Damped Pendulum
continuous-flows · 37 views
continuous-flowsperiodic
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 additionally detects Persistent Homology:max_h1_lifetime, Multifractal Spectrum:hurst_estimate. It sits beside Period-Doubled Wave in the atlas (standard-bank rank 41) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.17
asymmetry0.52
occupancy0.86
short-range corr0.95
long-range memory0.85
spectral colour0.18
periodicity0.90
complexity0.06
time-irreversibility0.33
volatility clustering0.95
multifractality0.62
dimensionality0.15
nonstationarity0.39
What the atlas adds
Persistent Homology:max_h1_lifetime+5.9z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Multifractal Spectrum:hurst_estimate+2.0z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
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 1.3σ |
Bispectrum:bicoherence_concentration | -2.3z | bank-miss 1.1σ |
Laplacian:curvature_autocorrelation | +2.0z | bank-miss 1.2σ |
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 > free_plate_nodal
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 | 2.49 | cross-origin |
| Period-Doubled Wave | 3.31 | cross-origin |
| Triangle Wave | 3.38 | cross-origin |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:d2_saturation | rank 2/307 | 0.9972 |
Chladni › Chladni:modal_nodal_cascade | rank 307/307 | -0.6527 |
Fisher Information › Fisher Information:velocity_spectral_gini | rank 5/307 | 0.7780 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_variance | rank 3/307 | 3.3435 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 5/307 | 0.1389 |
Navier-Stokes › Navier-Stokes:sl_fit_quality | rank 304/307 | -0.9946 |
Nonstationarity › Nonstationarity:metric_volatility | rank 4/307 | 3.2640 |
Ordinal Partition › Ordinal Partition:time_irreversibility | rank 305/307 | 0.0038 |
Persistent Homology › Persistent Homology:max_h1_lifetime | rank 3/307 | 0.8862 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 4/307 | 0.9698 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 305/307 | 0.2986 |
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