Spring Pendulum
What It Is
Elastic pendulum (mass on stretchable spring swinging in a vertical plane). 2-DOF Hamiltonian with parameters tuned to 1:2 resonance (k = 4g/L₀), where energy swaps chaotically between radial (spring) and angular (pendulum) modes --- canonical internal-resonance chaos. RK4 with dt=0.002. Output: spring length r(t).
Interpretation
Standard analysis sees: left-skewed; rich, high-entropy values; smooth / autocorrelated; long-range memory (persistent); low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal. The atlas detects no named structure beyond this. It sits beside Hénon-Heiles in the atlas (standard-bank rank 32) — a neighbor conventional features miss.
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
Render Gallery
_(centered)/signed_log_z/Spring_Pendulum.png)
_(centered)/xy_path/Spring_Pendulum.png)
/barcode/Spring_Pendulum.png)
/d_curve/Spring_Pendulum.png)
/phi_spectrum/Spring_Pendulum.png)
/default/Spring_Pendulum.png)
/default/Spring_Pendulum.png)
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Hénon-Heiles | 2.68 | cross-domain |
| Magnetic Pendulum (3-Magnet) | 2.88 | |
| FPUT N=16 | 3.10 | cross-domain |
Which Geometries Light Up
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 3/298 | 5.9013 |
Hölder Regularity › Hölder Regularity:hurst_exponent | rank 5/298 | 0.9150 |
Multifractal Spectrum › Multifractal Spectrum:hurst_estimate | rank 5/298 | 0.8987 |