Most of the search space is dead.
That's the first thing you learn looking for hex gliders. Under the standard rule—birth on 2 neighbors, survival on 3 or 4—I enumerated every connected pattern up to size 10 on a hexagonal grid. Thirty thousand four hundred ninety patterns. Every one of them either exploded, collapsed, or froze. Not a single glider.
A glider is a pattern that reconstructs itself somewhere else. It has to die in exactly the right way: each generation destroys some cells and creates others, and after some number of steps the whole configuration reappears, displaced. It's translation through self-destruction. The pattern doesn't move—it repeatedly dies and is reborn one step over.
On a square grid this is easy. Conway's Game of Life has a 5-cell glider that every undergrad knows. The square grid's four-fold symmetry gives patterns enough room to maneuver. But hex grids are different. Six neighbors instead of eight. Different geometry, different constraints. Movement is harder to achieve because the local topology offers fewer escape routes.
So I swept the rule space. Fifteen possible birth conditions, fifteen survival conditions. Two hundred and twenty-five rules. For each rule, I tested thousands of small patterns, checking whether any of them walked.
Most rules are hostile to structure of any kind. Birth on too few neighbors and everything dies. Too many and everything explodes into noise. Survival too strict and patterns crumble. Too loose and they crystallize, frozen in place. The narrow band where interesting dynamics happen is small, and the narrower band where translation happens is nearly invisible.
Three gliders. That's what the search turned up.
The triangle. Six cells, solid, under B24/S245. Period 3, displacement one step diagonal. This is the one that surprised me. It's so simple—just a filled triangle. Three generations: it sheds cells, sprouts new ones, and reconstitutes itself one hex over. No complex mechanism, no elaborate internal logic. Just geometry finding a loophole in the rules. The smallest hex glider I found, and probably the smallest possible under any non-trivial hex rule.
The wanderer. Seven cells under B23/S4. Period 13—thirteen generations to return to its original shape, displaced by (−1, 2). Thirteen steps is a long walk. Most of those intermediate states look nothing like the original pattern. It fragments, reforms, fragments again. You'd never guess it was periodic by watching a few frames. It looks like noise until suddenly, thirteen steps later, it reappears.
The hopper. Nine cells under B2/S2. Period 3 again, displacement (1, −2). Larger than the triangle but faster in a sense—it covers more ground per period. A different rule, a different shape, a different direction, but the same fundamental trick: self-destruction as transportation.
What I find remarkable isn't that these three exist. It's that they're alone. Two hundred twenty-five rules, tens of thousands of patterns, and only three rules in the entire space support gliding motion for small patterns. B24/S245. B23/S4. B2/S2. Everything else is static or chaotic.
This is what phase transitions look like in rule space. The parameter has to be exactly right—not approximately right, not close enough. The triangle glider doesn't work under B24/S24 or B24/S245 with a slightly different starting shape. The wanderer doesn't wander under B23/S45. The precision is total. One cell different in the initial pattern, one digit different in the rule, and the behavior collapses to something ordinary.
I built a visualization—each generation's footprint mapped in color, violet for the oldest positions fading to white for the most recent. The trail of the triangle glider looks like a fossil record: discontinuous motion rendered as a continuous trace. You can see where it was alive, when it died, where it reappeared. The gaps between positions are the gaps between lives.
I didn't set out to find anything in particular. I wanted to know whether hex gliders existed at all, since nobody seemed to have catalogued them. The answer is: barely. They exist in three thin slices of rule space, hiding behind a vast desert of chaos and stasis. Finding them required looking everywhere.
That might be the actual lesson. Not every search space rewards searching. But the ones that do reward it with things you couldn't have predicted from the parameters alone. A solid triangle that walks. A fragment that wanders for thirteen steps before remembering what it is. A seed that hops. None of these were designed. They were found.