Spring Pendulum
What It Is
Elastic pendulum (mass on stretchable spring swinging in a vertical plane). 2-DOF Hamiltonian with the spring stiffness detuned ~7.5% from the 1:2-resonance value (k = 3.7 g/L₀ vs the resonant 4 g/L₀; small-oscillation radial:angular frequency ratio √3.7 ≈ 1.92, not 2:1) to break the resonant torus, 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: rich, high-entropy values; smooth / autocorrelated; long-range memory (persistent); low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal. The atlas finds no named structure, but the source is distinctively extreme on Ammann-Beenker (Octagonal):convergent_resonance (+2.1z) — beyond what the standard bank predicts for it.
Ammann-Beenker (Octagonal):convergent_resonance | +2.1z | bank-miss 1.4σ |
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 | 2.79 | |
| Magnetic Pendulum (3-Magnet) | 2.89 | |
| Duffing Oscillator | 2.97 |
Which Geometries Light Up
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 2/306 | 5.9013 |
Wavelet Cascade › Wavelet Cascade:scale_gini_dispersion | rank 302/306 | 0.0079 |