Beta Noise
stochastic-process · 37 views
stochastic-processstochastic
What It Is
IID Beta(a, b) noise with a, b each drawn in [0.2, 0.5] per call (both < 1) --- U-shaped density concentrating mass at both extremes with a valley in the middle, structurally opposite to Gaussian
Interpretation
Standard analysis sees: bounded / light-tailed; aperiodic / broadband; high-complexity (noise-like). The atlas detects no named structure beyond this. It sits beside Benford's Law in the atlas (standard-bank rank 41) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.08
asymmetry0.57
occupancy0.53
short-range corr0.32
long-range memory0.25
spectral colour0.81
periodicity0.07
complexity0.90
time-irreversibility0.43
volatility clustering0.28
multifractality0.17
dimensionality0.75
nonstationarity0.19
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
dtypefloat64
range[7.753e-11, 1]
unique values16384 / 16384
mean ± std0.581 ± 0.382
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/Beta_Noise.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Beta_Noise.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Beta_Noise.png)
Inflation (Substitution) > barcode
/d_curve/Beta_Noise.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/Beta_Noise.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/Beta_Noise.png)
Ulam Spiral (Sacks) > default
/default/Beta_Noise.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Benford's Law | 2.95 | |
| MT19937 (Mersenne Twister) | 2.98 | cross-origin |
| Gzip (level 9) | 2.98 | cross-origin |
Which Geometries Light Up
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 5/306 | 0.9993 |
Hölder Regularity › Hölder Regularity:holder_std | rank 3/306 | 1.8885 |
Mostow Rigidity › Mostow Rigidity:volume_entropy | rank 1/306 | 4.5176 |
Mostow Rigidity › Mostow Rigidity:mean_turn_angle | rank 306/306 | 0.0407 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 302/306 | 0.0003 |
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