scaleinvariance 0.5.0

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

FIF validation scripts, which test scaling over multiple ranges of scale, live in tests/automated/ (see test_1D_FIF_hurst.py and test_2D_FIF_hurst.py). They are designed to be run as standalone Python programs, not via pytest, and they generate many large FIF realizations to reach statistical convergence. These scripts are also known to produce some failures, especially near grid scales, because finite-size effects are not fully mitigated by the LS2010 corrections.

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

Requirements

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