COMPUTATIONAL WORLDS / EXPERIMENT 03
Worlds at the Boundary.
A thin wall of a second rule.
One pattern gets through. Most do not.
The question.
A ring of cells runs one elementary rule, except for a wall of one to eight cells that runs another. A 4-cell block to the left of the wall is overwritten with one of 16 patterns, and we watch whether anything changes in a guarded window to the right of it. Can a wall let one chosen pattern through while stopping random patterns of the same size?
Why the score matters.
Blocking everything is easy, and so is letting everything through. The score, J, is how often the chosen signal gets through minus how often a random pattern does. A wall that blocks everything scores 0, and so does one that passes everything. Each wall is also compared with worlds made entirely of either of its two rules; it counts only by its margin over the better of them.
Loading the sweep results…
What the sweep found.
We ran every pair of the 256 rules at four wall widths: 262,144 worlds, 64 runs each. Most walls do nothing selective. The best world made of a single rule scores 0.41, so some selectivity needs no wall at all. 139 walls beat both of their single-rule worlds by at least 0.5.
The 30 walls with the largest margins were tested again on 256 fresh runs each, with their signal fixed in advance. Their margins were +0.55 to +0.77, and they held on four layouts the sweep never saw: a farther source, a longer settling time, a wider ring and a longer wait. Rerunning the whole sweep in mirror image, with the source on the right, reproduced it as closely as the sweep agrees with itself (correlation 0.76 against 0.77).
How the walls work.
The strongest walls sit in a handful of backgrounds, such as Rule 6, where structures drift away from the wall. On its own, a written pattern drifts away too and never reaches the window. With the wall in place, the chosen pattern instead launches a defect that travels toward the wall, and the wall passes its arrival on into the window. In some worlds the change spreads widely on the far side; in others it barely crosses, which is still enough to count.
The difference comes from the settling period. While the world forms, the wall's activity washes over the background in front of it and leaves it in a state that carries the signal. Switching the wall on only when the pattern is written removes most of the effect: margins fall to +0.02 to +0.17. The wall is not a passive filter. It prepares the path its signal travels.
What this does not show.
Protection is partial: about one random pattern in five still gets through. The detector only asks whether something changed, not whether the far side can tell which pattern was sent. Noise is tested only as an overwrite of the same block at the same moment. We do not yet know why these particular backgrounds work.
Where this sits.
Cellular automata that mix rules have been studied for decades, as have the domains, defects and gliders that move through them. A focused search found no study of rule interfaces as selective filters, but it was not a full literature review. This is an exploratory Mind37 result, reproducible from our research code.