How compressible is the signal — a direct proxy for algorithmic randomness.
The geometry once carried Shannon block entropies and mutual-information channels at multiple lags. Those were pruned (|r| > 0.9 with ordinal/spectral metrics) and the geometry now ships a single workhorse: Lempel-Ziv compression ratio. Entropy and mutual-information signals continue to live in OrdinalPartition, Predictability, and SpectralAnalysis.
Lempel-Ziv compression ratio: compressed_size / original_size. 1.0 means incompressible (Wichmann-Hill, MINSTD, XorShift32 — good PRNGs are incompressible). 0.0 means trivially compressible (constants). Logistic period-2 scores 0.002 (alternating between two values compresses almost completely). This is a direct proxy for Kolmogorov complexity.
| Source | Origin | Value |
|---|---|---|
| Bzip2 (level 9) | algorithmic-bytes | 1.0000 |
| AES Encrypted | algorithmic-bytes | 1.0000 |
| e Digits | number-theory | 1.0000 |
| ··· | ||
| Logistic r=3.2 (Period-2) | iterated-maps | 0.0022 |
| Square Wave | signal-synthesis | 0.0023 |
| Periodic Word | symbolic-dynamics | 0.0024 |
Compression ratio alone separates PRNGs and crypto (incompressible, ~1.0) from every other class of signal in the atlas. In the distributional view it anchors the noise/structure axis: anything that lands near 1.0 has no exploitable redundancy at the byte level, regardless of what shape its dynamics take.