Pomeau-Manneville
chaos · 36 views
chaos
What It Is
Pomeau-Manneville type-I intermittency --- near a tangent bifurcation, the orbit lingers in long laminar phases before erupting into chaotic bursts. Power-law laminar length distribution
Interpretation
Standard analysis sees: right-skewed; time-irreversible (slow rise, sharp collapse); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on Laplacian:laplacian_evolutionary_index (+3.9z) — beyond what the standard bank predicts for it. It sits beside ECG Normal in the atlas (standard-bank rank 39) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.77
asymmetry0.88
occupancy0.34
short-range corr0.57
long-range memory0.68
spectral colour0.43
periodicity0.45
complexity0.18
time-irreversibility0.02
volatility clustering0.55
multifractality0.85
dimensionality0.01
nonstationarity0.75
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Laplacian:laplacian_evolutionary_index | +3.9z | bank-miss 2.6σ |
Hyperbolic (Poincaré):spatio_temporal_corr | -3.6z | bank-miss 1.2σ |
Hölder Regularity:alpha_autocorrelation | +3.6z | bank-miss 2.1σ |
Nonstationarity:change_quantiles_high | +3.5z | bank-miss 2.3σ |
Visibility Graph:assortativity | +3.3z | bank-miss 3.2σ |
Hodge–Laplacian:source_fraction | +3.1z | bank-miss 1.4σ |
G2 Root System:short_long_ratio | -2.8z | bank-miss 2.5σ |
H² × ℝ (Thurston):depth_height_corr | -2.7z | bank-miss 1.4σ |
Composition
dtypefloat64
range[0.000189, 0.9995]
unique values16384 / 16384
mean ± std0.124 ± 0.223
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/Pomeau-Manneville.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Pomeau-Manneville.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Pomeau-Manneville.png)
Inflation (Substitution) > barcode
/d_curve/Pomeau-Manneville.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/Pomeau-Manneville.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/Pomeau-Manneville.png)
Ulam Spiral (Sacks) > default
/default/Pomeau-Manneville.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Minkowski Question Mark | 4.60 | cross-domain |
| Hawkes Process | 4.92 | cross-domain |
| ECG Normal | 5.06 | cross-domain |
Which Geometries Light Up
G2 Root System › G2 Root System:short_long_ratio | rank 297/298 | 0.2062 |
Hodge–Laplacian › Hodge–Laplacian:source_fraction | rank 1/298 | 0.7421 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 298/298 | -0.5625 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):depth_height_corr | rank 294/298 | -0.7918 |
Laplacian › Laplacian:laplacian_evolutionary_index | rank 1/298 | 0.5955 |
Lorentzian › Lorentzian:causal_persistence | rank 3/298 | 0.9085 |
Möbius-S³ › Möbius-S³:phi_return_cv | rank 4/298 | 5.0156 |
Nonstationarity › Nonstationarity:change_quantiles_high | rank 4/298 | 0.1927 |
Visibility Graph › Visibility Graph:assortativity | rank 1/298 | 0.7742 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 1/298 | 0.9572 |
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