Catalan G Digits
number_theory · 36 views
number_theory
What It Is
Base-256 digits of Catalan's constant G = Σ(−1)ⁿ/(2n+1)². Irrationality and transcendence both unproven; normality unknown.
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); monofractal; high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.21
asymmetry0.52
occupancy0.96
short-range corr0.27
long-range memory0.26
spectral colour0.78
periodicity0.14
complexity0.96
time-irreversibility0.63
volatility clustering0.23
multifractality0.11
dimensionality0.90
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
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/Catalan_G_Digits.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Catalan_G_Digits.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Catalan_G_Digits.png)
Inflation (Substitution) > barcode
/d_curve/Catalan_G_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/Catalan_G_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/Catalan_G_Digits.png)
Ulam Spiral (Sacks) > default
/default/Catalan_G_Digits.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| ln(2) Digits | 1.70 | |
| glibc LCG | 1.71 | cross-domain |
| Golden Ratio Digits | 1.74 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:filling_ratio | rank 4/298 | 0.9825 |
AutoRegressive › AutoRegressive:ar_residual_frac | rank 3/298 | 0.9997 |
Boltzmann › Boltzmann:coupling_strength | rank 294/298 | 0.0054 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 5/298 | 0.9993 |
Klein Bottle › Klein Bottle:rank_deficit | rank 294/298 | 0.0496 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 294/298 | 0.0003 |
Persistent Homology › Persistent Homology:persistence_entropy | rank 3/298 | 4.9885 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):hapax_ratio | rank 5/298 | 0.8806 |
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