Henon Map
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Classic 2D chaotic map --- the strange attractor has fractal cross-sections and correlation dimension ~1.25, a benchmark for testing dimension estimators
Interpretation
Standard analysis sees: left-skewed; rich, high-entropy values; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); monofractal. The atlas additionally detects discrete-map sensitive dependence, Time Reversibility:ordinal_reversal_distance.
What standard analysis sees
tail heaviness0.39
asymmetry0.07
occupancy0.85
short-range corr0.11
long-range memory0.14
spectral colour0.92
periodicity0.27
complexity0.38
time-irreversibility0.06
volatility clustering0.46
multifractality0.14
dimensionality0.79
nonstationarity0.17
What the atlas adds
discrete-map sensitive dependence+4.1z
deterministic chaos (positive λ_max, sensitive dependence)
names a discrete-map-scoped estimate, NOT chaos in general — continuous-flow chaos (Lorenz, Rössler) reads weak/neutral here despite being genuinely chaotic; spiky arithmetic sources can false-positive on the finite-time estimateTime Reversibility:ordinal_reversal_distance+2.6z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Möbius-S³:spinorial_asymmetry | +6.2z | bank-miss 2.3σ |
Nonstationarity:change_quantiles_low | +5.3z | bank-miss 1.6σ |
Hölder Regularity:alpha_autocorrelation | +3.0z | bank-miss 1.7σ |
Composition
dtypefloat64
range[-1.279, 1.272]
unique values16222 / 16384
mean ± std0.257 ± 0.721
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/Henon_Map.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Henon_Map.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Henon_Map.png)
Inflation (Substitution) > barcode
/d_curve/Henon_Map.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/Henon_Map.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/Henon_Map.png)
Ulam Spiral (Sacks) > default
/default/Henon_Map.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Logistic r=3.9 (Near-Full Chaos) | 3.48 | |
| Tent Map | 3.98 | |
| Clifford Attractor | 4.04 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:lyapunov_max | rank 5/306 | 0.3976 |
Catch24 › Catch24:CO_trev_1_num | rank 304/306 | -2.9043 |
Möbius-S³ › Möbius-S³:spinorial_asymmetry | rank 1/306 | 0.3254 |
Nonstationarity › Nonstationarity:change_quantiles_low | rank 1/306 | 0.1748 |
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