Golden Ratio Digits
number-theory · 37 views
number-theoryhigh-entropy
What It Is
Base-256 digits of φ = (1+√5)/2's fractional part. Algebraic of degree 2 (root of x²−x−1); normality unknown. Contrast vs Pi/e/ln2 tests the transcendental-vs-algebraic split.
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); monofractal; high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.23
asymmetry0.34
occupancy0.97
short-range corr0.37
long-range memory0.36
spectral colour0.66
periodicity0.02
complexity0.99
time-irreversibility0.32
volatility clustering0.28
multifractality0.13
dimensionality0.95
nonstationarity0.21
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
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 > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Golden_Ratio_Digits.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Golden_Ratio_Digits.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Golden_Ratio_Digits.png)
Inflation (Substitution) > barcode
/d_curve/Golden_Ratio_Digits.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/Golden_Ratio_Digits.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/Golden_Ratio_Digits.png)
Ulam Spiral (Sacks) > default
/default/Golden_Ratio_Digits.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Catalan G Digits | 1.69 | |
| ChaCha20 | 1.75 | cross-origin |
| Euler-Mascheroni γ Digits | 1.81 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:filling_ratio | rank 5/306 | 0.9823 |
D4 Triality › D4 Triality:gram_consistency | rank 3/306 | 2.4969 |
Moiré › Moiré:moire_max_coherence | rank 302/306 | 0.0229 |
Mostow Rigidity › Mostow Rigidity:volume_sum_jitter_stability | rank 2/306 | 0.9685 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 304/306 | 0.0005 |
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