Logistic r=3.65 (Banded Chaos)
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Logistic map at r=3.65 --- banded (2-band) chaos: chaotic within two disjoint bands the orbit alternates between, mixing local unpredictability with global period-2 band cycling
Interpretation
Standard analysis sees: no strongly notable standard properties. The atlas additionally detects discrete-map sensitive dependence, Time Reversibility:ordinal_reversal_distance.
What the atlas adds
discrete-map sensitive dependence+2.4z
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+2.4z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
E8 Lattice:coset_transition | +11.4z | bank-miss 3.3σ |
Heisenberg (Nil) (centered):area_length_ratio | +5.3z | bank-miss 1.1σ |
Julia Set:potential_variance | +4.8z | bank-miss 3.0σ |
Julia Set:potential_smoothness | +4.7z | bank-miss 3.0σ |
Boltzmann:coupling_strength | +3.7z | bank-miss 3.0σ |
Sol (Thurston):path_length | +3.1z | bank-miss 1.2σ |
Julia Set:escape_entropy | -3.0z | bank-miss 2.4σ |
Inflation (Substitution):return_concentration | +2.8z | bank-miss 1.5σ |
Composition
dtypefloat64
range[0.2914, 0.9125]
unique values16384 / 16384
mean ± std0.655 ± 0.216
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=3.65_(Banded_Chaos).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Logistic_r=3.65_(Banded_Chaos).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Logistic_r=3.65_(Banded_Chaos).png)
Inflation (Substitution) > barcode
/d_curve/Logistic_r=3.65_(Banded_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=3.65_(Banded_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=3.65_(Banded_Chaos).png)
Ulam Spiral (Sacks) > default
/default/Logistic_r=3.65_(Banded_Chaos).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Quartic Map (Feigenbaum) | 4.18 | |
| Logistic Edge-of-Chaos | 4.34 | |
| Logistic r=3.9 (Near-Full Chaos) | 4.47 |
Which Geometries Light Up
E8 Lattice › E8 Lattice:coset_transition | rank 1/307 | 0.6094 |
Fisher Information › Fisher Information:effective_dimension | rank 307/307 | 1.0381 |
Lorentzian › Lorentzian:spacelike_fraction | rank 4/307 | 0.1768 |
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