Logistic r=3.68 (Banded Chaos)
chaos · 36 views
chaos
What It Is
Logistic map in banded chaos --- chaotic within disjoint bands that the orbit cycles through, mixing local unpredictability with global periodicity
Interpretation
Standard analysis sees: left-skewed; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); time-irreversible (slow rise, sharp collapse). The atlas additionally detects deterministic chaos.
What standard analysis sees
tail heaviness0.48
asymmetry0.04
occupancy0.71
short-range corr0.02
long-range memory0.13
spectral colour0.92
periodicity0.40
complexity0.26
time-irreversibility0.12
volatility clustering0.49
multifractality0.55
dimensionality0.59
nonstationarity0.18
What the atlas adds
deterministic chaos+4.0z
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
E8 Lattice:coset_transition | +9.4z | bank-miss 1.4σ |
Persistent Homology:max_lifetime | -2.3z | bank-miss 1.9σ |
Composition
dtypefloat64
range[0.2708, 0.92]
unique values16384 / 16384
mean ± std0.672 ± 0.195
Render Gallery
.png)
Native > phase_plotraw
.png)
Native > timeseriesraw
.png)
Native > triple_latticeraw
.png)
Boltzmann > lag_map
.png)
Boltzmann > spin_grid
.png)
Cayley > default
.png)
Chladni > plate_bottom
.png)
Chladni > plate_top
_(centered)/signed_log_z/Logistic_r=3.68_(Banded_Chaos).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Logistic_r=3.68_(Banded_Chaos).png)
Heisenberg (Nil) (centered) > xy_path
.png)
Hodge–Laplacian > default
/barcode/Logistic_r=3.68_(Banded_Chaos).png)
Inflation (Substitution) > barcode
/d_curve/Logistic_r=3.68_(Banded_Chaos).png)
Inflation (Substitution) > d_curve
.png)
Information Theory > default
.png)
Julia Set > escape_histogram
.png)
Klein Bottle > default
.png)
Laplacian > default
.png)
Logarithmic Spiral > default
.png)
Möbius-S³ > mobius_cylinder
.png)
Möbius-S³ > s2_base_map
.png)
Ordinal Partition > default
/phi_spectrum/Logistic_r=3.68_(Banded_Chaos).png)
Penrose (Quasicrystal) > phi_spectrum
.png)
Persistent Homology > barcode
.png)
Persistent Homology > h1_diagram
.png)
Predictability > default
.png)
Recurrence Quantification > default
.png)
Spectral Analysis > default
.png)
Spectral Graph > default
.png)
Spirograph > mode_spectrum
.png)
Spirograph > phasor_trajectory
.png)
Symplectic > flux_grid
.png)
Symplectic > phase_space
/default/Logistic_r=3.68_(Banded_Chaos).png)
Ulam Spiral (Sacks) > default
/default/Logistic_r=3.68_(Banded_Chaos).png)
Ulam Spiral (Square) > default
.png)
Visibility Graph > default
.png)
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Henon Near-Crisis (a=1.2) | 2.76 | |
| Logistic r=3.9 (Near-Full Chaos) | 3.82 | |
| Uniform Chaos (Logistic Scramble) | 4.16 |
Which Geometries Light Up
E8 Lattice › E8 Lattice:coset_transition | rank 1/298 | 0.4574 |
H4 600-Cell › H4 600-Cell:lattice_closure | rank 2/298 | 1.0000 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):spatio_temporal_corr | rank 5/298 | 0.8029 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources