Perlin Noise
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Spectral Perlin-like noise --- coherent smooth fluctuations with 1/f amplitude falloff, widely used for procedural terrain and texture generation
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); volatility-clustering (bursty). The atlas additionally detects Nonstationarity:adf_pvalue.
What standard analysis sees
tail heaviness0.52
asymmetry0.54
occupancy0.74
short-range corr0.89
long-range memory0.91
spectral colour0.15
periodicity0.81
complexity0.61
time-irreversibility0.60
volatility clustering0.89
multifractality0.45
dimensionality0.22
nonstationarity0.84
What the atlas adds
Nonstationarity:adf_pvalue+2.4z
unit-root nonstationarity (ADF cannot reject random-walk null)
Atlas-extreme metrics the standard bank can’t predict for this source
Moiré:moire_peak_alpha | +2.5z | bank-miss 1.5σ |
Spectral Analysis:spectral_r2 | +2.0z | bank-miss 1.5σ |
Composition
dtypefloat64
range[-4.926, 3.454]
unique values16384 / 16384
mean ± std0 ± 1.81
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Perlin_Noise.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Perlin_Noise.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Perlin_Noise.png)
Inflation (Substitution) > barcode
/d_curve/Perlin_Noise.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/Perlin_Noise.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/Perlin_Noise.png)
Ulam Spiral (Sacks) > default
/default/Perlin_Noise.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| fBm (Persistent) | 1.98 | |
| fBm (Antipersistent) | 2.21 | |
| Brownian Walk | 2.30 |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_resonance | rank 3/306 | 0.9370 |
Catch24 › Catch24:SP_Summaries_welch_rect_centroid | rank 305/306 | 0.0004 |
Chladni › Chladni:nodal_clustering | rank 4/306 | 7.8920 |
Moiré › Moiré:moire_phi_response | rank 304/306 | -0.1181 |
Möbius-S³ › Möbius-S³:phi_return_cv | rank 4/306 | 5.4511 |
Sol (Thurston) › Sol (Thurston):integrated_walk_smoothness | rank 2/306 | 0.9127 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 2/306 | 0.9999 |
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