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.
Spectral self-similarity under silver-ratio scaling. Unlike Penrose, no source in the atlas achieves a perfect score. DNA Centromere leads at 0.285: repetitive genomic elements may produce weak silver-ratio correlations. LIGO Hanford (0.216) and Logistic Chaos (0.210) score modestly — these are likely coincidental partial matches rather than genuine octagonal order. The absence of strong detections is itself informative: no 1D source in the atlas has true eightfold quasicrystalline structure.
Autocorrelation self-similarity at silver-ratio lags. Scores are near zero across the entire atlas. Kuramoto (0.005) is the highest — its coupled oscillator dynamics produce weak ratio-scaled correlations. This confirms that silver-ratio long-range order is genuinely rare in 1D signals.
| Source | Domain | Value |
|---|---|---|
| DNA Centromere | bio | 0.2848 |
| LIGO Hanford | astro | 0.2163 |
| Logistic Chaos | chaos | 0.2103 |
| ··· | ||
| Rossler Attractor | chaos | 0.0000 |
| fBm (Antipersistent) | noise | 0.0000 |
| Constant 0xFF | noise | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Kuramoto Oscillators | exotic | 0.0046 |
| Chirikov Standard Map | chaos | 0.0006 |
| Solar Wind IMF | astro | 0.0000 |
| ··· | ||
| Logistic Chaos | chaos | 0.0000 |
| Henon Map | chaos | 0.0000 |
| Tent Map | chaos | 0.0000 |
Ammann-Beenker serves as a null control within the quasicrystal lens. Its consistently near-zero scores across the atlas validate that the detection machinery is specific: the same algorithm that produces 1.0 for golden-ratio sources on Penrose produces near-zero for silver-ratio sources on Ammann-Beenker, confirming that the Penrose detections are ratio-specific rather than artifacts of the spectral analysis method. If a source ever does score highly on eightfold_symmetry, it would genuinely deserve investigation as a silver-ratio quasicrystal.