√2 Digits
number_theory · 36 views
number_theory
What It Is
Base-256 digits of √2's fractional part. Algebraic of degree 2; irrational (Theaetetus / Pythagoreans, ~5th c. BC); normality unknown.
Interpretation
Standard analysis sees: rich, high-entropy values; high-complexity (noise-like); monofractal; high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.21
asymmetry0.50
occupancy0.95
short-range corr0.25
long-range memory0.27
spectral colour0.81
periodicity0.16
complexity0.96
time-irreversibility0.69
volatility clustering0.19
multifractality0.12
dimensionality0.93
nonstationarity0.27
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 ± std127 ± 74.5
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/√2_Digits.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/√2_Digits.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/√2_Digits.png)
Inflation (Substitution) > barcode
/d_curve/√2_Digits.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/√2_Digits.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/√2_Digits.png)
Ulam Spiral (Sacks) > default
/default/√2_Digits.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| AES Encrypted | 1.86 | cross-domain |
| ChaCha20 | 1.91 | cross-domain |
| Golden Ratio Digits | 1.93 |
Which Geometries Light Up
2-adic › 2-adic:mean_distance | rank 5/298 | 0.6677 |
Boltzmann › Boltzmann:coupling_temporal_variance | rank 5/298 | 1.6061 |
Boltzmann › Boltzmann:coupling_strength | rank 296/298 | 0.0050 |
Klein Bottle › Klein Bottle:rank_deficit | rank 295/298 | 0.0496 |
Predictability › Predictability:cond_entropy_k8 | rank 3/298 | 2.9998 |
Symplectic › Symplectic:recurrence_rate | rank 294/298 | 0.0279 |
Zariski › Zariski:nonsep_fraction | rank 297/298 | 0.0065 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):bigram_predictability | rank 294/298 | 0.0106 |
← von Mangoldt Functionin waveform
← μ-law Sinealphabetical
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources