White Noise
stochastic-process · 37 views
stochastic-processstochastic
What It Is
IID uniform random floats in [0,1) --- the null model, maximum entropy with zero sequential correlation
Interpretation
Standard analysis sees: rich, high-entropy values; high-complexity (noise-like); homoskedastic; high-dimensional / space-filling. The atlas finds no named structure, but the source is distinctively extreme on Zipf–Mandelbrot (8-bit):zipf_r_squared (-2.8z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.26
asymmetry0.54
occupancy0.94
short-range corr0.30
long-range memory0.31
spectral colour0.68
periodicity0.19
complexity0.89
time-irreversibility0.62
volatility clustering0.12
multifractality0.17
dimensionality0.88
nonstationarity0.20
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Zipf–Mandelbrot (8-bit):zipf_r_squared | -2.8z | bank-miss 1.7σ |
Composition
dtypefloat64
range[7.939e-05, 1]
unique values16384 / 16384
mean ± std0.502 ± 0.288
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/White_Noise.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/White_Noise.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/White_Noise.png)
Inflation (Substitution) > barcode
/d_curve/White_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/White_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/White_Noise.png)
Ulam Spiral (Sacks) > default
/default/White_Noise.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| XorShift32 | 1.53 | cross-origin |
| glibc LCG | 1.62 | cross-origin |
| MT19937 (Mersenne Twister) | 1.76 | cross-origin |
Which Geometries Light Up
2-adic › 2-adic:mean_distance | rank 1/307 | 0.6685 |
Catch24 › Catch24:SB_TransitionMatrix_3ac_sumdiagcov | rank 306/307 | 0.0000 |
Klein Bottle › Klein Bottle:rank_deficit | rank 304/307 | 0.0496 |
Symplectic › Symplectic:recurrence_rate | rank 304/307 | 0.0278 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources