Exponential Chirp
exotic · 36 views
exotic
What It Is
Exponential frequency sweep --- instantaneous frequency grows geometrically, creating equal time per octave. Used in acoustic measurements and radar
Interpretation
Standard analysis sees: bounded / light-tailed; smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); volatility-clustering (bursty); low-dimensional. The atlas additionally detects critical slowing down. It sits beside Chua's Circuit in the atlas (standard-bank rank 64) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.10
asymmetry0.64
occupancy0.74
short-range corr0.96
long-range memory0.94
spectral colour0.12
periodicity0.57
complexity0.06
time-irreversibility0.80
volatility clustering0.93
multifractality0.83
dimensionality0.13
nonstationarity0.82
What the atlas adds
critical slowing down+5.2z
lag-1 autocorrelation rises across the series — the early-warning signature of an approaching tipping point / regime shift (also fired by frequency chirps)
also fires on nonstationary arithmetic sequences whose autocorrelation drifts for non-dynamical reasonsAtlas-extreme metrics the standard bank can’t predict for this source
Symplectic:phase_volume_explored | +2.2z | bank-miss 2.2σ |
Composition
dtypefloat64
range[-1, 1]
unique values16384 / 16384
mean ± std0.0637 ± 0.709
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/Exponential_Chirp.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Exponential_Chirp.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Exponential_Chirp.png)
Inflation (Substitution) > barcode
/d_curve/Exponential_Chirp.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/Exponential_Chirp.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/Exponential_Chirp.png)
Ulam Spiral (Sacks) > default
/default/Exponential_Chirp.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Chua's Circuit | 3.48 | |
| Magnetic Pendulum (3-Magnet) | 3.71 | cross-domain |
| Triple Pendulum | 3.83 | cross-domain |
Which Geometries Light Up
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0 | rank 3/298 | 2182.4400 |
Hölder Regularity › Hölder Regularity:increment_autocorrelation | rank 4/298 | 0.9994 |
Klein Bottle › Klein Bottle:orientation_coherence | rank 4/298 | 0.9968 |
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 3/298 | 0.9994 |
Laplacian › Laplacian:curvature_autocorrelation | rank 3/298 | 0.9994 |
Laplacian › Laplacian:gradient_sign_persistence | rank 3/298 | 0.9969 |
Laplacian › Laplacian:biharmonic_ratio | rank 296/298 | 0.0000 |
Nonstationarity › Nonstationarity:ac1_trend | rank 3/298 | 0.3840 |
Nonstationarity › Nonstationarity:variance_trend | rank 3/298 | 0.7378 |
Projective ℙ² › Projective ℙ²:mean_distance | rank 295/298 | 0.0000 |
Projective ℙ² › Projective ℙ²:distance_std | rank 296/298 | 0.0000 |
Symplectic › Symplectic:flux_sign_persistence | rank 2/298 | 318.1572 |
Symplectic › Symplectic:phase_volume_explored | rank 2/298 | 0.8298 |
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergence | rank 1/298 | 0.9986 |
Wasserstein › Wasserstein:transport_variability | rank 1/298 | 0.2024 |
Wasserstein › Wasserstein:recurrence_distance | rank 2/298 | 0.1017 |
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