Brownian Walk
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Cumulative sum of Gaussian increments --- the canonical random walk, self-affine with Hurst exponent H=0.5 and PSD ~ 1/f²
Interpretation
Standard analysis sees: left-skewed; smooth / autocorrelated; long-range memory (persistent); volatility-clustering (bursty). The atlas additionally detects Nonstationarity:adf_pvalue.
What standard analysis sees
tail heaviness0.32
asymmetry0.12
occupancy0.79
short-range corr0.93
long-range memory0.91
spectral colour0.26
periodicity0.79
complexity0.70
time-irreversibility0.39
volatility clustering0.91
multifractality0.42
dimensionality0.15
nonstationarity0.82
What the atlas adds
Nonstationarity:adf_pvalue+2.7z
unit-root nonstationarity (ADF cannot reject random-walk null)
Atlas-extreme metrics the standard bank can’t predict for this source
Dodecagonal (Stampfli):pisot_triplet_coherence | +3.4z | bank-miss 1.3σ |
Composition
dtypefloat64
range[-111.9, 132.9]
unique values16384 / 16384
mean ± std14.5 ± 56.1
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/Brownian_Walk.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Brownian_Walk.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Brownian_Walk.png)
Inflation (Substitution) > barcode
/d_curve/Brownian_Walk.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/Brownian_Walk.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/Brownian_Walk.png)
Ulam Spiral (Sacks) > default
/default/Brownian_Walk.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Geometric Brownian Motion | 2.29 | |
| Perlin Noise | 2.30 | |
| Regime Switching | 2.58 |
Which Geometries Light Up
Catch24 › Catch24:CO_f1ecac | rank 4/306 | 2334.6222 |
Catch24 › Catch24:DN_OutlierInclude_n_001_mdrmd | rank 4/306 | 0.3049 |
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