Multifractal Spectrum f(α)

Turbulence Intermittency · Singularity Spectrum · Wavelet Leaders · She-Leveque

Signal Generation

Parameters

1024
0.33
0.20
5

Structure Functions τ(q)

Theory

Multifractal: local Hölder exponent α(x) varies
f(α) = Hausdorff dim of set where H(x) = α
Structure function: S_q(ℓ) = ⟨|δu_ℓ|^q⟩ ~ ℓ^{ζ_q}
Legendre transform: f(α) = min_q[qα − τ(q)+1]
K41 monofractal: ζ_q = q/3, narrow f(α)
She-Leveque: ζ_q = q/9 + 2[1−(2/3)^{q/3}]
Width of f(α) curve → degree of intermittency
α* = h+1 at maximum f(α)=1 (fractal lines)

Singularity Exponents

Run analysis to see results.