Pi Digits
number-theory · 37 views
number-theoryhigh-entropy
What It Is
Digits of pi in base 256 --- conjectured normal (equidistributed), but entirely deterministic. Passes most statistical randomness tests
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); homoskedastic; monofractal; high-dimensional / space-filling. The atlas detects no named structure beyond this. It sits beside Golden Ratio Digits in the atlas (standard-bank rank 20) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.27
asymmetry0.47
occupancy0.96
short-range corr0.23
long-range memory0.26
spectral colour0.75
periodicity0.00
complexity0.98
time-irreversibility0.68
volatility clustering0.15
multifractality0.13
dimensionality0.98
nonstationarity0.24
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 ± 73.6
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/Pi_Digits.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Pi_Digits.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Pi_Digits.png)
Inflation (Substitution) > barcode
/d_curve/Pi_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/Pi_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/Pi_Digits.png)
Ulam Spiral (Sacks) > default
/default/Pi_Digits.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| AES Encrypted | 1.69 | cross-origin |
| MT19937 (Mersenne Twister) | 1.81 | cross-origin |
| Golden Ratio Digits | 1.86 |
Which Geometries Light Up
2-adic › 2-adic:multiscale_markov_predictability | rank 306/307 | 0.0267 |
Cantor Set › Cantor Set:jump_entropy | rank 304/307 | 0.0553 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 1/307 | 0.9994 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 307/307 | 0.0003 |
Predictability › Predictability:sample_entropy | rank 4/307 | 2.2151 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 303/307 | 0.0000 |
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