Standard Map K=0.5 (Mixed)
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Chirikov standard map at K=0.5 --- mixed phase space where large KAM islands coexist with thin chaotic layers, the transitional regime between integrable and fully chaotic
Interpretation
Standard analysis sees: bounded / light-tailed; anti-persistent; strongly periodic; time-irreversible (slow rise, sharp collapse); homoskedastic; monofractal; low-dimensional; stationary. The atlas additionally detects Time Reversibility:ordinal_reversal_distance.
What standard analysis sees
tail heaviness0.14
asymmetry0.40
occupancy0.79
short-range corr0.15
long-range memory0.10
spectral colour0.75
periodicity0.89
complexity0.30
time-irreversibility0.06
volatility clustering0.07
multifractality0.11
dimensionality0.12
nonstationarity0.07
What the atlas adds
Time Reversibility:ordinal_reversal_distance+2.1z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Multi-Scale Wasserstein:w_max_ratio | +3.9z | bank-miss 1.4σ |
Composition
dtypefloat64
range[0.0002895, 6.283]
unique values16384 / 16384
mean ± std3.14 ± 2.02
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 > free_plate_nodal
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Chladni > plate_bottom
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Chladni > plate_top
_(centered)/signed_log_z/Standard_Map_K=0.5_(Mixed).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Standard_Map_K=0.5_(Mixed).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Standard_Map_K=0.5_(Mixed).png)
Inflation (Substitution) > barcode
/d_curve/Standard_Map_K=0.5_(Mixed).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/Standard_Map_K=0.5_(Mixed).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/Standard_Map_K=0.5_(Mixed).png)
Ulam Spiral (Sacks) > default
/default/Standard_Map_K=0.5_(Mixed).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Chirikov Standard Map | 3.19 | |
| Phyllotaxis | 3.98 | cross-origin |
| Critical Circle Map | 4.00 |
Which Geometries Light Up
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_max_ratio | rank 5/306 | 1424.0251 |
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