DLA Fjord Statistics
Diffusion-limited aggregation with harmonic measure and fjord depth analysis
DLA (Witten-Sander 1981): Particles undergo Brownian motion and stick on contact. The resulting fractal has dimension d_f ≈ 1.71 in 2D (exactly: 1.7155±0.0004). The harmonic measure — probability flux at each surface point — is multifractal: tip sites capture most flux while fjords (deep valleys) are exponentially screened. Fjord depth distribution obeys log-normal statistics. Noise reduction (η) suppresses noise-induced branching, revealing the underlying Laplacian instability more cleanly.