fBm (Persistent)
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Fractional Brownian motion with H=0.7 --- persistent (trend-following), smoother trajectories with long-range dependence
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); volatility-clustering (bursty); low-dimensional; nonstationary / drifting. The atlas additionally detects Nonstationarity:adf_pvalue.
What standard analysis sees
tail heaviness0.50
asymmetry0.16
occupancy0.77
short-range corr0.99
long-range memory0.98
spectral colour0.25
periodicity0.83
complexity0.51
time-irreversibility0.59
volatility clustering0.99
multifractality0.54
dimensionality0.11
nonstationarity0.85
What the atlas adds
Nonstationarity:adf_pvalue+4.8z
unit-root nonstationarity (ADF cannot reject random-walk null)
Atlas-extreme metrics the standard bank can’t predict for this source
Chladni:nodal_clustering | +2.7z | bank-miss 1.5σ |
Composition
dtypefloat64
range[-27.61, 18.02]
unique values16384 / 16384
mean ± std0 ± 11.6
Render Gallery
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Native > phase_plotraw
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Native > timeseriesraw
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Native > triple_latticeraw
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Boltzmann > lag_map
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Boltzmann > spin_grid
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Cayley > default
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Chladni > free_plate_nodal
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Chladni > plate_bottom
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Chladni > plate_top
_(centered)/signed_log_z/fBm_(Persistent).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/fBm_(Persistent).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/fBm_(Persistent).png)
Inflation (Substitution) > barcode
/d_curve/fBm_(Persistent).png)
Inflation (Substitution) > d_curve
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Information Theory > default
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Julia Set > escape_histogram
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Klein Bottle > default
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Laplacian > default
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Logarithmic Spiral > default
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Möbius-S³ > mobius_cylinder
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Möbius-S³ > s2_base_map
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Ordinal Partition > default
/phi_spectrum/fBm_(Persistent).png)
Penrose (Quasicrystal) > phi_spectrum
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Persistent Homology > barcode
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Persistent Homology > h1_diagram
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Predictability > default
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Recurrence Quantification > default
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Spectral Analysis > default
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Spectral Graph > default
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Spirograph > mode_spectrum
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Spirograph > phasor_trajectory
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Symplectic > flux_grid
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Symplectic > phase_space
/default/fBm_(Persistent).png)
Ulam Spiral (Sacks) > default
/default/fBm_(Persistent).png)
Ulam Spiral (Square) > default
.png)
Visibility Graph > default
.png)
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Perlin Noise | 1.97 | |
| Brownian Walk | 2.96 | |
| Geometric Brownian Motion | 2.97 |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_resonance | rank 1/307 | 0.9988 |
Catch24 › Catch24:SB_BinaryStats_mean_longstretch1 | rank 2/307 | 6235.3000 |
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiff | rank 3/307 | 37.4338 |
Catch24 › Catch24:CO_FirstMin_ac | rank 4/307 | 6414.8000 |
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1 | rank 5/307 | 0.9999 |
Catch24 › Catch24:FC_LocalSimple_mean3_stderr | rank 304/307 | 0.0090 |
Catch24 › Catch24:SP_Summaries_welch_rect_centroid | rank 307/307 | 0.0004 |
Chladni › Chladni:nodal_clustering | rank 2/307 | 8.4143 |
Chladni › Chladni:plate_low_mode_fraction | rank 2/307 | 0.9955 |
Moiré › Moiré:moire_phi_response | rank 307/307 | -0.1351 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_slope | rank 306/307 | -0.6048 |
Nonstationarity › Nonstationarity:adf_pvalue | rank 3/307 | 0.7993 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):trace_autocorrelation | rank 5/307 | 0.9990 |
Sol (Thurston) › Sol (Thurston):integrated_walk_smoothness | rank 1/307 | 0.9179 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 1/307 | 0.9999 |
Spectral Analysis › Spectral Analysis:spectral_bandwidth | rank 303/307 | 0.0010 |
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