fBm (Persistent)

noise · 36 views

noise

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 finds no named structure, but the source is distinctively extreme on Chladni:nodal_clustering (+2.4z) — beyond what the standard bank predicts for it. It sits beside Geometric Brownian Motion in the atlas (standard-bank rank 26) — a neighbor conventional features miss.

What standard analysis sees

tail heaviness0.51

asymmetry0.16

occupancy0.76

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

nonstationarity0.86

What the atlas adds

Atlas-extreme metrics the standard bank can’t predict for this source

Chladni:nodal_clustering +2.4z bank-miss 1.0σ

Composition

dtypefloat64

range[-27.61, 18.02]

unique values16384 / 16384

mean ± std0 ± 11.6

Render Gallery

Native > phase_plotraw

Native > timeseriesraw

Native > triple_latticeraw

Boltzmann > lag_map

Boltzmann > spin_grid

Cayley > default

Chladni > plate_bottom

Chladni > plate_top

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

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

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

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Nearest neighbor	Distance
Perlin Noise	1.87
Brownian Walk	2.66
Geometric Brownian Motion	3.20

Open in Atlas →

Which Geometries Light Up

Ammann-Beenker (Octagonal) › `Ammann-Beenker (Octagonal):convergent_resonance`	rank 1/298	0.9990
Catch24 › `Catch24:SB_BinaryStats_mean_longstretch1`	rank 2/298	5802.0400
Catch24 › `Catch24:CO_Embed2_Dist_tau_d_expfit_meandiff`	rank 3/298	37.6678
Catch24 › `Catch24:CO_FirstMin_ac`	rank 5/298	6216.7200
Catch24 › `Catch24:SP_Summaries_welch_rect_area_5_1`	rank 5/298	0.9999
Catch24 › `Catch24:FC_LocalSimple_mean3_stderr`	rank 295/298	0.0090
Catch24 › `Catch24:SP_Summaries_welch_rect_centroid`	rank 295/298	0.0004
Chladni › `Chladni:plate_low_mode_fraction`	rank 2/298	0.9955
Chladni › `Chladni:captured_power_fraction`	rank 294/298	0.0017
Chladni › `Chladni:nodal_gap_ratio`	rank 294/298	0.2324
Heisenberg (Nil) (centered) › `Heisenberg (Nil) (centered):xy_aspect`	rank 296/298	0.0002
Moiré › `Moiré:moire_phi_response`	rank 298/298	-0.1645
Multi-Scale Wasserstein › `Multi-Scale Wasserstein:w_slope`	rank 297/298	-0.5999
Nonstationarity › `Nonstationarity:adf_pvalue`	rank 3/298	0.8003
SL(2,ℝ) (Thurston) › `SL(2,ℝ) (Thurston):trace_autocorrelation`	rank 5/298	0.9990
Sol (Thurston) › `Sol (Thurston):sol_step_persistence`	rank 1/298	0.9099
Spectral Analysis › `Spectral Analysis:spectral_r2`	rank 1/298	0.9999
Spectral Analysis › `Spectral Analysis:spectral_bandwidth`	rank 294/298	0.0010
Wasserstein › `Wasserstein:recurrence_distance`	rank 5/298	0.0811
p-Variation › `p-Variation:var_p2`	rank 296/298	0.0000

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