Coherence-Rupture-Regeneration Drone Formation

CRR Multi-agent Drone coordination

Formation Field t = 0.000s
Global Coherence C
0.000
Formation Error
0.0
Memory Gain exp(C/Ω)
1.00
Ruptures δ
0
95% Convergence
—
Sacred Formations
CRR Parameters
Memory Parameter Ω 0.35
Drone Count 8
Simulation Speed 1.0×
Control
Coherence History
CRR Verification
✓ Coherence accumulated via ∫L(x,τ)dτ
✓ Rupture detection: C < θ ∧ dC/dt < 0
✓ Memory gain: exp(C/Ω) weighting
✓ Ω modulates memory sharpness
✓ Formation-relative coherence

CRR Mathematical Framework

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Coherence Accumulation
C(x,t) = ∫₀ᵗ L(x,τ) dτ
Local coherence rate L(x,t) integrates over time. L measures alignment to target AND relative positions to neighbors.
L = 0.5·exp(-d_target/scale) + 0.5·mean(exp(-d_relative/scale))
Rupture Event
δ(now): C < θ ∧ dC/dt < 0
Rupture occurs when coherence drops below threshold θ while decreasing. Triggers coherence collapse and regeneration.
if (C < 0.12 && dC/dt < 0 && t - t_last > 0.15) → rupture
Regeneration
R = ∫ φ(x,τ)·exp(C(τ)/Ω) dτ
Reconstruction field φ points toward target. Memory gain exp(C/Ω) amplifies high-coherence moments.
v = φ · k_p · distance · (exp(C/Ω) / normalizer)