Henon Near-Crisis (a=1.2)
chaos · 36 views
chaos
What It Is
Henon map at a=1.2, b=0.3 --- near the boundary crisis where the attractor collides with its basin boundary, producing intermittent bursts of transient chaos
Interpretation
Standard analysis sees: left-skewed; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); stationary. The atlas additionally detects deterministic chaos.
What standard analysis sees
tail heaviness0.46
asymmetry0.06
occupancy0.81
short-range corr0.04
long-range memory0.12
spectral colour0.96
periodicity0.35
complexity0.31
time-irreversibility0.09
volatility clustering0.42
multifractality0.22
dimensionality0.73
nonstationarity0.14
What the atlas adds
deterministic chaos+3.5z
positive largest Lyapunov exponent — nearby trajectories diverge exponentially (sensitive dependence)
discrete-map biased — continuous-flow chaos (Lorenz) reads weak; spiky arithmetic sources can false-positive on the finite-time estimateComposition
dtypefloat64
range[-1.033, 1.295]
unique values16384 / 16384
mean ± std0.382 ± 0.681
Render Gallery
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Native > phase_plotraw
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Native > timeseriesraw
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Native > triple_latticeraw
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Boltzmann > lag_map
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Boltzmann > spin_grid
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Cayley > default
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Chladni > plate_bottom
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Chladni > plate_top
_(centered)/signed_log_z/Henon_Near-Crisis_(a=1.2).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Henon_Near-Crisis_(a=1.2).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Henon_Near-Crisis_(a=1.2).png)
Inflation (Substitution) > barcode
/d_curve/Henon_Near-Crisis_(a=1.2).png)
Inflation (Substitution) > d_curve
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Information Theory > default
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Julia Set > escape_histogram
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Klein Bottle > default
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Laplacian > default
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Logarithmic Spiral > default
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Möbius-S³ > mobius_cylinder
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Möbius-S³ > s2_base_map
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Ordinal Partition > default
/phi_spectrum/Henon_Near-Crisis_(a=1.2).png)
Penrose (Quasicrystal) > phi_spectrum
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Persistent Homology > barcode
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Persistent Homology > h1_diagram
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Predictability > default
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Recurrence Quantification > default
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Spectral Analysis > default
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Spectral Graph > default
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Spirograph > mode_spectrum
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Spirograph > phasor_trajectory
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Symplectic > flux_grid
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Symplectic > phase_space
/default/Henon_Near-Crisis_(a=1.2).png)
Ulam Spiral (Sacks) > default
/default/Henon_Near-Crisis_(a=1.2).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Logistic r=3.68 (Banded Chaos) | 2.76 | |
| Henon Map | 3.30 | |
| Logistic r=3.9 (Near-Full Chaos) | 3.58 |
Which Geometries Light Up
Spectral Analysis › Spectral Analysis:phase_coherence | rank 296/298 | 0.0005 |
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