Uniform Chaos (Logistic Scramble)
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Logistic map at r=4 pushed through its arcsine invariant CDF F(x)=(2/π)arcsin(√x). Chaotic dynamics with a flat (uniform) histogram; preserves temporal correlations while erasing the arcsine marginal.
Interpretation
Standard analysis sees: anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); high-dimensional / space-filling. The atlas additionally detects discrete-map sensitive dependence, Time Reversibility:ordinal_reversal_distance.
What standard analysis sees
tail heaviness0.19
asymmetry0.20
occupancy0.82
short-range corr0.05
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
discrete-map sensitive dependence+3.9z
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+2.8z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Hölder Regularity:alpha_autocorrelation | +4.8z | bank-miss 1.3σ |
G2 Root System:short_long_ratio | -2.0z | bank-miss 1.1σ |
Composition
dtypefloat64
range[4.93e-05, 1]
unique values16384 / 16384
mean ± std0.502 ± 0.288
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/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
Which Geometries Light Up
G2 Root System › G2 Root System:short_long_ratio | rank 303/307 | 0.2971 |
Hölder Regularity › Hölder Regularity:alpha_autocorrelation | rank 4/307 | 0.3730 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 304/307 | 0.0005 |
← Tent Mapin continuous-flows
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources