Geometric Waiting Times
stochastic-process · 37 views
stochastic-processpoint-process
What It Is
Geometric(p) inter-arrival times with p ~ Uniform(0.05, 0.2). Strongly peaked at low values with an exponential tail; memoryless by construction, no temporal correlations.
Interpretation
Standard analysis sees: heavy-tailed; right-skewed; aperiodic / broadband; high-complexity (noise-like). The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.86
asymmetry0.91
occupancy0.26
short-range corr0.29
long-range memory0.35
spectral colour0.71
periodicity0.07
complexity0.85
time-irreversibility0.56
volatility clustering0.31
multifractality0.35
dimensionality0.60
nonstationarity0.37
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
dtypefloat64
range[1, 59]
unique values53 / 16384
mean ± std6.82 ± 6.31
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/Geometric_Waiting_Times.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Geometric_Waiting_Times.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Geometric_Waiting_Times.png)
Inflation (Substitution) > barcode
/d_curve/Geometric_Waiting_Times.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/Geometric_Waiting_Times.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/Geometric_Waiting_Times.png)
Ulam Spiral (Sacks) > default
/default/Geometric_Waiting_Times.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Poisson Spacings | 1.93 | cross-origin |
| Prime Gaps | 2.23 | cross-origin |
| Zipf Distribution | 2.61 |
Which Geometries Light Up
Klein Bottle › Klein Bottle:wht_spectral_kurtosis | rank 304/307 | 1.3833 |
Nonstationarity › Nonstationarity:trajectory_dim | rank 2/307 | 0.8220 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):zipf_r_squared | rank 5/307 | 0.9874 |
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