Intermittency Type-III
iterated-maps · 37 views
iterated-mapsintermittent
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 additionally detects Time Reversibility:ordinal_reversal_distance. It sits beside MFPT Inner Unloaded in the atlas (standard-bank rank 52) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.97
asymmetry0.77
occupancy0.23
short-range corr0.02
long-range memory0.45
spectral colour0.92
periodicity0.38
complexity0.11
time-irreversibility0.84
volatility clustering0.57
multifractality0.83
dimensionality0.12
nonstationarity0.56
What the atlas adds
Time Reversibility:ordinal_reversal_distance+3.0z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
SL(2,ℝ) (Thurston):parabolic_fraction | +6.4z | bank-miss 4.8σ |
Fisher Information:geodesic_velocity | +3.2z | bank-miss 1.0σ |
Wavelet Cascade:scale_gini_dispersion | +3.1z | bank-miss 1.3σ |
Möbius-S³:hopf_fiber_coherence | -3.0z | bank-miss 2.1σ |
Fractal (Mandelbrot):interior_fraction | +2.4z | bank-miss 4.1σ |
Visibility Graph:avg_clustering_coeff | +2.3z | bank-miss 1.8σ |
Hyperbolic (Poincaré):spatio_temporal_corr | +2.3z | bank-miss 4.5σ |
Level Statistics:wd_classification | -2.2z | bank-miss 1.7σ |
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 > free_plate_nodal
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 | 5.06 | |
| BTC Returns | 5.66 | cross-origin |
| MFPT Inner Unloaded | 5.67 | cross-origin |
Which Geometries Light Up
Fisher Information › Fisher Information:geodesic_velocity | rank 4/307 | 1.6420 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 2/307 | 0.8760 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):mean_hyperbolic_radius | rank 305/307 | 0.1364 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 306/307 | -1.9619 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 304/307 | -0.1128 |
Lorentzian › Lorentzian:causal_persistence | rank 2/307 | 0.9685 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 305/307 | 0.0705 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):parabolic_fraction | rank 4/307 | 0.6942 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):hyperbolic_fraction | rank 305/307 | 0.0071 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_spectral_radius | rank 306/307 | 1.0125 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 2/307 | 0.9545 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):zipf_r_squared | rank 3/307 | 0.9946 |
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