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.
How well the spectral peak structure conforms to the Pell number sequence (1, 2, 5, 12, 29, ...), the convergents of the silver ratio's continued fraction. Evolved via ShinkaEvolve. Not yet in the atlas.
Degree of 8-fold rotational symmetry in the spectral autocorrelation structure. Not yet in the atlas.
Sharpness of spectral peaks at silver-ratio-scaled positions, using prominence-based detection with null-ratio controls. Not yet in the atlas.
| Source | Domain | Value |
|---|---|---|
| Ambient Microseism | geophysics | 0.9434 |
| Deep Earthquake P-wave | geophysics | 0.9329 |
| Lorenz Attractor | chaos | 0.9301 |
| ··· | ||
| Logistic Edge-of-Chaos | chaos | -0.2866 |
| Logistic r=3.5 (Period-4) | chaos | -0.2021 |
| fBm (Antipersistent) | noise | -0.1818 |
| Source | Domain | Value |
|---|---|---|
| fBm (Antipersistent) | noise | 0.9088 |
| Perlin Noise | noise | 0.8951 |
| Chua's Circuit | exotic | 0.8036 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Critical Circle Map | chaos | 0.0000 |
| Fibonacci Word | exotic | 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.