Whether nearby values cooperate or compete.
Treats each window of your data as a miniature spin glass — a system where local constraints may be impossible to satisfy simultaneously. Fits the maximum-entropy pairwise interaction model and extracts three properties of the resulting energy landscape.
How strongly do positions in a window constrain each other? Monotonic signals have extreme coupling (each value predicts the next). Noise has near-zero coupling. Periodic orbits of the logistic map dominate the atlas: the period-3 window (r=3.83) scores 15.3, while white noise scores 0.01.
What fraction of local constraints are mutually contradictory? Three positions A, B, C are frustrated when A wants B up, B wants C up, but A wants C down — they can't all be satisfied. The Fibonacci word scores 1.0 (maximally frustrated): the golden ratio creates irreconcilable correlations at every scale. Pink noise scores 0.0 (all correlations agree). White noise scores ~0.5 (random constraints, half frustrated by chance). Quantum walk probability amplitudes also hit 1.0 — a different mechanism (interference) producing the same geometric signature.
How degenerate is the coupling spectrum? Near 0 means one dominant interaction mode (hierarchical structure). Near 1 means all modes are equally important. L-System (Dragon Curve) and Rule 110 score ~1.0; logistic period-4 scores 0.14.
How strongly does the nearest-neighbor coupling dominate over longer-range interactions? EEG Seizure (3.80), Ocean Swell (3.79), and Mackey-Glass (3.78) score highest — their smooth, locally correlated dynamics concentrate coupling at the nearest lag. Forest fire and constants score 0.0 (no dominant coupling distance). Evolved via ShinkaEvolve.
How much does the coupling matrix change between the first and second halves of the signal? Devil's Staircase (2.0) and Middle-Square (1.86) score highest — their dynamics shift character midstream, producing different interaction structures in each half. Sine wave scores near 0.0 (stable coupling throughout). This is a direct stationarity test on the Ising model's interaction structure. Evolved via ShinkaEvolve.
| Source | Domain | Value |
|---|---|---|
| Logistic r=3.83 (Period-3 Window) | chaos | 15.2634 |
| Logistic r=3.74 (Period-5 Window) | chaos | 14.6394 |
| Logistic Edge-of-Chaos | chaos | 12.4844 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Forest Fire | exotic | 0.0000 |
| Rule 30 | exotic | 0.0056 |
| Source | Domain | Value |
|---|---|---|
| Devil's Staircase | exotic | 2.0000 |
| Middle-Square (von Neumann) | binary | 1.8625 |
| Rule 30 | exotic | 1.5955 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Forest Fire | exotic | 0.0000 |
| Logistic r=3.5 (Period-4) | chaos | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Quantum Walk | quantum | 1.0000 |
| Fibonacci Word | exotic | 1.0000 |
| Blue Noise | noise | 0.9871 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Pink Noise | noise | 0.0000 |
| fBm (Persistent) | noise | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| EEG Seizure | medical | 3.7916 |
| Earthquake P-wave | geophysics | 3.7898 |
| Ocean Swell | geophysics | 3.7828 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Forest Fire | exotic | 0.0000 |
| L-System (Dragon Curve) | exotic | 0.0002 |
| Source | Domain | Value |
|---|---|---|
| Constant 0x00 | noise | 1.0000 |
| Forest Fire | exotic | 1.0000 |
| L-System (Dragon Curve) | exotic | 0.9998 |
| ··· | ||
| Logistic r=3.5 (Period-4) | chaos | 0.1429 |
| Logistic Edge-of-Chaos | chaos | 0.1429 |
| Logistic r=3.2 (Period-2) | chaos | 0.1429 |
Boltzmann frustration is the framework's most specific quasicrystal detector. In the atlas, Fibonacci word is the only non-quantum source to achieve frustration = 1.0. The metric is encoding-invariant: it depends only on which positions are above or below the median, not on the byte values themselves.