Levy Flight
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Random walk with Cauchy-distributed jumps --- infinite variance, occasional extreme leaps create fractal clustering of visited sites
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); time-irreversible (slow rise, sharp collapse); volatility-clustering (bursty); multifractal; nonstationary / drifting. The atlas additionally detects Nonstationarity:adf_pvalue. It sits beside Regime Switching in the atlas (standard-bank rank 38) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.49
asymmetry0.22
occupancy0.69
short-range corr0.90
long-range memory0.95
spectral colour0.26
periodicity0.79
complexity0.68
time-irreversibility0.14
volatility clustering0.89
multifractality0.93
dimensionality0.19
nonstationarity0.87
What the atlas adds
Nonstationarity:adf_pvalue+3.9z
unit-root nonstationarity (ADF cannot reject random-walk null)
Composition
dtypefloat64
range[-1150, 236.3]
unique values16058 / 16384
mean ± std-481 ± 256
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/Levy_Flight.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Levy_Flight.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Levy_Flight.png)
Inflation (Substitution) > barcode
/d_curve/Levy_Flight.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/Levy_Flight.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/Levy_Flight.png)
Ulam Spiral (Sacks) > default
/default/Levy_Flight.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| BTC Close Price | 2.83 | cross-origin |
| ETH/BTC Ratio | 2.98 | cross-origin |
| Regime Switching | 3.00 |
Which Geometries Light Up
Catch24 › Catch24:CO_f1ecac | rank 1/306 | 2722.4283 |
Catch24 › Catch24:SB_BinaryStats_mean_longstretch1 | rank 1/306 | 6449.7000 |
Catch24 › Catch24:CO_FirstMin_ac | rank 2/306 | 6815.5000 |
Catch24 › Catch24:SP_Summaries_welch_rect_centroid | rank 302/306 | 0.0005 |
Chladni › Chladni:plate_low_mode_fraction | rank 5/306 | 0.9940 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):boundary_dynamics | rank 4/306 | 0.1225 |
Inflation (Substitution) › Inflation (Substitution):discrepancy | rank 3/306 | 25.3316 |
Moiré › Moiré:moire_phi_response | rank 303/306 | -0.1154 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_slope | rank 303/306 | -0.5733 |
Sol (Thurston) › Sol (Thurston):integrated_walk_smoothness | rank 3/306 | 0.9008 |
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