Uniform Chaos (Logistic Scramble)
chaos · 36 views
chaos
What It Is
Logistic map at r ≈ 3.9 pushed through its invariant CDF. Chaotic dynamics with a flat histogram; preserves temporal correlations while erasing the arcsine marginal.
Interpretation
Standard analysis sees: anti-correlated (alternating); blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); high-dimensional / space-filling. The atlas additionally detects deterministic chaos.
What standard analysis sees
tail heaviness0.19
asymmetry0.20
occupancy0.82
short-range corr0.06
long-range memory0.15
spectral colour0.95
periodicity0.27
complexity0.37
time-irreversibility0.07
volatility clustering0.26
multifractality0.24
dimensionality0.93
nonstationarity0.23
What the atlas adds
deterministic chaos+5.2z
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
Nonstationarity:change_quantiles_low | +2.6z | bank-miss 2.2σ |
Composition
dtypefloat64
range[0.1856, 0.9061]
unique values16384 / 16384
mean ± std0.567 ± 0.233
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/Uniform_Chaos_(Logistic_Scramble).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Uniform_Chaos_(Logistic_Scramble).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Uniform_Chaos_(Logistic_Scramble).png)
Inflation (Substitution) > barcode
/d_curve/Uniform_Chaos_(Logistic_Scramble).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/Uniform_Chaos_(Logistic_Scramble).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/Uniform_Chaos_(Logistic_Scramble).png)
Ulam Spiral (Sacks) > default
/default/Uniform_Chaos_(Logistic_Scramble).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=3.9 (Near-Full Chaos) | 2.97 | |
| Henon Map | 3.92 | |
| Henon Near-Crisis (a=1.2) | 4.11 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:lyapunov_max | rank 4/298 | 0.4309 |
Catch24 › Catch24:CO_trev_1_num | rank 296/298 | -3.0935 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_trace | rank 294/298 | -1.8135 |
← Tent Mapin motion
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources