Logistic r=3.9 (Near-Full Chaos)
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Logistic map at r=3.9 --- nearly full chaos on a connected attractor (no real gaps at r=3.9; genuine periodic-window gaps in the support require lower r, e.g. r≈3.835)
Interpretation
Standard analysis sees: bounded / light-tailed; anti-correlated (alternating); blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse); homoskedastic; monofractal; stationary. The atlas additionally detects discrete-map sensitive dependence, Time Reversibility:ordinal_reversal_distance.
What standard analysis sees
tail heaviness0.13
asymmetry0.18
occupancy0.75
short-range corr0.06
long-range memory0.16
spectral colour0.95
periodicity0.26
complexity0.41
time-irreversibility0.07
volatility clustering0.07
multifractality0.07
dimensionality0.84
nonstationarity0.14
What the atlas adds
discrete-map sensitive dependence+5.0z
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+2.6z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Bispectrum:coupling_frequency_centroid | +2.7z | bank-miss 1.2σ |
Composition
dtypefloat64
range[0.09506, 0.975]
unique values16384 / 16384
mean ± std0.591 ± 0.3
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/Logistic_r=3.9_(Near-Full_Chaos).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Logistic_r=3.9_(Near-Full_Chaos).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Logistic_r=3.9_(Near-Full_Chaos).png)
Inflation (Substitution) > barcode
/d_curve/Logistic_r=3.9_(Near-Full_Chaos).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/Logistic_r=3.9_(Near-Full_Chaos).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/Logistic_r=3.9_(Near-Full_Chaos).png)
Ulam Spiral (Sacks) > default
/default/Logistic_r=3.9_(Near-Full_Chaos).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:lyapunov_max | rank 4/307 | 0.4859 |
Bispectrum › Bispectrum:coupling_frequency_centroid | rank 3/307 | 0.6752 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 2/307 | 0.1038 |
Penrose (Quasicrystal) › Penrose (Quasicrystal):phi_tower | rank 303/307 | -1.7230 |
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