scaleinvariance 0.1.0

Simulation and analysis of multifractal fields

ScaleInvariance

⚠️ This package is under active development. Current functionality is limited to Hurst exponent estimation and fractional Brownian motion simulation.

Simulation and analysis tools for scale-invariant processes and multifractal fields.

Current Features

Simulation

• 1D fractional Brownian motion: acausal_fBm_1D() - Spectral synthesis method
• 2D fractional Brownian motion: acausal_fBm_2D() - Isotropic 2D fields with proper frequency normalization

Hurst Exponent Estimation

• Haar fluctuation method: haar_fluctuation_hurst()
• Structure function method: structure_function_hurst()
• Spectral method: spectral_hurst()

All methods support multi-dimensional arrays and return uncertainty estimates.

Installation

pip install scaleinvariance

Basic Usage

from scaleinvariance import acausal_fBm_1D, acausal_fBm_2D, haar_fluctuation_hurst

# Generate 1D fractional Brownian motion
fBm_1d = acausal_fBm_1D(1024, H=0.7)

# Generate 2D fractional Brownian motion  
fBm_2d = acausal_fBm_2D((512, 1024), H=0.7)

# Estimate Hurst exponent
H_est, H_err = haar_fluctuation_hurst(fBm_1d)
print(f"Estimated H = {H_est:.3f} ± {H_err:.3f}")

Testing

# Test 1D fBm generation and Hurst estimation
python tests/test_acausal_fBm_hurst_estimation.py 0.7

# Test 2D fBm with isotropy validation
python tests/test_2d_fbm.py 0.7

Planned Features

• Fractionally integrated flux (FIF) simulation
• Advanced multifractal analysis tools
• Additional Hurst estimation methods
• Comprehensive documentation

Requirements

• Python ≥ 3.8
• NumPy, SciPy, PyTorch, Matplotlib