scaleinvariance 0.4.0

Simulation and analysis of multifractal fields

scaleinvariance

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

Documentation

Current Features

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, averaging over dimensions that are orthogonal to the specified dimension along which spectra are calculated (specified by axis. Plotting data and fit line may be returned with return_fit=True.

Simulation

pytorch is leveraged for parallel and efficient simulation.

View example simulation outputs here

• 1D fractionally integrated flux (FIF): FIF_1D() - Multifractal cascade simulation; causal/acausal
• 2D fractionally integrated flux (FIF): FIF_2D() - Isotropic 2D multifractals (Example shown above)
• 1D fractional Brownian motion: acausal_fBm_1D() - 1D acausal fBm fields
• 2D fractional Brownian motion: acausal_fBm_2D() - Isotropic 2D fBm fields

Installation

pip install scaleinvariance

Basic Usage

from scaleinvariance import acausal_fBm_1D, acausal_fBm_2D, FIF_1D, 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)

# Generate multifractal FIF timeseries
fif = FIF_1D(2**16, alpha=1.8, C1=0.1, H=0.3)

# 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

Examples

See the examples/ directory for comprehensive demonstrations:

• fif_comparison_demo.py: Compare Hurst estimation methods on multifractal FIF simulations with different intermittency parameters
• multi_dataset_haar_analysis.py: Real-world data analysis using Haar fluctuation method

Run examples:

python examples/fif_comparison_demo.py

Data source for LGMR: https://www.ncei.noaa.gov/access/paleo-search/study/33112

Planned Features

• Estimation of multifractal parameters C1 and alpha

Requirements

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