fBm (Antipersistent)
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Fractional Brownian motion with H=0.3 --- antipersistent (trend-reversing), rougher than standard Brownian motion
Interpretation
Standard analysis sees: left-skewed. The atlas finds no named structure, but the source is distinctively extreme on Ammann-Beenker (Octagonal):convergent_resonance (+2.2z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.63
asymmetry0.15
occupancy0.67
short-range corr0.79
long-range memory0.84
spectral colour0.35
periodicity0.74
complexity0.71
time-irreversibility0.30
volatility clustering0.79
multifractality0.49
dimensionality0.35
nonstationarity0.78
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Ammann-Beenker (Octagonal):convergent_resonance | +2.1z | bank-miss 1.2σ |
Spectral Analysis:spectral_r2 | +2.0z | bank-miss 2.1σ |
Composition
dtypefloat64
range[-0.9858, 0.7774]
unique values16384 / 16384
mean ± std0 ± 0.307
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_(Antipersistent).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/fBm_(Antipersistent).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/fBm_(Antipersistent).png)
Inflation (Substitution) > barcode
/d_curve/fBm_(Antipersistent).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_(Antipersistent).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_(Antipersistent).png)
Ulam Spiral (Sacks) > default
/default/fBm_(Antipersistent).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Perlin Noise | 2.20 | |
| Langevin Double-Well | 2.72 | cross-origin |
| Stochastic Resonance | 2.98 | cross-origin |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_resonance | rank 5/307 | 0.8568 |
Catch24 › Catch24:PD_PeriodicityWang_th0_01 | rank 5/307 | 3287.1000 |
Catch24 › Catch24:FC_LocalSimple_mean1_tauresrat | rank 305/307 | 0.0003 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 3/307 | 0.9999 |
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