Benford's Law
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Benford-distributed significands --- leading-digit law P(d) = log₁₀(1+1/d), the distribution of first digits in real-world datasets spanning multiple orders of magnitude
Interpretation
Standard analysis sees: aperiodic / broadband; high-complexity (noise-like). The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.51
asymmetry0.80
occupancy0.76
short-range corr0.36
long-range memory0.33
spectral colour0.70
periodicity0.05
complexity0.95
time-irreversibility0.64
volatility clustering0.27
multifractality0.20
dimensionality0.70
nonstationarity0.32
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[1, 9.999]
unique values16384 / 16384
mean ± std3.73 ± 2.44
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/Benfords_Law.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Benfords_Law.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Benfords_Law.png)
Inflation (Substitution) > barcode
/d_curve/Benfords_Law.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/Benfords_Law.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/Benfords_Law.png)
Ulam Spiral (Sacks) > default
/default/Benfords_Law.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| BSL Residues | 2.84 | cross-origin |
| Wichmann-Hill | 2.91 | cross-origin |
| MT19937 (Mersenne Twister) | 2.92 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:SB_MotifThree_quantile_hh | rank 3/306 | 2.1971 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 302/306 | 0.0005 |
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