Intermittency Type-III
chaos · 36 views
chaos
What It Is
Type-III intermittency near a subcritical period-doubling (flip) bifurcation. The laminar phase is a growing period-2 subharmonic: the sign alternates every step while the amplitude grows, until it bursts and is reinjected near zero. Lag-1 autocorrelation is strongly negative -- the clean signature distinguishing it from type-I and type-II
Interpretation
Standard analysis sees: heavy-tailed; anti-correlated (alternating); blue spectrum (high-frequency power); low-complexity (predictable, not noise-like); low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on SL(2,ℝ) (Thurston):parabolic_fraction (+6.3z) — beyond what the standard bank predicts for it. It sits beside Logistic r=3.68 (Banded Chaos) in the atlas (standard-bank rank 27) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.97
asymmetry0.77
occupancy0.23
short-range corr0.03
long-range memory0.45
spectral colour0.91
periodicity0.38
complexity0.11
time-irreversibility0.84
volatility clustering0.57
multifractality0.83
dimensionality0.12
nonstationarity0.57
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
SL(2,ℝ) (Thurston):parabolic_fraction | +6.3z | bank-miss 4.7σ |
Hölder Regularity:alpha_autocorrelation | +5.6z | bank-miss 1.2σ |
Fisher Information:geodesic_velocity | +3.2z | bank-miss 1.2σ |
Möbius-S³:hopf_fiber_coherence | -3.1z | bank-miss 2.3σ |
Isochronicity:amplitude_exploration | +2.7z | bank-miss 1.3σ |
Fractal (Mandelbrot):interior_fraction | +2.4z | bank-miss 4.3σ |
Visibility Graph:avg_clustering_coeff | +2.3z | bank-miss 1.8σ |
Hyperbolic (Poincaré):spatio_temporal_corr | +2.2z | bank-miss 4.7σ |
Composition
dtypefloat64
range[-2.023, 2.03]
unique values16384 / 16384
mean ± std0.00118 ± 0.197
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-III.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Intermittency_Type-III.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Intermittency_Type-III.png)
Inflation (Substitution) > barcode
/d_curve/Intermittency_Type-III.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-III.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-III.png)
Ulam Spiral (Sacks) > default
/default/Intermittency_Type-III.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Intermittency Type-II | 5.30 | |
| BTC Returns | 5.98 | cross-domain |
| Logistic r=3.68 (Banded Chaos) | 6.08 |
Which Geometries Light Up
Fisher Information › Fisher Information:geodesic_velocity | rank 2/298 | 1.6664 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):interior_fraction | rank 4/298 | 0.9766 |
G2 Root System › G2 Root System:kurtosis_differential | rank 3/298 | 2.7376 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 2/298 | 0.8765 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):mean_hyperbolic_radius | rank 298/298 | 0.1330 |
Hölder Regularity › Hölder Regularity:alpha_autocorrelation | rank 4/298 | 0.3637 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 297/298 | -1.9631 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 296/298 | -0.1155 |
Lorentzian › Lorentzian:causal_persistence | rank 2/298 | 0.9691 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 296/298 | 0.0712 |
Persistent Homology › Persistent Homology:max_lifetime | rank 294/298 | 0.6854 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):parabolic_fraction | rank 1/298 | 0.7029 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):lyapunov_exponent | rank 294/298 | 0.0203 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):lyapunov_std | rank 295/298 | 0.0125 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_spectral_radius | rank 297/298 | 1.0121 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):hyperbolic_fraction | rank 298/298 | 0.0070 |
Spectral Graph › Spectral Graph:weyl_exponent | rank 5/298 | 2.0927 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 2/298 | 0.9545 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):zipf_r_squared | rank 3/298 | 0.9945 |
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