Rudin-Shapiro
number_theory · 36 views
number_theory
What It Is
Partial sums of Rudin-Shapiro --- deterministic random walk with flat spectral density
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); strongly periodic; volatility-clustering (bursty); monofractal. The atlas finds no named structure, but the source is distinctively extreme on Dodecagonal (Stampfli):pisot_triplet_coherence (+4.1z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.33
asymmetry0.20
occupancy0.52
short-range corr0.89
long-range memory0.89
spectral colour0.24
periodicity0.91
complexity0.34
time-irreversibility0.61
volatility clustering0.86
multifractality0.15
dimensionality0.21
nonstationarity0.77
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Dodecagonal (Stampfli):pisot_triplet_coherence | +4.1z | bank-miss 1.0σ |
H3 Icosahedral:nn_enrichment | +3.0z | bank-miss 3.2σ |
Hölder Regularity:holder_min | +2.5z | bank-miss 2.7σ |
Laplacian:gradient_curvature_anticorrelation | +2.4z | bank-miss 1.9σ |
Composition
dtypefloat64
range[-199, 56]
unique values256 / 16384
mean ± std-61.5 ± 59.9
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/Rudin-Shapiro.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Rudin-Shapiro.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Rudin-Shapiro.png)
Inflation (Substitution) > barcode
/d_curve/Rudin-Shapiro.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/Rudin-Shapiro.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/Rudin-Shapiro.png)
Ulam Spiral (Sacks) > default
/default/Rudin-Shapiro.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Mertens Function | 3.02 | |
| Hilbert Walk | 3.72 | cross-domain |
| Brownian Walk | 3.73 | cross-domain |
Which Geometries Light Up
Catch24 › Catch24:PD_PeriodicityWang_th0_01 | rank 3/298 | 3529.8000 |
Catch24 › Catch24:CO_FirstMin_ac | rank 4/298 | 6455.5333 |
Catch24 › Catch24:CO_f1ecac | rank 5/298 | 2305.0053 |
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiff | rank 297/298 | 0.0000 |
Chladni › Chladni:domain_ks_exponential | rank 3/298 | 0.7272 |
D4 Triality › D4 Triality:edge_ortho_polarity | rank 2/298 | 0.7570 |
Dodecagonal (Stampfli) › Dodecagonal (Stampfli):pisot_triplet_coherence | rank 5/298 | 0.5402 |
Hölder Regularity › Hölder Regularity:holder_min | rank 1/298 | 1.0000 |
Inflation (Substitution) › Inflation (Substitution):discrepancy | rank 5/298 | 23.0286 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 1/298 | 1.0000 |
Möbius-S³ › Möbius-S³:phi_return_cv | rank 5/298 | 4.9571 |
Navier-Stokes › Navier-Stokes:ess_quality | rank 297/298 | -0.0012 |
Symplectic › Symplectic:phase_reflection_symmetry | rank 4/298 | 0.9983 |
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