Sine Wave
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Pure sinusoid --- perfectly periodic, single-frequency, minimal complexity. The baseline for all oscillatory comparisons
Interpretation
Standard analysis sees: bounded / light-tailed; 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 51) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.11
asymmetry0.50
occupancy0.79
short-range corr0.98
long-range memory0.96
spectral colour0.21
periodicity0.99
complexity0.05
time-irreversibility0.43
volatility clustering0.98
multifractality0.75
dimensionality0.10
nonstationarity0.34
What the atlas adds
Persistent Homology:max_h1_lifetime+6.1z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Multifractal Spectrum:hurst_estimate+2.7z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:dynamic_coupling | +2.5z | bank-miss 1.7σ |
Nonstationarity:trajectory_dim | -2.1z | bank-miss 2.2σ |
Composition
dtypefloat64
range[-1, 1]
unique values16384 / 16384
mean ± std-0.00488 ± 0.708
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/Sine_Wave.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Sine_Wave.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Sine_Wave.png)
Inflation (Substitution) > barcode
/d_curve/Sine_Wave.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/Sine_Wave.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/Sine_Wave.png)
Ulam Spiral (Sacks) > default
/default/Sine_Wave.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Damped Pendulum | 2.49 | cross-origin |
| Period-Doubled Wave | 2.74 | |
| Duffing Oscillator | 3.47 | cross-origin |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:d2_saturation | rank 5/307 | 0.9958 |
Catch24 › Catch24:FC_LocalSimple_mean1_tauresrat | rank 2/307 | 1.0003 |
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiff | rank 307/307 | 0.0000 |
Chladni › Chladni:captured_power_fraction | rank 307/307 | 0.0001 |
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 1/307 | 7.0095 |
Hodge–Laplacian › Hodge–Laplacian:solenoidal_fraction | rank 1/307 | 0.9989 |
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 2/307 | 0.9995 |
Laplacian › Laplacian:curvature_autocorrelation | rank 2/307 | 0.9995 |
Laplacian › Laplacian:biharmonic_ratio | rank 307/307 | 0.0000 |
Navier-Stokes › Navier-Stokes:sl_fit_quality | rank 307/307 | -1.0000 |
Persistent Homology › Persistent Homology:max_h1_lifetime | rank 2/307 | 0.9163 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 3/307 | 0.9812 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 5/307 | 0.9594 |
Symplectic › Symplectic:flux_sign_persistence | rank 4/307 | 288.8150 |
Visibility Graph › Visibility Graph:degree_exponent_gamma | rank 303/307 | 0.3237 |
Wavelet Cascade › Wavelet Cascade:scale_gini_dispersion | rank 304/307 | 0.0078 |
p-Variation › p-Variation:volatility_clustering | rank 3/307 | 0.9996 |
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