Sawtooth Wave
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Sawtooth wave --- linear ramp with discontinuous reset, rich in harmonics (1/n Fourier decay)
Interpretation
Standard analysis sees: rich, high-entropy values; long-range memory (persistent); low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); volatility-clustering (bursty); low-dimensional. The atlas additionally detects Time Reversibility:ordinal_reversal_distance. It sits beside Rossler Attractor in the atlas (standard-bank rank 38) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.20
asymmetry0.30
occupancy0.98
short-range corr0.74
long-range memory0.86
spectral colour0.38
periodicity0.84
complexity0.00
time-irreversibility0.01
volatility clustering0.98
multifractality0.75
dimensionality0.07
nonstationarity0.35
What the atlas adds
Time Reversibility:ordinal_reversal_distance+3.1z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Symplectic:flux_sign_persistence | +5.4z | bank-miss 1.4σ |
Wavelet Cascade:coarse_scale_kurtosis_slope | -3.7z | bank-miss 1.9σ |
Multifractal Spectrum:spectrum_width | +3.4z | bank-miss 2.3σ |
WaveformAsymmetry:waveform_asymmetry | +3.3z | bank-miss 2.3σ |
Laplacian:laplacian_evolutionary_index | +3.2z | bank-miss 3.6σ |
Higher-Order Statistics:kurt_max | +2.9z | bank-miss 1.7σ |
Laplacian:gradient_curvature_anticorrelation | +2.5z | bank-miss 2.7σ |
Composition
dtypefloat64
range[-0.9994, 1]
unique values16384 / 16384
mean ± std0.00361 ± 0.579
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/Sawtooth_Wave.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Sawtooth_Wave.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Sawtooth_Wave.png)
Inflation (Substitution) > barcode
/d_curve/Sawtooth_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/Sawtooth_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/Sawtooth_Wave.png)
Ulam Spiral (Sacks) > default
/default/Sawtooth_Wave.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Tank Drain Cascade | 4.52 | cross-origin |
| Rossler Attractor | 4.96 | cross-origin |
| Duffing Oscillator | 5.06 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:CO_HistogramAMI_even_2_5 | rank 2/306 | 1.5092 |
Cayley › Cayley:local_linearity | rank 4/306 | 1.0000 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 2/306 | 0.7409 |
Fisher Information › Fisher Information:velocity_spectral_gini | rank 1/306 | 0.8190 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 304/306 | 0.0120 |
Hölder Regularity › Hölder Regularity:holder_min | rank 2/306 | 1.0000 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 5/306 | 1.0040 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 2/306 | 1.0000 |
Laplacian › Laplacian:laplacian_evolutionary_index | rank 3/306 | 0.4980 |
Laplacian › Laplacian:gradient_sign_persistence | rank 5/306 | 0.9960 |
Laplacian › Laplacian:poisson_recovery_error | rank 304/306 | 0.0033 |
Modular Residue › Modular Residue:occupancy_entropy | rank 4/306 | 1.0000 |
Navier-Stokes › Navier-Stokes:cascade_asymmetry | rank 304/306 | -0.9994 |
Predictability › Predictability:excess_predictability | rank 4/306 | 2.8852 |
Predictability › Predictability:sample_entropy | rank 304/306 | 0.0193 |
Spectral Graph › Spectral Graph:weyl_exponent | rank 4/306 | 2.1286 |
Symplectic › Symplectic:flux_sign_persistence | rank 3/306 | 292.0574 |
Time Reversibility › Time Reversibility:increment_skewness_max | rank 1/306 | 1.0000 |
WaveformAsymmetry › WaveformAsymmetry:waveform_asymmetry | rank 1/306 | 0.9960 |
Wavelet Cascade › Wavelet Cascade:coarse_scale_kurtosis_slope | rank 304/306 | -2.6338 |
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