Square Wave
waveform · 36 views
waveform
What It Is
Square wave --- binary oscillation (0 or 255), maximal harmonic content with 1/n odd-harmonic Fourier series
Interpretation
Standard analysis sees: bounded / light-tailed; few distinct values; long-range memory (persistent); strongly periodic; low-complexity (predictable, not noise-like); multifractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on E8 Lattice:coset_transition (+7.3z) — beyond what the standard bank predicts for it. It sits beside Morse Code in the atlas (standard-bank rank 35) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.01
asymmetry0.51
occupancy0.06
short-range corr0.81
long-range memory0.97
spectral colour0.39
periodicity0.95
complexity0.00
time-irreversibility0.49
volatility clustering0.82
multifractality0.99
dimensionality0.40
nonstationarity0.08
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
E8 Lattice:coset_transition | +7.3z | bank-miss 2.2σ |
Mostow Rigidity:margulis_ratio | +3.5z | bank-miss 2.2σ |
Wavelet Cascade:intermittency_slope | -3.4z | bank-miss 1.5σ |
Spherical S²:angular_spread | +3.4z | bank-miss 2.1σ |
Mostow Rigidity:volume_entropy | -3.0z | bank-miss 1.4σ |
Visibility Graph:avg_clustering_coeff | -3.0z | bank-miss 2.4σ |
Mostow Rigidity:mean_turn_angle | +2.9z | bank-miss 1.9σ |
Laplacian:poisson_recovery_error | -2.4z | bank-miss 1.8σ |
Composition
dtypefloat64
range[-1, 1]
unique values2 / 16384
mean ± std-0.00598 ± 1
Binary sequence — two distinct symbols.
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/Square_Wave.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Square_Wave.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Square_Wave.png)
Inflation (Substitution) > barcode
/d_curve/Square_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/Square_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/Square_Wave.png)
Ulam Spiral (Sacks) > default
/default/Square_Wave.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Pulse-Width Modulation | 3.92 | |
| Morse Code | 5.19 | |
| μ-law Sine | 5.55 |
Which Geometries Light Up
2-adic › 2-adic:valuation_transition_predictability | rank 3/298 | 0.9882 |
2-adic › 2-adic:multiscale_markov_predictability | rank 4/298 | 0.9900 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 297/298 | 0.0074 |
E8 Lattice › E8 Lattice:coset_transition | rank 2/298 | 0.3659 |
Fisher Information › Fisher Information:velocity_spectral_gini | rank 5/298 | 0.7793 |
G2 Root System › G2 Root System:short_long_ratio | rank 2/298 | 0.9979 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 297/298 | 0.0120 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structure | rank 294/298 | 1.9677 |
Information Theory › Information Theory:compression_ratio | rank 297/298 | 0.0023 |
Klein Bottle › Klein Bottle:rank_deficit | rank 5/298 | 0.9642 |
Laplacian › Laplacian:poisson_recovery_error | rank 297/298 | 0.0020 |
Mostow Rigidity › Mostow Rigidity:margulis_ratio | rank 2/298 | 0.9801 |
Mostow Rigidity › Mostow Rigidity:mean_turn_angle | rank 2/298 | 0.9893 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_std | rank 1/298 | 0.1674 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_mean | rank 2/298 | 0.1483 |
Ordinal Partition › Ordinal Partition:forbidden_transitions | rank 1/298 | 0.8800 |
Persistent Homology › Persistent Homology:persistence_entropy | rank 295/298 | 0.4693 |
Projective ℙ² › Projective ℙ²:cross_ratio_std | rank 296/298 | 0.0000 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 294/298 | 0.0063 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources