Worlds at the Boundary.

A ring of 160 cells runs one elementary rule (the background), except for a thin wall of one to eight cells that runs a different rule. A short distance left of the wall is a 4-cell source block; right of it is a guarded window. After the world has settled, the source block is overwritten with a 4-cell pattern. The question is whether the change reaches the window.

Confirmed walls

Six of the strongest walls from the research sweep, ready to replay.

Score cards

How often the chosen signal gets through, how often a random pattern does, the selectivity J, and the best score of a world made of a single rule.

Pass rate of every pattern

A bar for each of the 16 possible 4-cell patterns: the fraction of 64 runs in which it changed the window. The dashed line is their mean, the random-pattern rate.

Four panels

01 the world left alone; 02 the same world with the pattern written; 03 where they disagree; 04 which rule each cell runs. The dashed line marks the moment of writing, the green box the source block and the orange column the guarded window.

Confirmation table

The selected wall retested on 256 fresh runs with its signal fixed in advance, on the original layout and four layouts the sweep never used.

Confirmed wall buttons

Load one of the confirmed walls.

Wall present while the world settles

Yes (as in the sweep) or No, where the wall only appears at the moment the pattern is written. Compare the two: this switch is the key to how the walls work.

Pattern bars

Select a pattern to watch it, and step through its 64 runs with Previous run / Next run.

Design your own wall

Pick the background rule, wall rule, wall width and position, the gap from source to wall, and the 4-cell signal. Your world is scored on the same 64 runs.

Copy share link

Save the current world and selection as a link.

Try this: load the first confirmed wall, watch the signal pattern pass, then select a pattern with a low bar and watch it stop. Then switch the wall to “added at the overwrite” and see the signal mostly stop too.

Mixed-rule cellular automata

A non-uniform cellular automaton lets different cells follow different rules. Here there are only two rules, and the interface between them is the object of study. Elementary rules often organize into regions (domains) separated by boundaries and defects that move through them; those moving defects can carry information, like signals in a wire.

The score, J

A wall that blocks everything is easy to make, and so is one that lets everything through; neither is interesting. The selectivity score is

J = P(signal reaches the window) − P(random pattern reaches the window)

Blocking everything gives J = 0, and so does passing everything. Some single-rule worlds are already a little selective, so each wall is also scored by its margin: its J minus the better J of the two worlds made entirely of its background rule or its wall rule. Only the margin counts as the wall’s own effect.

The search

The research sweep tried every ordered pair of the 256 rules at four wall widths: 262,144 worlds, 64 runs each. The 30 walls with the largest margins were then retested on 256 fresh runs each, with their signal fixed in advance, on four layouts the sweep never saw (a farther source, a longer settling time, a wider ring and a longer wait). The whole sweep was also rerun in mirror image, with the source on the right.

• Most walls do nothing selective. The best single-rule world scores 0.41, and 139 walls beat both of their single-rule worlds by at least 0.5.
• The best walls hold up. On fresh runs their margins were +0.55 to +0.77, and they held on all four new layouts. The mirror-image sweep agreed with the original about as well as the sweep agrees with itself (correlation 0.76 against 0.77), so the result isn’t an artifact of direction.
• The wall prepares the path. In backgrounds such as Rule 6, structures drift away from the wall, so a written pattern normally never reaches the window. With the wall present while the world settles, its activity leaves the background in front of it in a state where the chosen pattern launches a defect that travels to the wall and through it. Adding the wall only at the moment of writing cuts margins to +0.02 to +0.17.

What this means: the walls are not passive filters that check each pattern as it arrives. They shape their surroundings in advance so that one pattern, and mostly only that one, has a route through. That is closer to how a receptor and its environment work together than to a sieve.

• Protection is partial: about one random pattern in five still gets through the best walls.
• The detector asks only whether something changed in the window, not whether the far side could tell which pattern was sent.
• Noise is tested only as an overwrite of the same block at the same moment.
• Why these particular backgrounds work is not yet understood.
• Walls you design yourself are scored on the same 64 runs with no held-out test, so a high score there is exploratory.