Abstract
Pattern emergence is fundamentally wave-like. This article explains wavelength anchoring—where stable nodes occur only at resonant scales—and how nexum propagation tracks these resonances across field dynamics.
1. Wave Fundamentals
Field patterns behave like waves with wavelength (λ) and frequency. Only specific resonant scale waves persist.
2. Wavelength Anchoring
Stability requires resonance peaks:
λ = 2π / k
Only integer k harmonics allow stable pattern nodes.
3. Field-Wave Emergence
Define:
R(k) = W(k) / W_threshold
Emergence occurs when R(k) ≥ 1.
4. Nexum & Wave Propagation
Pattern logic travels in wave harmonics:
ψ(x,t) = A cos(kx - ωt)Velocity v = ω / k maps nexum speed.
5. Examples
| System | λ Anchoring | Pattern Emerged |
|---|---|---|
| Drum membrane | Diameter harmonic | Chladni figures |
| Neural brain | Oscillation frequency | Brainwave coherence |
| Optical cavity | Length cavity match | Laser modes |
6. Implications
Wavelength anchoring shows how wave-guided patterns stabilize; nexum uses this to connect pattern nodes across domains.