pattingalloang 0.0.1

JAX-Accelerated Aizawa Attractor Analysis with Comprehensive Chaos Metrics

pattingalloang: A JAX-Accelerated Framework for the Aizawa Strange Attractor

JAX-accelerated Python library for simulating and analyzing the Aizawa strange attractor with comprehensive chaos metrics.

This library is named after Karaeng Pattingalloang III (1600–1654), an eminent scholar-statesman of the Gowa-Tallo Sultanate in South Sulawesi, Indonesia. Serving as Grand Vizier from 1639 until his death, Pattingalloang was renowned throughout the early modern maritime world for his exceptional intellectual pursuits. Contemporary European accounts document his mastery of multiple languages, his extensive library of Western scientific and cartographic works, and his sophisticated engagement with mathematics, astronomy, and natural philosophy. His scholarly reputation earned him the epithet "Father of Makassar" among European observers. This library honors his legacy as a patron of cross-cultural scientific exchange during the Age of Exploration.

Governing Equations

$$\dot{x} = (z - b)x - dy$$

$$\dot{y} = dx + (z - b)y$$

$$\dot{z} = c + az - \frac{z^3}{3} - (x^2 + y^2)(1 + ez) + fzx^3$$

Standard Parameters: $a=0.95$, $b=0.7$, $c=0.6$, $d=3.5$, $e=0.25$, $f=0.1$

Installation

pip install pattingalloang          # From PyPI
pip install jax[cuda12]             # Optional: GPU support

Quick Start

CLI:

pattingalloang case1              # Standard Aizawa
pattingalloang --all              # Run all 8 cases
pattingalloang case1 --gpu        # GPU acceleration

Python API:

from pattingalloang import AizawaSystem, AizawaSolver, compute_all_metrics

system = AizawaSystem(a=0.95, b=0.7, c=0.6, d=3.5, e=0.25, f=0.1)
solver = AizawaSolver(dt=0.01, use_gpu=False)
result = solver.solve(system, n_steps=80000, initial_state=[0.1, 0.0, 0.0])

lyap_result = solver.solve_with_lyapunov(system, n_steps=30000)
metrics = compute_all_metrics(result['trajectory'], result['time'], 
                              system.params.to_tuple(), dt=0.01,
                              log_diags=lyap_result['log_diags'])

print(f"λ₁={metrics['lyapunov_1']:.4f}, D_KY={metrics['kaplan_yorke_dim']:.4f}")

Test Cases

Case	Description	Steps	Focus
1	Standard Aizawa	80K	Classic butterfly structure
2	High Resolution	150K	Fine attractor detail
3	Long Trajectory	300K	Accurate chaos metrics
4	Parameter Variation	80K	Effect of parameter changes
5	Multi-Trajectory	80K	Sensitivity to initial conditions
6	Butterfly Wings	120K	Wing structure emphasis
7	Chaotic Spiral	100K	Spiral-like dynamics
8	Double Loop	100K	Double-loop structure

Chaos Metrics

Metric	Description
Lyapunov Exponents	Rate of trajectory divergence ($\lambda_1 > 0$ → chaos)
Kaplan-Yorke Dimension	Fractal dimension from Lyapunov spectrum
Correlation Dimension	Grassberger-Procaccia attractor complexity
KS Entropy	Information production rate ($\sum \lambda_i$ for $\lambda_i > 0$)
Recurrence Rate	Fraction of recurrent points
Determinism	Predictability from recurrence plot

Output Files

• CSV: *_trajectory.csv, *_chaos_metrics.csv
• NetCDF: CF-compliant with all variables and metadata
• PNG: High-resolution static visualizations
• GIF: Animated 3D rotation

License

MIT © Sandy H. S. Herho

Citation

@software{herho2025_pattingalloang,
  title   = {{\texttt{pattingalloang}: A JAX-Accelerated Framework for the Aizawa Strange Attractor}},
  author  = {Herho, Sandy H. S.},
  year    = {2025},
  url     = {https://github.com/sandyherho/pattingalloang}
}