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.

What standard analysis sees
tail heaviness0.03
asymmetry0.21
occupancy0.06
short-range corr0.70
long-range memory0.75
spectral colour0.43
periodicity0.71
complexity0.02
time-irreversibility0.25
volatility clustering0.72
multifractality0.97
dimensionality0.44
nonstationarity0.66
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
E8 Lattice:coset_transition+4.7zbank-miss 2.3σ
S² × ℝ (Thurston):height_drift-4.4zbank-miss 2.1σ
G2 Root System:pair_angle_kurtosis+3.3zbank-miss 1.5σ
Wavelet Cascade:scale_gini_dispersion+3.1zbank-miss 1.7σ
Visibility Graph:avg_clustering_coeff-3.0zbank-miss 1.5σ
Mostow Rigidity:margulis_ratio+3.0zbank-miss 1.7σ
Modular Residue:occupancy_entropy-2.3zbank-miss 1.7σ
Septagonal (Danzer):z_primary+2.1zbank-miss 1.5σ

Composition

dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.474 ± 0.499

Binary sequence — two distinct symbols.

Render Gallery

Native > phase_plot
Native > phase_plotraw
Native > timeseries
Native > timeseriesraw
Native > triple_lattice
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > lag_map
Boltzmann > spin_grid
Boltzmann > spin_grid
Cayley > default
Cayley > default
Chladni > free_plate_nodal
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_bottom
Chladni > plate_top
Chladni > plate_top
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > xy_path
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
Hodge–Laplacian > default
Inflation (Substitution) > barcode
Inflation (Substitution) > barcode
Inflation (Substitution) > d_curve
Inflation (Substitution) > d_curve
Information Theory > default
Information Theory > default
Julia Set > escape_histogram
Julia Set > escape_histogram
Klein Bottle > default
Klein Bottle > default
Laplacian > default
Laplacian > default
Logarithmic Spiral > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Möbius-S³ > s2_base_map
Ordinal Partition > default
Ordinal Partition > default
Penrose (Quasicrystal) > phi_spectrum
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > barcode
Persistent Homology > h1_diagram
Persistent Homology > h1_diagram
Predictability > default
Predictability > default
Recurrence Quantification > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Analysis > default
Spectral Graph > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > flux_grid
Symplectic > phase_space
Symplectic > phase_space
Ulam Spiral (Sacks) > default
Ulam Spiral (Sacks) > default
Ulam Spiral (Square) > default
Ulam Spiral (Square) > default
Visibility Graph > default
Visibility Graph > default
Wavelet Cascade > default
Wavelet Cascade > default

Atlas Position

Nearest neighborDistance
Square Wave3.81
Morse Code4.28
Symbolic Lorenz4.94cross-origin

Open in Atlas →

Which Geometries Light Up

2-adic › 2-adic:valuation_transition_predictabilityrank 5/3060.9557
Catch24 › Catch24:SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1rank 2/3060.8340
D4 Triality › D4 Triality:edge_ortho_polarityrank 303/3060.0184
E8 Lattice › E8 Lattice:coset_transitionrank 3/3060.2736
G2 Root System › G2 Root System:pair_angle_kurtosisrank 4/30695.3851
G2 Root System › G2 Root System:short_long_ratiorank 4/3060.9930
Klein Bottle › Klein Bottle:rank_deficitrank 5/3060.9456
Laplacian › Laplacian:poisson_recovery_errorrank 302/3060.0097
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_meanrank 1/3060.1872
Ordinal Partition › Ordinal Partition:forbidden_transitionsrank 2/3060.8800
Projective ℙ² › Projective ℙ²:cross_ratio_stdrank 303/3060.0102
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_driftrank 305/306-0.8000
Visibility Graph › Visibility Graph:avg_clustering_coeffrank 302/3060.3751
Wasserstein › Wasserstein:recurrence_distancerank 5/3060.0823
Wasserstein › Wasserstein:transport_variabilityrank 5/3060.1334
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Structure Atlas — Open Atlas · GitHub