Benford's Law
number_theory · 36 views
number_theory
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: no strongly notable standard properties. The atlas detects no named structure beyond this. It sits beside Beta Noise in the atlas (standard-bank rank 63) — a neighbor conventional features miss.
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 > 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 | |
|---|---|---|
| Zipf Distribution | 2.78 | cross-domain |
| BSL Residues | 3.15 | |
| Beta Noise | 3.18 | cross-domain |
Which Geometries Light Up
Catch24 › Catch24:SB_MotifThree_quantile_hh | rank 3/298 | 2.1971 |
D4 Triality › D4 Triality:spectral_transition | rank 5/298 | 0.2479 |
Gottwald-Melbourne › Gottwald-Melbourne:radial_spectral_structure | rank 295/298 | 0.4369 |
Spectral Analysis › Spectral Analysis:phase_coherence | rank 294/298 | 0.0005 |
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