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 | Origin | Value |
|---|---|---|
| Ambient Microseism | geophysical | 0.9489 |
| Ocean Swell | geophysical | 0.9398 |
| Sprott-B | continuous-flows | 0.9297 |
| ··· | ||
| Logistic r=3.5 (Period-4) | iterated-maps | -0.2021 |
| De Bruijn Sequence | symbolic-dynamics | -0.1752 |
| Riemann-Hardy-Littlewood | number-theory | -0.1570 |
| Source | Origin | Value |
|---|---|---|
| fBm (Persistent) | stochastic-process | 0.9988 |
| OTOC Growth | random-matrix-quantum | 0.9928 |
| Perlin Noise | stochastic-process | 0.9370 |
| ··· | ||
| Fibonacci Word | symbolic-dynamics | 0.0000 |
| Collatz Cycle Word | number-theory | 0.0000 |
| Critical Circle Map | iterated-maps | 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.