Multiplicative Cascade
exotic · 36 views
exotic
What It Is
Random multiplicative process on dyadic tree --- multifractal burstiness at all scales
Interpretation
Standard analysis sees: heavy-tailed; right-skewed; nonstationary / drifting. The atlas finds no named structure, but the source is distinctively extreme on Level Statistics:wd_classification (-2.1z) — beyond what the standard bank predicts for it. It sits beside Intermittent Silence in the atlas (standard-bank rank 31) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.91
asymmetry0.94
occupancy0.28
short-range corr0.55
long-range memory0.72
spectral colour0.47
periodicity0.60
complexity0.81
time-irreversibility0.77
volatility clustering0.55
multifractality0.81
dimensionality0.20
nonstationarity0.96
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Level Statistics:wd_classification | -2.1z | bank-miss 1.3σ |
Composition
dtypefloat64
range[9.144e-05, 4.45]
unique values16384 / 16384
mean ± std0.428 ± 0.575
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/Multiplicative_Cascade.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Multiplicative_Cascade.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Multiplicative_Cascade.png)
Inflation (Substitution) > barcode
/d_curve/Multiplicative_Cascade.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/Multiplicative_Cascade.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/Multiplicative_Cascade.png)
Ulam Spiral (Sacks) > default
/default/Multiplicative_Cascade.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Minkowski Question Mark | 3.10 | |
| Wind Speed | 3.82 | cross-domain |
| Intermittent Silence | 3.90 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:lyap_sum | rank 4/298 | 2.6135 |
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