Copeland-Erdős
number-theory · 37 views
number-theoryhigh-entropy
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: time-irreversible (slow rise, sharp collapse); homoskedastic. The atlas additionally detects Time Reversibility:ordinal_reversal_distance.
What standard analysis sees
tail heaviness0.17
asymmetry0.71
occupancy0.43
short-range corr0.19
long-range memory0.58
spectral colour0.56
periodicity0.73
complexity0.39
time-irreversibility0.14
volatility clustering0.09
multifractality0.57
dimensionality0.50
nonstationarity0.67
What the atlas adds
Time Reversibility:ordinal_reversal_distance+2.4z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Predictability:entropy_decay_rate | -5.3z | bank-miss 2.7σ |
Nonstationarity:variance_trend | +3.3z | bank-miss 1.5σ |
Wasserstein:distributional_stationarity | -2.7z | bank-miss 2.0σ |
Nonstationarity:ac1_trend | -2.6z | bank-miss 2.0σ |
Ulam Spiral (Square):polynomial_concentration | +2.1z | bank-miss 1.6σ |
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 > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Copeland-Erdős.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Copeland-Erdős.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Copeland-Erdős.png)
Inflation (Substitution) > barcode
/d_curve/Copeland-Erdős.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/Copeland-Erdős.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/Copeland-Erdős.png)
Ulam Spiral (Sacks) > default
/default/Copeland-Erdős.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Champernowne | 4.82 | |
| Middle-Square (von Neumann) | 4.86 | cross-origin |
| Linux ELF x86-64 | 4.89 | cross-origin |
Which Geometries Light Up
2-adic › 2-adic:distance_entropy | rank 2/306 | 2.3325 |
AutoRegressive › AutoRegressive:ar_coef_2 | rank 5/306 | 0.4904 |
Catch24 › Catch24:DN_HistogramMode_10 | rank 304/306 | -1.1043 |
Julia Set › Julia Set:potential_variance | rank 303/306 | 1255.1082 |
Julia Set › Julia Set:potential_smoothness | rank 304/306 | 28.1751 |
Nonstationarity › Nonstationarity:regime_persistence | rank 2/306 | 0.9967 |
Nonstationarity › Nonstationarity:variance_trend | rank 4/306 | 0.3541 |
Nonstationarity › Nonstationarity:ac1_trend | rank 303/306 | -0.1822 |
Ordinal Partition › Ordinal Partition:memory_order | rank 4/306 | 0.8273 |
Predictability › Predictability:entropy_decay_rate | rank 305/306 | -0.3053 |
Spectral Analysis › Spectral Analysis:spectral_bandwidth | rank 5/306 | 0.1921 |
Spirograph › Spirograph:rational_grid_proximity | rank 304/306 | 0.4593 |
WaveformAsymmetry › WaveformAsymmetry:waveform_asymmetry | rank 5/306 | 0.8883 |
Wavelet Cascade › Wavelet Cascade:coarse_scale_kurtosis_slope | rank 4/306 | 0.7671 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):hapax_ratio | rank 2/306 | 0.9117 |
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