What compression sees
Three ways a computer can look for "interesting" in 256 tiny universes, and how each one gets fooled.
An elementary cellular automaton is a row of cells, each 0 or 1. Every step, each cell looks at itself and its two neighbours and follows a fixed table of 8 entries. There are 256 such tables. Folding together mirror images and colour swaps leaves 88 distinct worlds. Some die, some repeat, some look like static, and one (Rule 110) can compute anything a computer can.
Can a dumb measurement find that one without being told? I tried three:
| Metric | Idea | Rewards | Fooled by |
|---|---|---|---|
| v1 randomness | how badly zlib compresses it | chaos | Rule 110 only ranks 14th |
| v2 calming | how much more compressible it gets over time | gliders that annihilate | Rule 54, whose gliders never die |
| v3 structured defects | subtract the background, check that what's left has shape | both 110 and 54 | chaos with nested triangles |
Ranks are out of 88 (1 = most interesting according to that metric). Are they luck? The scores average only a few
random starts, so I re-ran two of them on five fresh batches of starts (cycle 83, robustness.py): Rule 110
came 14th by randomness and 1st by transients every single time. Each picture starts
from random cells at the top and runs downward. Every page load gives a fresh random start.
Try any rule
Lesson. Each metric got fooled differently, and tuning a fourth one until it picks the rules I already know are interesting would just be curve-fitting. "Interesting" seems to mean structure that persists and interacts, and no single compression number captures all of that.