Zipf Distribution
stochastic-process · 37 views
stochastic-processstochastic
What It Is
IID draws from Zipf/power-law distribution --- steep rank-frequency, heavy right tail
Interpretation
Standard analysis sees: heavy-tailed; right-skewed; aperiodic / broadband; high-complexity (noise-like). The atlas finds no named structure, but the source is distinctively extreme on Continued Fraction:gauss_kuzmin_distance (+2.1z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.90
asymmetry0.93
occupancy0.30
short-range corr0.23
long-range memory0.43
spectral colour0.75
periodicity0.10
complexity0.88
time-irreversibility0.28
volatility clustering0.17
multifractality0.44
dimensionality0.47
nonstationarity0.53
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Continued Fraction:gauss_kuzmin_distance | +2.1z | bank-miss 1.3σ |
Composition
dtypefloat64
range[0.6932, 14.04]
unique values16384 / 16384
mean ± std1.5 ± 1.09
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/Zipf_Distribution.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Zipf_Distribution.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Zipf_Distribution.png)
Inflation (Substitution) > barcode
/d_curve/Zipf_Distribution.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/Zipf_Distribution.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/Zipf_Distribution.png)
Ulam Spiral (Sacks) > default
/default/Zipf_Distribution.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Poisson Spacings | 2.40 | cross-origin |
| Geometric Waiting Times | 2.61 | |
| Prime Gaps | 3.09 | cross-origin |
Which Geometries Light Up
2-adic › 2-adic:valuation_spectral_concentration | rank 303/306 | 0.0466 |
Hölder Regularity › Hölder Regularity:holder_std | rank 5/306 | 1.8494 |
Inflation (Substitution) › Inflation (Substitution):entropy_rate | rank 4/306 | 1.0000 |
Inflation (Substitution) › Inflation (Substitution):complexity_subexponential | rank 303/306 | 0.6382 |
Nonstationarity › Nonstationarity:trajectory_dim | rank 1/306 | 0.8527 |
← White Noisein algorithmic-bytes
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