Tent Map
chaos · 36 views
chaos
What It Is
Piecewise-linear chaos --- a V-shaped map near slope 2, producing uniform invariant density with maximal topological entropy
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; time-irreversible (slow rise, sharp collapse); high-dimensional / space-filling. The atlas additionally detects deterministic chaos.
What standard analysis sees
tail heaviness0.27
asymmetry0.34
occupancy0.91
short-range corr0.20
long-range memory0.37
spectral colour0.84
periodicity0.02
complexity0.43
time-irreversibility0.03
volatility clustering0.28
multifractality0.30
dimensionality0.98
nonstationarity0.38
What the atlas adds
deterministic chaos+7.0z
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 estimateAtlas-extreme metrics the standard bank can’t predict for this source
Hölder Regularity:alpha_autocorrelation | +5.7z | bank-miss 1.2σ |
H² × ℝ (Thurston):depth_height_corr | -2.4z | bank-miss 1.9σ |
G2 Root System:short_long_ratio | -2.0z | bank-miss 1.4σ |
Composition
dtypefloat64
range[0.001038, 0.9995]
unique values16384 / 16384
mean ± std0.502 ± 0.287
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Tent_Map.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Tent_Map.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Tent_Map.png)
Inflation (Substitution) > barcode
/d_curve/Tent_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/Tent_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/Tent_Map.png)
Ulam Spiral (Sacks) > default
/default/Tent_Map.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Baker Map | 2.58 | |
| Logistic Chaos | 3.06 | |
| Logistic r=3.9 (Near-Full Chaos) | 4.14 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:lyapunov_max | rank 1/298 | 0.5712 |
G2 Root System › G2 Root System:short_long_ratio | rank 295/298 | 0.2990 |
Hölder Regularity › Hölder Regularity:alpha_autocorrelation | rank 3/298 | 0.3698 |
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