not just illustrate it.

Phase (θ)
Where an oscillation currently sits in its repeating cycle, given as an angle (0–360°) or a fraction of one full cycle. It's what the arrow's direction represents — not how big the signal is (that's amplitude), just where it is right now in its rotation.
Synchrony (phase-locking)
Two or more oscillators maintaining a consistent phase relationship over time, rather than one that drifts. Requires matched frequency (or a clean integer ratio between frequencies) — the specific lag doesn't have to be zero, it just has to hold steady.

One Oscillation

z = r·eiθ
r (amplitude)
0.80
θ (phase)
0°
f (frequency)
0.60 Hz
The waveform below is the arrow's vertical projection over time — sin(θ) scaled by r. This is the same signal a single EEG channel is reporting: one oscillator, one trace.

In Phase — Synchrony

Δφ = θB − θA
Δφ = 0°
Δφ = 0°
Arrow A Arrow B
The box above is the one thing to watch. With Frequency A and B matched, it stays green for any value of Δφ0 you drag to — that's the real definition on this slide: synchrony means a consistent phase relationship, not specifically a zero one. "IN PHASE" (0°) is only the tightest special case of synchronous; a steady 45° lag is still synchronous, just not in phase — the box says which. It also holds green regardless of the amplitude difference, which is the slide's other point: synchrony is a phase relationship, not a power level. Try a clean ratio too — 0.75 Hz and 1.5 Hz, for instance — and the box stays green as "2:1 PHASE-LOCKED": harmonic frequencies can be genuinely synchronous without being equal. The box only turns amber — genuinely not synchronous — when the frequencies share no clean small-integer relationship at all, so the offset can't hold still at anything.

Out of Phase

stable = locked  ·  drifting = lost
LOCKED · Δφ ≈ 0°
LOCKED · Δφ ≈ 0°
Δφ here is a stand-in, not the real metric. Real PLV isn't this instantaneous angle — it's a 0–1 consistency score computed over a sliding time window (Lachaux et al., 1999, Hum. Brain Mapp.): how steady the phase relationship stayed across that window, not what it happens to be this instant. Steady Δφ here → high PLV in real data; drifting Δφ → low PLV. The angle is what drives the number, but it isn't the number itself.
Arrow A Arrow B
They start in phase (matched frequencies, no offset). Mismatch Frequency A and B and watch them drift apart on their own — no switch needed, that's just what different-speed oscillators do. Auto-drift is a separate, additional effect for when you want drift even with frequencies matched. Once drifting, from either cause, the "PLV correction" slider appears so you can drag them back to lock live. That's standing in for phase-locking value (PLV) / connectivity training — re-coupling two drifted rhythms — which is a different target from μ-tuning (slide 33): μ is about one oscillator's own distance from criticality, this is about the relationship between two.