ln(2) Digits
number_theory · 36 views
number_theory
What It Is
Base-256 digits of ln(2)'s fractional part. Transcendental (Hermite-Lindemann); conjectured normal but unproven.
Interpretation
Standard analysis sees: rich, high-entropy values; high-complexity (noise-like); high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.24
asymmetry0.55
occupancy0.96
short-range corr0.32
long-range memory0.26
spectral colour0.77
periodicity0.16
complexity0.94
time-irreversibility0.26
volatility clustering0.20
multifractality0.21
dimensionality0.89
nonstationarity0.29
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
dtypeuint8
range[0, 255]
unique values256 / 16384
mean ± std128 ± 74.3
Render Gallery
_Digits.png)
Native > phase_plotraw
_Digits.png)
Native > timeseriesraw
_Digits.png)
Native > triple_latticeraw
_Digits.png)
Boltzmann > lag_map
_Digits.png)
Boltzmann > spin_grid
_Digits.png)
Cayley > default
_Digits.png)
Chladni > plate_bottom
_Digits.png)
Chladni > plate_top
_(centered)/signed_log_z/ln(2)_Digits.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/ln(2)_Digits.png)
Heisenberg (Nil) (centered) > xy_path
_Digits.png)
Hodge–Laplacian > default
/barcode/ln(2)_Digits.png)
Inflation (Substitution) > barcode
/d_curve/ln(2)_Digits.png)
Inflation (Substitution) > d_curve
_Digits.png)
Information Theory > default
_Digits.png)
Julia Set > escape_histogram
_Digits.png)
Klein Bottle > default
_Digits.png)
Laplacian > default
_Digits.png)
Logarithmic Spiral > default
_Digits.png)
Möbius-S³ > mobius_cylinder
_Digits.png)
Möbius-S³ > s2_base_map
_Digits.png)
Ordinal Partition > default
/phi_spectrum/ln(2)_Digits.png)
Penrose (Quasicrystal) > phi_spectrum
_Digits.png)
Persistent Homology > barcode
_Digits.png)
Persistent Homology > h1_diagram
_Digits.png)
Predictability > default
_Digits.png)
Recurrence Quantification > default
_Digits.png)
Spectral Analysis > default
_Digits.png)
Spectral Graph > default
_Digits.png)
Spirograph > mode_spectrum
_Digits.png)
Spirograph > phasor_trajectory
_Digits.png)
Symplectic > flux_grid
_Digits.png)
Symplectic > phase_space
/default/ln(2)_Digits.png)
Ulam Spiral (Sacks) > default
/default/ln(2)_Digits.png)
Ulam Spiral (Square) > default
_Digits.png)
Visibility Graph > default
_Digits.png)
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Catalan G Digits | 1.70 | |
| AES Encrypted | 1.76 | cross-domain |
| glibc LCG | 1.83 | cross-domain |
Which Geometries Light Up
2-adic › 2-adic:multiscale_markov_predictability | rank 298/298 | 0.0267 |
Cantor Set › Cantor Set:jump_entropy | rank 297/298 | 0.0549 |
D4 Triality › D4 Triality:gram_consistency | rank 5/298 | 2.4955 |
Gottwald-Melbourne › Gottwald-Melbourne:k_statistic | rank 2/298 | 0.9987 |
Inflation (Substitution) › Inflation (Substitution):entropy_rate | rank 4/298 | 1.0000 |
Inflation (Substitution) › Inflation (Substitution):complexity_linearity | rank 296/298 | 0.6382 |
Modular Residue › Modular Residue:drift_anomaly | rank 297/298 | 0.0025 |
Persistent Homology › Persistent Homology:persistence_entropy | rank 4/298 | 4.9827 |
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