Does the signal have twelvefold diffraction symmetry — the signature of square-triangle Stampfli tilings?
Tests for spectral self-similarity at the dodecagonal ratio (2 + sqrt(3) = 3.732...) and also checks sqrt(3) scaling, which relates to the triangle height in square-triangle tilings. Dodecagonal quasicrystals (found in Ta-Te and V-Ni-Si alloys) have the highest rotational symmetry known in real quasicrystals.
Phase-aware spectral self-coherence at the dodecagonal ratio (2 + sqrt(3) ~ 3.732). Tests whether complex spectral structure (not just power) repeats under scaling by the inflation factor of square-triangle Stampfli tilings.
Spectral self-coherence at sqrt(3) scaling, corresponding to the triangle height/base ratio in the tiling. EEG signals show moderate scores — brain oscillation bands have frequency ratios near sqrt(3) between adjacent bands (theta/alpha/beta).
Combined coherence across the three Pisot-Vijayaraghavan numbers associated with 12-fold symmetry. Wave Height (0.82) and Fibonacci QC (0.80) score highest. fBm and logistic periodic orbits score 0.0. The PV numbers for dodecagonal tilings form an algebraic triplet whose simultaneous spectral presence is a stronger test than any single ratio.
| Source | Domain | Value |
|---|---|---|
| Solar Wind Speed | astro | 1.0000 |
| Sunspot Number | astro | 1.0000 |
| EEG Eyes Open | medical | 1.0000 |
| ··· | ||
| Logistic r=3.5 (Period-4) | chaos | -0.0000 |
| Constant 0xFF | noise | 0.0000 |
| Logistic r=3.2 (Period-2) | chaos | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Wave Height (Buoy) | geophysics | 0.8180 |
| Fibonacci Quasicrystal | number_theory | 0.7990 |
| Devil's Staircase | exotic | 0.7593 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| fBm (Antipersistent) | noise | 0.0000 |
| fBm (Persistent) | noise | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Solar Wind IMF | astro | 1.0000 |
| Solar Wind Speed | astro | 1.0000 |
| Sunspot Number | astro | 1.0000 |
| ··· | ||
| Logistic r=3.5 (Period-4) | chaos | -0.0000 |
| Constant 0xFF | noise | 0.0000 |
| Logistic r=3.2 (Period-2) | chaos | 0.0000 |
Dodecagonal tests for the highest rotational symmetry known in real quasicrystals (12-fold, found in Ta-Te and V-Ni-Si alloys). The sqrt(3) coherence in EEG signals is an interesting cross-domain finding, though likely reflects harmonic relationships in neural oscillation bands rather than genuine dodecagonal order.