Does the signal have sevenfold diffraction symmetry — the rarest rotational order in known quasicrystals?
Tests spectral self-similarity at the septagonal ratio (approximately 2.247, which equals 1 + 2cos(2pi/7), the largest root of x^3 - 2*x^2 - x + 1). Sevenfold symmetry is crystallographically forbidden and extremely rare even among quasicrystals. The Danzer tiling is the canonical theoretical example.
Spectral self-similarity under septagonal-ratio scaling. DNA Centromere (0.371) scores highest, followed by Tohoku Aftershock (0.284) and LIGO Hanford (0.280). These are all broadband signals with complex spectral structure — the moderate scores likely reflect coincidental partial matches with the septagonal ratio rather than genuine 7-fold order. Divisor Count, Rossler, and constants score 0.0.
Autocorrelation self-similarity at septagonal-ratio lags. Accelerometer Jog (0.017) and Kicked Rotor (0.011) are the only sources with nonzero scores, both very weak. The atlas contains no source with genuine septagonal long-range order.
| Source | Domain | Value |
|---|---|---|
| Accel Jog | motion | 0.0170 |
| Kicked Rotor | quantum | 0.0105 |
| Speech "Nine" | speech | 0.0002 |
| ··· | ||
| Logistic Chaos | chaos | 0.0000 |
| Henon Map | chaos | 0.0000 |
| Tent Map | chaos | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| DNA Centromere | bio | 0.3713 |
| Tohoku Aftershock Intervals | geophysics | 0.2844 |
| LIGO Hanford | astro | 0.2803 |
| ··· | ||
| Divisor Count | number_theory | 0.0000 |
| Rossler Attractor | chaos | 0.0000 |
| Constant 0xFF | noise | 0.0000 |
Septagonal is the most exotic geometry in the quasicrystal lens. Its value is primarily theoretical — it would light up if a signal with genuine 7-fold quasicrystalline order were presented, but no such signal exists in the current atlas. The moderate sevenfold_symmetry scores in DNA Centromere and seismic/gravitational wave data are intriguing but not convincing: they lack corresponding long_range_order confirmation. A true septagonal quasicrystal would need both metrics to be high simultaneously, analogous to how Fibonacci QC scores 1.0 on both fivefold_symmetry and long_range_order for Penrose. Septagonal completes the quasicrystal lens's coverage of crystallographically forbidden symmetries (5, 7, 8, 10, 12-fold).