Pulse-Width Modulation
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Pulse-width modulation --- binary carrier (0/255) whose duty cycle sweeps smoothly via sine modulation, encoding an analog signal in digital on/off timing
Interpretation
Standard analysis sees: bounded / light-tailed; few distinct values; low-complexity (predictable, not noise-like); multifractal. The atlas finds no named structure, but the source is distinctively extreme on E8 Lattice:coset_transition (+4.7z) — beyond what the standard bank predicts for it. It sits beside Morse Code in the atlas (standard-bank rank 21) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.03
asymmetry0.24
occupancy0.04
short-range corr0.69
long-range memory0.74
spectral colour0.45
periodicity0.72
complexity0.02
time-irreversibility0.26
volatility clustering0.72
multifractality0.97
dimensionality0.41
nonstationarity0.69
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
E8 Lattice:coset_transition | +4.7z | bank-miss 2.2σ |
S² × ℝ (Thurston):height_drift | -4.5z | bank-miss 1.7σ |
Mostow Rigidity:margulis_ratio | +3.2z | bank-miss 1.5σ |
Wavelet Cascade:scale_gini_dispersion | +3.2z | bank-miss 1.6σ |
Visibility Graph:avg_clustering_coeff | -3.0z | bank-miss 1.2σ |
Wasserstein:recurrence_distance | +2.7z | bank-miss 1.5σ |
G2 Root System:pair_angle_kurtosis | +2.5z | bank-miss 1.6σ |
Modular Residue:occupancy_entropy | -2.4z | bank-miss 1.1σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.474 ± 0.499
Binary sequence — two distinct symbols.
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/Pulse-Width_Modulation.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Pulse-Width_Modulation.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Pulse-Width_Modulation.png)
Inflation (Substitution) > barcode
/d_curve/Pulse-Width_Modulation.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/Pulse-Width_Modulation.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/Pulse-Width_Modulation.png)
Ulam Spiral (Sacks) > default
/default/Pulse-Width_Modulation.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Square Wave | 3.82 | |
| Morse Code | 4.27 | |
| Symbolic Lorenz | 4.93 | cross-origin |
Which Geometries Light Up
2-adic › 2-adic:valuation_transition_predictability | rank 5/307 | 0.9557 |
Catch24 › Catch24:SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1 | rank 2/307 | 0.8340 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 304/307 | 0.0184 |
E8 Lattice › E8 Lattice:coset_transition | rank 3/307 | 0.2736 |
G2 Root System › G2 Root System:pair_angle_kurtosis | rank 4/307 | 95.3851 |
G2 Root System › G2 Root System:short_long_ratio | rank 4/307 | 0.9930 |
Laplacian › Laplacian:poisson_recovery_error | rank 303/307 | 0.0097 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_mean | rank 1/307 | 0.1872 |
Ordinal Partition › Ordinal Partition:forbidden_transitions | rank 3/307 | 0.8800 |
Projective ℙ² › Projective ℙ²:cross_ratio_std | rank 304/307 | 0.0102 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_drift | rank 306/307 | -0.8000 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 303/307 | 0.3751 |
Wasserstein › Wasserstein:recurrence_distance | rank 5/307 | 0.0823 |
Wasserstein › Wasserstein:transport_variability | rank 5/307 | 0.1334 |
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