Golden Ratio Digits
number_theory · 36 views
number_theory
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); high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.23
asymmetry0.33
occupancy0.98
short-range corr0.35
long-range memory0.25
spectral colour0.69
periodicity0.03
complexity0.95
time-irreversibility0.37
volatility clustering0.15
multifractality0.19
dimensionality0.95
nonstationarity0.20
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 > 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 | 1.74 | |
| ChaCha20 | 1.75 | cross-domain |
| AES Encrypted | 1.77 | cross-domain |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:filling_ratio | rank 5/298 | 0.9823 |
D4 Triality › D4 Triality:gram_consistency | rank 3/298 | 2.4969 |
D4 Triality › D4 Triality:spectral_transition | rank 4/298 | 0.2480 |
Mostow Rigidity › Mostow Rigidity:volume_rigidity | rank 3/298 | 0.9685 |
Spectral Analysis › Spectral Analysis:phase_coherence | rank 295/298 | 0.0005 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources