CRR Mycelium Network Growth

C·Ω = 1 | B(C) = exp(C/Ω)·(C*−C) | R = ∫ φ·exp(C/Ω)·Θ dτ

Each hyphal tip accumulates coherence C from local environmental signal. Rupture (branching) occurs when C ≥ C* = 1/Ω. After rupture, the tip regenerates with coherence reset to zero. A 700×700 spatial coherence field C(x,t) tracks the integrated history of mycelial activity across the substrate, with local growth rate modulated by exp(C/Ω).

Mathematical Implementation

1. SPATIAL COHERENCE FIELD: C(x,t) = ∫₀ᵗ L(x,τ) dτ
Memory density: L[i] = growthActivity[i]×0.1 + branchActivity[i]×0.2 + density[i]×0.05
Integration: coherence[i] += L[i] × dt every frame
Decay: coherence[i] *= 0.9998 (slow dissipation)
2. PER-TIP RUPTURE: C ≥ C* triggers branching
Tip coherence accumulates: tip.C += L_local × dt
Evidence L = local environmental signal (nutrients, moisture, density)
Threshold: if (tip.C ≥ C_STAR) → branch where C_STAR = 1/Ω = π
Regeneration: tip.C = 0 after rupture
Beauty function: B = exp(C/Ω) × (C* − C) drives tip glow intensity
3. EXPONENTIAL REGENERATION: exp(C(x)/Ω)
φ(x,τ): signal = nutrients[i]×2 + moisture[i]×0.5 − density[i]×0.3
Amplification: speed = baseSpeed × exp(coherence[i] / Ω) × (1−stress)²
4. DAUGHTER DIAMETER: taper + local variation
d = 0.8 × parent.d × (1 + 0.1 × (local_nutrient − 0.5))
Variation derives from local nutrient heterogeneity at the branching point.
5. MEMORY KERNEL: K(t-τ) = exp(−|t−τ|/τ)
Sensor history: 10-frame buffer, exponentially weighted
Navigation: signal = current×0.7 + memoryWeighted×0.3
6. CV MEASUREMENT
Daughter diameter CV: averaged across generation cohorts (≥4 samples per cohort)
Branch interval CV: inter-rupture intervals across all tips
CRR prediction: CV = Ω/2 = 1/(2π) ≈ 0.1592

CRR Mycelium Network Growth

Network Process Visualisation

Environmental Parameters

Substrate Type:

Network Status & CRR Metrics

Health Status