Clipped Sine
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Sine wave hard-clipped at 70% --- flat tops and bottoms create a hybrid of smooth oscillation and constant segments, concentrating the distribution at extremes
Interpretation
Standard analysis sees: bounded / light-tailed; strongly periodic; low-complexity (predictable, not noise-like); multifractal; low-dimensional; stationary. The atlas additionally detects Persistent Homology:max_h1_lifetime, Multi-Scale Wasserstein:w_max_ratio.
What standard analysis sees
tail heaviness0.07
asymmetry0.40
occupancy0.31
short-range corr0.79
long-range memory0.47
spectral colour0.34
periodicity0.96
complexity0.03
time-irreversibility0.58
volatility clustering0.72
multifractality0.87
dimensionality0.11
nonstationarity0.04
What the atlas adds
Persistent Homology:max_h1_lifetime+6.4z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Multi-Scale Wasserstein:w_max_ratio+3.0z
scale-coherent dispersion mismatch (max/min Wasserstein across scales)
Atlas-extreme metrics the standard bank can’t predict for this source
E8 Lattice:std_profile | +4.1z | bank-miss 2.2σ |
Nonstationarity:metric_volatility | +3.4z | bank-miss 1.0σ |
AutoRegressive:ar_coef_1 | +2.7z | bank-miss 1.3σ |
Visibility Graph:degree_exponent_gamma | -2.5z | bank-miss 2.0σ |
Composition
dtypefloat64
range[-1, 1]
unique values8090 / 16384
mean ± std-0.00158 ± 0.828
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/Clipped_Sine.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Clipped_Sine.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Clipped_Sine.png)
Inflation (Substitution) > barcode
/d_curve/Clipped_Sine.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/Clipped_Sine.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/Clipped_Sine.png)
Ulam Spiral (Sacks) > default
/default/Clipped_Sine.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Damped Pendulum | 3.58 | cross-origin |
| Triangle Wave | 4.09 | |
| Sine Wave | 4.30 |
Which Geometries Light Up
2-adic › 2-adic:valuation_spectral_concentration | rank 5/307 | 0.7920 |
AutoRegressive › AutoRegressive:ar_coef_1 | rank 4/307 | 2.8283 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 303/307 | -0.0910 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 2/307 | 0.1629 |
Nonstationarity › Nonstationarity:metric_volatility | rank 1/307 | 3.4598 |
Persistent Homology › Persistent Homology:max_h1_lifetime | rank 1/307 | 0.9546 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 304/307 | 0.2817 |
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