Lorenz-96 N=8
continuous-flows · 37 views
continuous-flowschaotic
What It Is
Lorenz-96 with N=8 variables at standard forcing F=8. Observable is x_0(t). Weakly turbulent regime, attractor dim ~3.
Interpretation
Standard analysis sees: smooth / autocorrelated; red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); volatility-clustering (bursty). The atlas additionally detects Multifractal Spectrum:hurst_estimate.
What standard analysis sees
tail heaviness0.53
asymmetry0.34
occupancy0.76
short-range corr0.87
long-range memory0.82
spectral colour0.07
periodicity0.51
complexity0.10
time-irreversibility0.02
volatility clustering0.88
multifractality0.79
dimensionality0.31
nonstationarity0.72
What the atlas adds
Multifractal Spectrum:hurst_estimate+2.0z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
Laplacian:curvature_autocorrelation | +2.0z | bank-miss 1.0σ |
Composition
dtypefloat64
range[-6.463, 10.98]
unique values16384 / 16384
mean ± std2.2 ± 3.53
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Lorenz-96_N=8.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Lorenz-96_N=8.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Lorenz-96_N=8.png)
Inflation (Substitution) > barcode
/d_curve/Lorenz-96_N=8.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Lorenz-96_N=8.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Lorenz-96_N=8.png)
Ulam Spiral (Sacks) > default
/default/Lorenz-96_N=8.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Lorenz-96 N=36 | 2.08 | |
| Double Pendulum | 2.33 | |
| Berry Random Wave | 2.73 | cross-origin |
Which Geometries Light Up
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 5/307 | 4.5800 |
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