Baker Map
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Baker's map --- stretching and folding like kneading dough, the canonical model of chaotic mixing. Re-seeded every 40 iterations to avoid float collapse
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; time-irreversible (slow rise, sharp collapse); high-dimensional / space-filling. The atlas additionally detects Time Reversibility:ordinal_reversal_distance, discrete-map sensitive dependence.
What standard analysis sees
tail heaviness0.26
asymmetry0.37
occupancy0.93
short-range corr0.34
long-range memory0.38
spectral colour0.66
periodicity0.10
complexity0.45
time-irreversibility0.03
volatility clustering0.27
multifractality0.40
dimensionality0.90
nonstationarity0.29
What the atlas adds
Time Reversibility:ordinal_reversal_distance+2.7z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
discrete-map sensitive dependence+2.2z
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 estimateAtlas-extreme metrics the standard bank can’t predict for this source
Hölder Regularity:alpha_autocorrelation | +4.3z | bank-miss 1.7σ |
G2 Root System:short_long_ratio | -2.0z | bank-miss 1.1σ |
Composition
dtypefloat64
range[2.74e-05, 1]
unique values16296 / 16384
mean ± std0.495 ± 0.291
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/Baker_Map.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Baker_Map.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Baker_Map.png)
Inflation (Substitution) > barcode
/d_curve/Baker_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/Baker_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/Baker_Map.png)
Ulam Spiral (Sacks) > default
/default/Baker_Map.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Uniform Chaos (Logistic Scramble) | 2.33 | |
| Tent Map | 2.55 | |
| Logistic Chaos | 3.18 |
Which Geometries Light Up
G2 Root System › G2 Root System:short_long_ratio | rank 305/307 | 0.2948 |
Modular Residue › Modular Residue:occupancy_entropy | rank 5/307 | 1.0000 |
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