Berry Random Wave
random-matrix-quantum · 37 views
random-matrix-quantumstochastic
What It Is
Berry's random plane wave --- superposition model for chaotic eigenstate statistics, Gaussian amplitude distribution
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); low-complexity (predictable, not noise-like); volatility-clustering (bursty). The atlas finds no named structure, but the source is distinctively extreme on Moiré:moire_invariance_breadth (+2.6z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.54
asymmetry0.30
occupancy0.71
short-range corr0.96
long-range memory0.93
spectral colour0.18
periodicity0.59
complexity0.07
time-irreversibility0.67
volatility clustering0.97
multifractality0.77
dimensionality0.27
nonstationarity0.80
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Moiré:moire_invariance_breadth | +2.6z | bank-miss 1.7σ |
Composition
dtypefloat64
range[-1.302, 1.591]
unique values16384 / 16384
mean ± std0.0255 ± 0.627
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/Berry_Random_Wave.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Berry_Random_Wave.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Berry_Random_Wave.png)
Inflation (Substitution) > barcode
/d_curve/Berry_Random_Wave.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/Berry_Random_Wave.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/Berry_Random_Wave.png)
Ulam Spiral (Sacks) > default
/default/Berry_Random_Wave.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| FPUT N=16 | 2.62 | cross-origin |
| Lorenz-96 N=8 | 2.74 | cross-origin |
| Lorenz-96 N=36 | 2.77 | cross-origin |
Which Geometries Light Up
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 4/306 | 0.9993 |
Laplacian › Laplacian:curvature_autocorrelation | rank 4/306 | 0.9993 |
Laplacian › Laplacian:biharmonic_ratio | rank 305/306 | 0.0000 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 5/306 | 0.9642 |
p-Variation › p-Variation:volatility_clustering | rank 4/306 | 0.9995 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources