Brownian Walk
noise · 36 views
noise
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: smooth / autocorrelated; long-range memory (persistent); volatility-clustering (bursty); nonstationary / drifting. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.39
asymmetry0.16
occupancy0.78
short-range corr0.88
long-range memory0.90
spectral colour0.25
periodicity0.72
complexity0.68
time-irreversibility0.39
volatility clustering0.87
multifractality0.39
dimensionality0.19
nonstationarity0.87
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[-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 > 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 | |
|---|---|---|
| Perlin Noise | 2.13 | |
| Geometric Brownian Motion | 2.21 | |
| Regime Switching | 2.46 |
Which Geometries Light Up
Catch24 › Catch24:CO_f1ecac | rank 2/298 | 2382.8185 |
Catch24 › Catch24:SB_BinaryStats_mean_longstretch1 | rank 4/298 | 5363.3200 |
Dodecagonal (Stampfli) › Dodecagonal (Stampfli):pisot_triplet_coherence | rank 4/298 | 0.5697 |
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