Intermittency Type-II
chaos · 36 views
chaos
What It Is
Type-II intermittency near a subcritical Neimark-Sacker (Hopf) bifurcation. The laminar phase is a slow spiral: a rotation whose amplitude grows smoothly until it leaves the channel, bursts, and is reinjected near zero. Distinct from Pomeau-Manneville type-I (tangent bifurcation) and type-III (period-doubling); laminar length scales as epsilon^-1
Interpretation
Standard analysis sees: heavy-tailed. The atlas finds no named structure, but the source is distinctively extreme on SL(2,ℝ) (Thurston):parabolic_fraction (+6.2z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.96
asymmetry0.19
occupancy0.23
short-range corr0.49
long-range memory0.30
spectral colour0.57
periodicity0.67
complexity0.41
time-irreversibility0.74
volatility clustering0.50
multifractality0.68
dimensionality0.44
nonstationarity0.55
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
SL(2,ℝ) (Thurston):parabolic_fraction | +6.2z | bank-miss 2.1σ |
Boltzmann:dominant_lag | +3.9z | bank-miss 1.9σ |
Fisher Information:geodesic_velocity | +3.2z | bank-miss 2.9σ |
Fractal (Mandelbrot):interior_fraction | +2.4z | bank-miss 1.9σ |
H4 600-Cell:edge_walk_fraction | +2.1z | bank-miss 1.3σ |
Hyperbolic (Poincaré):spatio_temporal_corr | +2.0z | bank-miss 2.7σ |
Composition
dtypefloat64
range[-1.846, 2.012]
unique values16384 / 16384
mean ± std-0.000407 ± 0.184
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/Intermittency_Type-II.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Intermittency_Type-II.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Intermittency_Type-II.png)
Inflation (Substitution) > barcode
/d_curve/Intermittency_Type-II.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/Intermittency_Type-II.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/Intermittency_Type-II.png)
Ulam Spiral (Sacks) > default
/default/Intermittency_Type-II.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| IMS Bearing Failed | 4.23 | cross-domain |
| Sprott-B | 4.40 | |
| MFPT Inner Unloaded | 4.41 | cross-domain |
Which Geometries Light Up
Boltzmann › Boltzmann:dominant_lag | rank 5/298 | 987.0000 |
Boltzmann › Boltzmann:nn_dominance | rank 294/298 | 0.0272 |
Fisher Information › Fisher Information:geodesic_velocity | rank 3/298 | 1.6602 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):interior_fraction | rank 5/298 | 0.9765 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 4/298 | 0.8297 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):mean_hyperbolic_radius | rank 296/298 | 0.1517 |
Ordinal Partition › Ordinal Partition:memory_order | rank 4/298 | 0.9028 |
Predictability › Predictability:transition_entropy_variance | rank 3/298 | 0.0672 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):parabolic_fraction | rank 2/298 | 0.6915 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):lyapunov_std | rank 294/298 | 0.0140 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):hyperbolic_fraction | rank 295/298 | 0.0103 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_spectral_radius | rank 296/298 | 1.0168 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):zipf_r_squared | rank 4/298 | 0.9942 |
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