Damped Pendulum
motion · 36 views
motion
What It Is
Nonlinear pendulum with friction --- transient chaos at high amplitude, decay to limit cycle or fixed point
Interpretation
Standard analysis sees: rich, high-entropy values; smooth / autocorrelated; long-range memory (persistent); strongly periodic; low-complexity (predictable, not noise-like); volatility-clustering (bursty); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on Chladni:modal_nodal_cascade (-4.5z) — beyond what the standard bank predicts for it. It sits beside Sine Wave in the atlas (standard-bank rank 26) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.17
asymmetry0.52
occupancy0.86
short-range corr0.95
long-range memory0.86
spectral colour0.18
periodicity0.90
complexity0.06
time-irreversibility0.33
volatility clustering0.95
multifractality0.63
dimensionality0.15
nonstationarity0.40
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Chladni:modal_nodal_cascade | -4.5z | bank-miss 1.2σ |
Visibility Graph:degree_exponent_gamma | -2.8z | bank-miss 1.2σ |
Bispectrum:bicoherence_concentration | -2.3z | bank-miss 1.2σ |
Laplacian:curvature_autocorrelation | +2.0z | bank-miss 1.6σ |
Composition
dtypefloat64
range[-0.2449, 0.2449]
unique values16384 / 16384
mean ± std0.000209 ± 0.168
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Damped_Pendulum.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Damped_Pendulum.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Damped_Pendulum.png)
Inflation (Substitution) > barcode
/d_curve/Damped_Pendulum.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Damped_Pendulum.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Damped_Pendulum.png)
Ulam Spiral (Sacks) > default
/default/Damped_Pendulum.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Sine Wave | 2.56 | cross-domain |
| Duffing Oscillator | 3.32 | cross-domain |
| Period-Doubled Wave | 3.37 | cross-domain |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:d2_saturation | rank 2/298 | 0.9972 |
Chladni › Chladni:modal_nodal_cascade | rank 298/298 | -0.6527 |
Gottwald-Melbourne › Gottwald-Melbourne:radial_spectral_structure | rank 2/298 | 0.9996 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_variance | rank 2/298 | 3.3435 |
Laplacian › Laplacian:biharmonic_ratio | rank 294/298 | 0.0000 |
Moiré › Moiré:moire_invariance_breadth | rank 294/298 | 0.0032 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 5/298 | 0.1389 |
Navier-Stokes › Navier-Stokes:sl_fit_quality | rank 294/298 | -0.9946 |
Nonstationarity › Nonstationarity:metric_volatility | rank 2/298 | 3.2640 |
Nonstationarity › Nonstationarity:dynamic_coupling | rank 4/298 | 7.2831 |
Ordinal Partition › Ordinal Partition:time_irreversibility | rank 295/298 | 0.0038 |
Spectral Analysis › Spectral Analysis:phase_coherence | rank 4/298 | 0.9698 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 296/298 | 0.2986 |
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