μ-law Sine
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Sine wave with non-linear 8-bit μ-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); multifractal; low-dimensional; stationary. The atlas additionally detects Persistent Homology:max_h1_lifetime.
What standard analysis sees
tail heaviness0.04
asymmetry0.55
occupancy0.38
short-range corr0.87
long-range memory0.89
spectral colour0.07
periodicity0.95
complexity0.15
time-irreversibility0.22
volatility clustering0.81
multifractality0.91
dimensionality0.04
nonstationarity0.14
What the atlas adds
Persistent Homology:max_h1_lifetime+4.3z
reconstructed phase space contains a persistent topological loop (S¹) — a smooth simple limit cycle
Atlas-extreme metrics the standard bank can’t predict for this source
Hölder Regularity:alpha_autocorrelation | +8.0z | bank-miss 2.3σ |
Möbius-S³:spinorial_asymmetry | +4.0z | bank-miss 1.4σ |
Multifractal Spectrum:spectrum_width | +3.1z | bank-miss 2.4σ |
Wavelet Cascade:coarse_scale_kurtosis_slope | -2.6z | bank-miss 2.2σ |
Fisher Information:velocity_spectral_gini | +2.4z | bank-miss 1.3σ |
Bispectrum:bicoherence_gini | -2.3z | bank-miss 1.6σ |
Chladni:nodal_gap_ratio | +2.3z | bank-miss 1.1σ |
Attractor Reconstruction:kaplan_yorke_dim | -2.0z | bank-miss 1.5σ |
Composition
dtypefloat64
range[-1, 1]
unique values241 / 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 > free_plate_nodal
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 | 4.17 | cross-origin |
| Clipped Sine | 4.35 | |
| Lotka-Volterra | 4.82 | cross-origin |
Which Geometries Light Up
Fisher Information › Fisher Information:velocity_spectral_gini | rank 3/306 | 0.7819 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 304/306 | -0.3145 |
Hölder Regularity › Hölder Regularity:alpha_autocorrelation | rank 1/306 | 0.6014 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 306/306 | -0.2046 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_mean | rank 3/306 | 0.1450 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 3/306 | 0.1622 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 1/306 | 0.8116 |
Möbius-S³ › Möbius-S³:spinorial_asymmetry | rank 2/306 | 0.2215 |
Ordinal Partition › Ordinal Partition:forbidden_transitions | rank 4/306 | 0.8750 |
p-Variation › p-Variation:variation_index | rank 306/306 | 1.0001 |
← Triangle Wavein stochastic-process
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