μ-law Sine
waveform · 36 views
waveform
What It Is
Sine wave with non-linear mu-law quantization (G.711). Creates a structural bridge between analogue waves and discrete logic.
Interpretation
Standard analysis sees: bounded / light-tailed; smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); strongly periodic; low-complexity (predictable, not noise-like); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on Möbius-S³:spinorial_asymmetry (+4.0z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.04
asymmetry0.51
occupancy0.37
short-range corr0.94
long-range memory0.97
spectral colour0.04
periodicity0.98
complexity0.05
time-irreversibility0.68
volatility clustering0.83
multifractality0.83
dimensionality0.03
nonstationarity0.15
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Möbius-S³:spinorial_asymmetry | +4.0z | bank-miss 1.7σ |
Multifractal Spectrum:spectrum_width | +3.2z | bank-miss 2.2σ |
Visibility Graph:assortativity | +3.0z | bank-miss 2.4σ |
Wavelet Cascade:intermittency_slope | -2.6z | bank-miss 1.8σ |
Composition
dtypefloat64
range[-1, 1]
unique values16384 / 16384
mean ± std-0.00577 ± 0.891
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/μ-law_Sine.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/μ-law_Sine.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/μ-law_Sine.png)
Inflation (Substitution) > barcode
/d_curve/μ-law_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/μ-law_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/μ-law_Sine.png)
Ulam Spiral (Sacks) > default
/default/μ-law_Sine.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Van der Pol Oscillator | 3.51 | cross-domain |
| Lotka-Volterra | 4.35 | cross-domain |
| Sine Wave | 4.38 |
Which Geometries Light Up
Catch24 › Catch24:FC_LocalSimple_mean1_tauresrat | rank 2/298 | 1.0013 |
Fisher Information › Fisher Information:velocity_spectral_gini | rank 4/298 | 0.7804 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structure | rank 5/298 | 392.2011 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 297/298 | -0.4012 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 5/298 | 1.0021 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_mean | rank 3/298 | 0.1452 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 3/298 | 0.1625 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 2/298 | 0.8122 |
Möbius-S³ › Möbius-S³:spinorial_asymmetry | rank 2/298 | 0.2220 |
Symplectic › Symplectic:phase_reflection_symmetry | rank 2/298 | 0.9988 |
Visibility Graph › Visibility Graph:assortativity | rank 3/298 | 0.7110 |
Visibility Graph › Visibility Graph:degree_r_squared | rank 295/298 | 0.2656 |
p-Variation › p-Variation:variation_index | rank 298/298 | 1.0003 |
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