Fibonacci Quasicrystal
number_theory · 36 views
number_theory
What It Is
1D Fibonacci quasicrystal --- aperiodic tiling with long-range order, discrete diffraction
Interpretation
Standard analysis sees: bounded / light-tailed; left-skewed; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); strongly periodic; homoskedastic; monofractal; low-dimensional; stationary. The atlas additionally detects quasicrystalline order. It sits beside Critical Circle Map (Bronze Mean) in the atlas (standard-bank rank 24) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.07
asymmetry0.10
occupancy0.39
short-range corr0.04
long-range memory0.02
spectral colour0.98
periodicity0.96
complexity0.42
time-irreversibility0.22
volatility clustering0.06
multifractality0.01
dimensionality0.04
nonstationarity0.05
What the atlas adds
quasicrystalline order+4.1z
aperiodic long-range order at incommensurate (golden-ratio / Fibonacci) spacing — structure repeats at irrational ratios, not a fixed period
Atlas-extreme metrics the standard bank can’t predict for this source
Moiré:moire_phi_response | +6.1z | bank-miss 2.4σ |
Dodecagonal (Stampfli):pisot_triplet_coherence | +5.8z | bank-miss 1.6σ |
S² × ℝ (Thurston):height_drift | -2.9z | bank-miss 1.5σ |
Sol (Thurston):sol_step_persistence | -2.0z | bank-miss 1.3σ |
Composition
dtypefloat64
range[-13.13, 164.1]
unique values16384 / 16384
mean ± std79.1 ± 48.1
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/Fibonacci_Quasicrystal.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Fibonacci_Quasicrystal.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Fibonacci_Quasicrystal.png)
Inflation (Substitution) > barcode
/d_curve/Fibonacci_Quasicrystal.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/Fibonacci_Quasicrystal.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/Fibonacci_Quasicrystal.png)
Ulam Spiral (Sacks) > default
/default/Fibonacci_Quasicrystal.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Uniform Chaos (Logistic Scramble) | 4.43 | cross-domain |
| Standard Map K=0.5 (Mixed) | 4.50 | cross-domain |
| Circle Map Quasiperiodic | 4.55 | cross-domain |
Which Geometries Light Up
Dodecagonal (Stampfli) › Dodecagonal (Stampfli):pisot_triplet_coherence | rank 1/298 | 0.7992 |
Moiré › Moiré:moire_phi_response | rank 3/298 | 0.3316 |
Nonstationarity › Nonstationarity:vol_of_vol | rank 295/298 | 0.2983 |
Penrose (Quasicrystal) › Penrose (Quasicrystal):phi_tower | rank 4/298 | 0.7785 |
Septagonal (Danzer) › Septagonal (Danzer):cubic_coherence | rank 294/298 | -0.1898 |
Septagonal (Danzer) › Septagonal (Danzer):z_primary | rank 294/298 | -0.3797 |
Spectral Analysis › Spectral Analysis:spectral_slope | rank 5/298 | 1.6698 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_drift | rank 295/298 | -0.5329 |
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