Triangle Wave
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Triangle wave --- linear ramps up and down, smooth peaks with 1/n² Fourier decay (only odd harmonics)
Interpretation
Standard analysis sees: rich, high-entropy values; red spectrum (low-frequency / 1-over-f power); strongly periodic; low-complexity (predictable, not noise-like); low-dimensional; stationary. The atlas additionally detects Multi-Scale Wasserstein:w_max_ratio, Persistent Homology:max_h1_lifetime.
What standard analysis sees
tail heaviness0.26
asymmetry0.46
occupancy0.89
short-range corr0.78
long-range memory0.42
spectral colour0.08
periodicity0.96
complexity0.14
time-irreversibility0.53
volatility clustering0.76
multifractality0.37
dimensionality0.12
nonstationarity0.06
What the atlas adds
Multi-Scale Wasserstein:w_max_ratio+5.4z
scale-coherent dispersion mismatch (max/min Wasserstein across scales)
Persistent Homology:max_h1_lifetime+5.2z
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
Zipf–Mandelbrot (8-bit):zipf_r_squared | -3.6z | bank-miss 1.3σ |
Nonstationarity:dynamic_coupling | +2.6z | bank-miss 1.6σ |
Attractor Reconstruction:kaplan_yorke_dim | -2.2z | bank-miss 1.3σ |
Composition
dtypefloat64
range[-1, 1]
unique values16384 / 16384
mean ± std0.00145 ± 0.577
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/Triangle_Wave.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Triangle_Wave.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Triangle_Wave.png)
Inflation (Substitution) > barcode
/d_curve/Triangle_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/Triangle_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/Triangle_Wave.png)
Ulam Spiral (Sacks) > default
/default/Triangle_Wave.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Damped Pendulum | 3.38 | cross-origin |
| 2-Torus Quasiperiodic | 4.00 | cross-origin |
| Clipped Sine | 4.09 |
Which Geometries Light Up
2-adic › 2-adic:mean_distance | rank 3/307 | 0.6683 |
Attractor Reconstruction › Attractor Reconstruction:d2_saturation | rank 3/307 | 0.9969 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 3/307 | 0.7398 |
Fisher Information › Fisher Information:effective_dimension | rank 5/307 | 15.9997 |
Fisher Information › Fisher Information:log_det_fisher | rank 303/307 | 44.3616 |
Fisher Information › Fisher Information:trace_fisher | rank 303/307 | 256.0044 |
Modular Residue › Modular Residue:occupancy_entropy | rank 3/307 | 1.0000 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_max_ratio | rank 3/307 | 1974.5185 |
Nonstationarity › Nonstationarity:metric_volatility | rank 2/307 | 3.4401 |
Ordinal Partition › Ordinal Partition:time_irreversibility | rank 306/307 | 0.0027 |
Persistent Homology › Persistent Homology:max_h1_lifetime | rank 4/307 | 0.7899 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 304/307 | 0.1777 |
Wasserstein › Wasserstein:entropy | rank 5/307 | 5.0000 |
Wasserstein › Wasserstein:concentration | rank 303/307 | 1.0094 |
Wasserstein › Wasserstein:dist_from_uniform | rank 303/307 | 0.0006 |
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