Hilbert Walk
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
What It Is
1D trace of Hilbert space-filling curve --- preserves 2D locality, creating structured self-similar fluctuations at every scale
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); strongly periodic; volatility-clustering (bursty). The atlas additionally detects Nonstationarity:adf_pvalue.
What standard analysis sees
tail heaviness0.45
asymmetry0.22
occupancy0.69
short-range corr0.95
long-range memory0.91
spectral colour0.14
periodicity0.86
complexity0.24
time-irreversibility0.72
volatility clustering0.97
multifractality0.40
dimensionality0.16
nonstationarity0.43
What the atlas adds
Nonstationarity:adf_pvalue+3.4z
unit-root nonstationarity (ADF cannot reject random-walk null)
Atlas-extreme metrics the standard bank can’t predict for this source
Inflation (Substitution):discrepancy | +4.2z | bank-miss 1.5σ |
Ulam Spiral (Square):radial_periodicity | +3.2z | bank-miss 1.7σ |
Möbius-S³:phi_return_cv | +2.9z | bank-miss 1.7σ |
p-Variation:volatility_clustering | -2.5z | bank-miss 1.2σ |
Laplacian:curvature_autocorrelation | -2.2z | bank-miss 1.2σ |
Moiré:moire_integer_excess | -2.1z | bank-miss 2.2σ |
Composition
dtypefloat64
range[128, 255]
unique values128 / 16384
mean ± std206 ± 34
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/Hilbert_Walk.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Hilbert_Walk.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Hilbert_Walk.png)
Inflation (Substitution) > barcode
/d_curve/Hilbert_Walk.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/Hilbert_Walk.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/Hilbert_Walk.png)
Ulam Spiral (Sacks) > default
/default/Hilbert_Walk.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Mertens Function | 2.92 | cross-origin |
| Rudin-Shapiro | 3.73 | |
| Geometric Brownian Motion | 3.77 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:SB_BinaryStats_mean_longstretch1 | rank 3/307 | 5470.9000 |
Catch24 › Catch24:CO_HistogramAMI_even_2_5 | rank 5/307 | 1.4505 |
Catch24 › Catch24:SP_Summaries_welch_rect_centroid | rank 303/307 | 0.0005 |
Inflation (Substitution) › Inflation (Substitution):discrepancy | rank 2/307 | 27.2802 |
Moiré › Moiré:moire_integer_excess | rank 304/307 | -0.2283 |
Predictability › Predictability:excess_predictability | rank 3/307 | 2.8961 |
Sol (Thurston) › Sol (Thurston):integrated_walk_smoothness | rank 4/307 | 0.8882 |
p-Variation › p-Variation:volatility_clustering | rank 305/307 | -0.6000 |
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