glibc LCG
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What It Is
The C standard library LCG --- used by glibc rand() for decades. Low bits cycle with short period, high bits have lattice structure in dimensions >5
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); high-dimensional / space-filling. The atlas finds no named structure, but the source is distinctively extreme on Zipf–Mandelbrot (8-bit):zipf_r_squared (-2.8z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.30
asymmetry0.49
occupancy0.93
short-range corr0.27
long-range memory0.37
spectral colour0.71
periodicity0.05
complexity1.00
time-irreversibility0.60
volatility clustering0.29
multifractality0.20
dimensionality0.95
nonstationarity0.20
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Zipf–Mandelbrot (8-bit):zipf_r_squared | -2.9z | bank-miss 1.7σ |
Composition
dtypefloat64
range[4.763e-05, 1]
unique values16384 / 16384
mean ± std0.504 ± 0.288
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/glibc_LCG.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/glibc_LCG.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/glibc_LCG.png)
Inflation (Substitution) > barcode
/d_curve/glibc_LCG.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/glibc_LCG.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/glibc_LCG.png)
Ulam Spiral (Sacks) > default
/default/glibc_LCG.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| White Noise | 1.32 | cross-domain |
| XorShift32 | 1.48 | |
| RANDU | 1.49 |
Which Geometries Light Up
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 3/298 | 0.9993 |
Mostow Rigidity › Mostow Rigidity:volume_entropy | rank 4/298 | 4.5000 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 296/298 | 0.0003 |
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