Does the signal have fivefold diffraction symmetry — the hallmark of Penrose quasicrystalline order?
Computes the power spectrum and autocorrelation, then tests whether their peak structure is invariant under scaling by the golden ratio (1.618...). True Penrose/Fibonacci quasicrystals have spectral peaks at positions related by powers of the golden ratio, creating self-similar diffraction patterns with discrete Bragg peaks — the defining property that separates quasicrystals from both periodic crystals and amorphous matter.
Autocorrelation self-similarity at golden-ratio-scaled lags. 1.0 means the autocorrelation pattern repeats at lags related by powers of phi. Circle Map QP, Phyllotaxis, and Fibonacci QC all score 1.0. Chaotic systems score 0.0 — no long-range autocorrelation structure, let alone ratio-scaled self-similarity.
Multi-scale weighted coherence of detrended spectral residuals under phi scaling, with phi-specificity gap (target R² minus best null-ratio R²), cross-scale stability, and residual fit quality. Rewards signals where the phi self-similarity model is both the best fit and a good fit. Produces wide source spread for atlas discrimination. Evolved via ShinkaEvolve atlas v1.
| Source | Domain | Value |
|---|---|---|
| Circle Map Quasiperiodic | chaos | 0.8800 |
| Phyllotaxis | bio | 0.8339 |
| Fibonacci Word | exotic | 0.8128 |
| ··· | ||
| Gray Code Counter | exotic | -6.8812 |
| De Bruijn Sequence | number_theory | -4.4473 |
| Earthquake Intervals | geophysics | -1.7460 |
| Source | Domain | Value |
|---|---|---|
| Phyllotaxis | bio | 1.0000 |
| Fibonacci Quasicrystal | number_theory | 1.0000 |
| Fibonacci Word | exotic | 1.0000 |
| ··· | ||
| Logistic Chaos | chaos | 0.0000 |
| Henon Map | chaos | 0.0000 |
| Tent Map | chaos | 0.0000 |
Penrose is the primary golden-ratio quasicrystal detector. The algebraic_tower metric provides atlas discrimination (score 0.924) while maintaining ratio specificity: the coherence gap penalizes signals that score equally well at non-phi ratios. Sources governed by the golden ratio (Fibonacci QC, phyllotaxis, critical circle map at golden-mean rotation) stand out on both metrics simultaneously.