Does the signal have eightfold diffraction symmetry — the signature of Ammann-Beenker quasicrystals?
Uses the same spectral self-similarity machinery as Penrose but tests for the silver ratio (1 + sqrt(2) = 2.414...) instead of the golden ratio. Ammann-Beenker tilings fill the plane with squares and 45-degree rhombi, creating 8-fold rotational symmetry that is forbidden in periodic crystals.
Geometric mean of spectral self-coherence at Pell convergent ratios (2/1, 5/2, 12/5, 29/12) of the silver ratio. Tests whether the power spectrum repeats under scaling by the continued-fraction approximants of 1+sqrt(2). Evolved via ShinkaEvolve.
Coherence cascade shape across convergent scales with quadratic log-log detrending. Returns mean - std + 0.2*slope of coherences. The quadratic detrending (vs linear or moving-average) is key: it removes the spectral slope better, letting ratio-scale correlations emerge. IQR=0.615 — strong source discrimination, from Lorenz (0.95) to noise (~0). Evolved via ShinkaEvolve atlas v1.
| Source | Domain | Value |
|---|---|---|
| Ambient Microseism | geophysics | 0.9481 |
| Ocean Swell | geophysics | 0.9406 |
| Sprott-B | chaos | 0.9325 |
| ··· | ||
| Logistic r=3.5 (Period-4) | chaos | -0.2021 |
| De Bruijn Sequence | number_theory | -0.1752 |
| L-System (Dragon Curve) | exotic | -0.1716 |
| Source | Domain | Value |
|---|---|---|
| fBm (Persistent) | noise | 0.9990 |
| OTOC Growth | quantum | 0.9928 |
| Perlin Noise | noise | 0.9370 |
| ··· | ||
| Critical Circle Map (Bronze Mean) | chaos | 0.0000 |
| Critical Circle Map | chaos | 0.0000 |
| Circle Map Quasiperiodic | chaos | 0.0000 |
Ammann-Beenker complements Penrose: where Penrose tests for golden-ratio (phi) self-similarity, AB tests for silver-ratio (1+sqrt(2)) self-similarity. The convergent_profile metric provides genuine atlas discrimination (IQR=0.615), separating signals by how self-similar their detrended spectra are under Pell-convergent scaling. Sources with smooth spectral structure (Lorenz, Sine, Van der Pol) score high; white noise and chaos score near zero. The silver ratio's continued fraction [2; 2,2,2,...] means all convergents are ratios of Pell numbers — an algebraic constraint that only true octagonal QC structure would satisfy at all scales simultaneously.