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.
| Source | Domain | Value |
|---|---|---|
| Logistic r=3.83 (Period-3 Window) | chaos | 15.2634 |
| Logistic r=3.74 (Period-5 Window) | chaos | 14.6394 |
| Logistic r=3.2 (Period-2) | chaos | 12.4844 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Forest Fire | exotic | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Quantum Walk | quantum | 1.0000 |
| Fibonacci Word | exotic | 1.0000 |
| Blue Noise | noise | 0.9857 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Pink Noise | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Forest Fire | exotic | 1.0000 |
| L-System (Dragon Curve) | exotic | 0.9998 |
| Rule 110 | exotic | 0.9952 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Logistic r=3.5 (Period-4) | 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.