Phyllotaxis
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bio
What It Is
Golden-angle sunflower spiral --- successive seeds placed at 137.508° (= 360°/phi²), the most irrational angle. Quantized angular positions carry genuine quasicrystalline spectral structure with peaks at golden-ratio frequencies
Interpretation
Standard analysis sees: rich, high-entropy values; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); strongly periodic; time-irreversible (slow rise, sharp collapse); homoskedastic; monofractal; low-dimensional; stationary. The atlas additionally detects quasicrystalline order. It sits beside Critical Circle Map in the atlas (standard-bank rank 23) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.25
asymmetry0.44
occupancy0.99
short-range corr0.08
long-range memory0.07
spectral colour0.87
periodicity0.88
complexity0.20
time-irreversibility0.08
volatility clustering0.01
multifractality0.05
dimensionality0.08
nonstationarity0.05
What the atlas adds
quasicrystalline order+5.8z
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 | +6.7z | bank-miss 2.2σ |
Laplacian:laplacian_evolutionary_index | -3.3z | bank-miss 1.4σ |
D4 Triality:triplet_temporal | -2.8z | bank-miss 1.1σ |
Time Reversibility:increment_skewness_max | +2.3z | bank-miss 1.7σ |
Hodge–Laplacian:solenoidal_fraction | -2.1z | bank-miss 1.8σ |
Composition
dtypefloat64
range[8.762e-05, 6.283]
unique values16384 / 16384
mean ± std3.14 ± 1.81
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/Phyllotaxis.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Phyllotaxis.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Phyllotaxis.png)
Inflation (Substitution) > barcode
/d_curve/Phyllotaxis.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/Phyllotaxis.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/Phyllotaxis.png)
Ulam Spiral (Sacks) > default
/default/Phyllotaxis.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Circle Map Quasiperiodic | 2.21 | cross-domain |
| Critical Circle Map (Silver Mean) | 4.07 | cross-domain |
| Critical Circle Map (Bronze Mean) | 4.19 | cross-domain |
Which Geometries Light Up
Cayley › Cayley:local_linearity | rank 2/298 | 1.0000 |
Fisher Information › Fisher Information:effective_dimension | rank 4/298 | 16.0000 |
Fisher Information › Fisher Information:log_det_fisher | rank 295/298 | 44.3614 |
Fisher Information › Fisher Information:trace_fisher | rank 295/298 | 256.0002 |
Hodge–Laplacian › Hodge–Laplacian:solenoidal_fraction | rank 296/298 | 0.2384 |
Hodge–Laplacian › Hodge–Laplacian:curl_div_ratio | rank 297/298 | -1.2723 |
Inflation (Substitution) › Inflation (Substitution):acf_geometric | rank 4/298 | 0.8888 |
Laplacian › Laplacian:gradient_curvature_anticorrelation | rank 3/298 | 1.0000 |
Laplacian › Laplacian:curvature_autocorrelation | rank 294/298 | -0.3090 |
Laplacian › Laplacian:laplacian_evolutionary_index | rank 295/298 | -0.3090 |
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 297/298 | -0.5878 |
Modular Residue › Modular Residue:cycle_fraction | rank 2/298 | 1.0000 |
Modular Residue › Modular Residue:occupancy_entropy | rank 2/298 | 1.0000 |
Moiré › Moiré:moire_phi_response | rank 4/298 | 0.3242 |
Penrose (Quasicrystal) › Penrose (Quasicrystal):phi_tower | rank 3/298 | 0.8378 |
Septagonal (Danzer) › Septagonal (Danzer):cubic_coherence | rank 297/298 | -0.2615 |
Septagonal (Danzer) › Septagonal (Danzer):z_primary | rank 297/298 | -0.5526 |
Sol (Thurston) › Sol (Thurston):path_length | rank 296/298 | 8485.0615 |
Spectral Graph › Spectral Graph:weyl_exponent | rank 3/298 | 2.1521 |
Spherical S² › Spherical S²:hemisphere_balance | rank 5/298 | 0.9998 |
Wasserstein › Wasserstein:entropy | rank 4/298 | 5.0000 |
Wasserstein › Wasserstein:concentration | rank 296/298 | 1.0032 |
Wasserstein › Wasserstein:dist_from_uniform | rank 296/298 | 0.0000 |
p-Variation › p-Variation:volatility_clustering | rank 297/298 | -0.6180 |
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