De Bruijn Sequence
number_theory · 36 views
number_theory
What It Is
B(4,4) De Bruijn cycle --- every 4-symbol window over alphabet 0-3 appears exactly once
Interpretation
Standard analysis sees: rich, high-entropy values; stationary. The atlas additionally detects combinatorially flat (normal-sequence). It sits beside Gray Code Counter in the atlas (standard-bank rank 52) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.24
asymmetry0.42
occupancy0.99
short-range corr0.45
long-range memory0.54
spectral colour0.27
periodicity0.68
complexity0.75
time-irreversibility0.57
volatility clustering0.27
multifractality0.51
dimensionality0.78
nonstationarity0.00
What the atlas adds
combinatorially flat (normal-sequence)+5.2z
every fixed-length block is near-equiprobable and longer context yields no extra predictability — the De Bruijn / normal-number signature (distinct from random noise, which sits mid-scale)
names deterministic flatness — IID noise sits neutral, NOT at this poleAtlas-extreme metrics the standard bank can’t predict for this source
Multi-Scale Wasserstein:w_slope | +8.1z | bank-miss 1.9σ |
Penrose (Quasicrystal):phi_tower | -5.5z | bank-miss 1.6σ |
Hölder Regularity:hurst_exponent | -5.1z | bank-miss 3.0σ |
Fisher Information:velocity_spectral_gini | -4.2z | bank-miss 1.3σ |
Higher-Order Statistics:bicoherence_max | +2.2z | bank-miss 1.8σ |
Composition
dtypeuint8
range[0, 255]
unique values256 / 16384
mean ± std128 ± 73.9
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/De_Bruijn_Sequence.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/De_Bruijn_Sequence.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/De_Bruijn_Sequence.png)
Inflation (Substitution) > barcode
/d_curve/De_Bruijn_Sequence.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/De_Bruijn_Sequence.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/De_Bruijn_Sequence.png)
Ulam Spiral (Sacks) > default
/default/De_Bruijn_Sequence.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| LFSR (16-bit) | 5.14 | cross-domain |
| Gray Code Counter | 5.43 | cross-domain |
| Middle-Square (von Neumann) | 5.57 | cross-domain |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_profile | rank 297/298 | -0.1752 |
Cantor Set › Cantor Set:bit_plane_autocorrelation | rank 297/298 | 0.0001 |
Fisher Information › Fisher Information:effective_dimension | rank 2/298 | 16.0000 |
Fisher Information › Fisher Information:log_det_fisher | rank 297/298 | 44.3614 |
Fisher Information › Fisher Information:trace_fisher | rank 297/298 | 256.0000 |
Gottwald-Melbourne › Gottwald-Melbourne:k_variance | rank 4/298 | 0.7694 |
Higher-Order Statistics › Higher-Order Statistics:bicoherence_max | rank 1/298 | 1.0000 |
Modular Residue › Modular Residue:occupancy_entropy | rank 5/298 | 1.0000 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_slope | rank 1/298 | 6.3815 |
Penrose (Quasicrystal) › Penrose (Quasicrystal):phi_tower | rank 297/298 | -4.4473 |
Predictability › Predictability:excess_predictability | rank 1/298 | 3.0000 |
Predictability › Predictability:entropy_decay_rate | rank 298/298 | -0.3130 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 296/298 | 0.0013 |
Wasserstein › Wasserstein:entropy | rank 1/298 | 5.0000 |
Wasserstein › Wasserstein:dist_from_uniform | rank 297/298 | 0.0000 |
Wasserstein › Wasserstein:concentration | rank 298/298 | 1.0000 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficient | rank 295/298 | 0.0001 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):zipf_r_squared | rank 2/298 | 1.0000 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficient | rank 295/298 | 0.0000 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources