Copeland-Erdős

number_theory · 36 views

number_theory

What It Is

Provably normal number formed by concatenating primes in base 256 (Copeland-Erdős 1946). Same headline normality as Champernowne but driven by the prime sequence rather than the natural numbers --- bridges Champernowne's structured-byte-stream class into the prime-density-flavored corner of the atlas

Interpretation

Standard analysis sees: no strongly notable standard properties. The atlas additionally detects combinatorially flat (normal-sequence). It sits beside Windows PE x86-64 in the atlas (standard-bank rank 35) — a neighbor conventional features miss.

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 pole

Atlas-extreme metrics the standard bank can’t predict for this source

`Nonstationarity:variance_trend`	+3.4z	bank-miss 1.7σ
`Nonstationarity:ac1_trend`	-3.2z	bank-miss 1.8σ
`Ulam Spiral (Square):radial_periodicity`	+3.2z	bank-miss 1.0σ
`Wasserstein:self_similarity`	-3.1z	bank-miss 2.8σ
`Ulam Spiral (Square):polynomial_concentration`	+2.2z	bank-miss 2.2σ

Composition

dtypeuint8

range[0, 255]

unique values256 / 16384

mean ± std90.6 ± 85

Render Gallery

Native > phase_plotraw

Native > timeseriesraw

Native > triple_latticeraw

Boltzmann > lag_map

Boltzmann > spin_grid

Cayley > default

Chladni > plate_bottom

Chladni > plate_top

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

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

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

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Nearest neighbor	Distance
Champernowne	4.89
Middle-Square (von Neumann)	5.25	cross-domain
Linux ELF x86-64	5.26	cross-domain

Open in Atlas →

Which Geometries Light Up

2-adic › `2-adic:distance_entropy`	rank 2/298	2.3571
AutoRegressive › `AutoRegressive:ar_coef_2`	rank 5/298	0.4407
Catch24 › `Catch24:DN_HistogramMode_5`	rank 294/298	-0.9268
Catch24 › `Catch24:DN_HistogramMode_10`	rank 296/298	-1.0831
D4 Triality › `D4 Triality:triplet_temporal`	rank 5/298	0.4237
Julia Set › `Julia Set:potential_smoothness`	rank 295/298	28.8476
Julia Set › `Julia Set:potential_variance`	rank 295/298	1169.8436
Nonstationarity › `Nonstationarity:regime_persistence`	rank 3/298	0.9987
Nonstationarity › `Nonstationarity:variance_trend`	rank 5/298	0.4004
Nonstationarity › `Nonstationarity:ac1_trend`	rank 295/298	-0.2410
Predictability › `Predictability:entropy_decay_rate`	rank 297/298	-0.3095
Spectral Analysis › `Spectral Analysis:spectral_bandwidth`	rank 4/298	0.1862
Spirograph › `Spirograph:gear_rationality`	rank 295/298	0.4692
Wasserstein › `Wasserstein:self_similarity`	rank 296/298	0.8219
WaveformAsymmetry › `WaveformAsymmetry:waveform_asymmetry`	rank 4/298	0.8883
Wavelet Cascade › `Wavelet Cascade:intermittency_slope`	rank 3/298	0.8297
Zipf–Mandelbrot (16-bit) › `Zipf–Mandelbrot (16-bit):hapax_ratio`	rank 2/298	0.9158

← Continued Fractionsin number_theoryDe Bruijn Sequence →

← Continued FractionsalphabeticalCoupled Map Lattice →

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