This thread made me realize how nice it would be to have additional small stable glider-changing components, even if they are not perfect reflectors, as long as the reset steps don't result in glider loss (though admittedly, even this is no longer a problem since there are components that produce Herschels and excess gliders).

I went back and revisited the kinds of searches I did around 20 years ago, and I can't really claim progress, nor even a negative result, but I am closer to finally ruling out some simple ideas. What I thought I might be able to find is a small constellation of common objects that when hit by a glider, emits a new glider and creates another constellation that can be hit by a glider such that over a sequence of such interactions, you get the original constellation in the same place. Ideally, this would be without catalysts, because those permanently block diagonals.

While I don't have rigorous negative result, I am willing to conjecture that there are no new constellations like that fit in (hedging a bit) a 15x15 bounding box. Here is the only case I know that fits the above description, which I reported in 1994 and no longer recall how I found. It consists of 3 blocks in an 8x9 bounding box. Two are actually catalysts, but it can be considered a constellation that flips with glider collisions.

Code: Select all

```
x = 81, y = 80
2bo$obo$b2o67$72b2o5b2o$72b2o5b2o5$79b2o$79b2o$67b2o$66bobo$68bo!
```

It shifts gliders, which I thought might be useful in recirculating a glider-positive collision, but actually even this blocks a lot of diagonals.

I used a search method that I don't recall trying before.

(1) I began with millions of random starting seeds, generated them to find a stable ash with 20x20 bounding box constraints, normalized their orientation and phase (with blinkers), removed duplicates and obtained a list of 49905 "natural" stable and period-2 targets.

(2) Set up all glider collisions giving the glider 30 steps before hitting, which is usually enough to make it work coming from infinity.

(3) Tested these collisions for output gliders and non-zero stable ash fitting in a 20x20 bounding box.

(4) Collected the ash and dedupped again to use as another round of targets.

Repeat above until the set of targets is stable. There are some other things you can do to remove junk, such as taking the intersection of targets from current and some past round.

The point is that ultimately a target is

*only reusable if it consists of collision ash*. However, even these may be uninteresting as so many collisions produce ash that does not ultimately lead to a cycle.

In practice, the final set is winnowed down to the hundreds, and some other filters can be applied to check manually if there is something interesting.

I believe this method is good, because I was able to find both the stable shifter above and the

glider/biloaf collision without going out of my way to look for them (and I completely forgot about the biloaf). However, I did not come up with anything new.

The one improvement over 20 years is that I am pretty sure I completed a process in a few hours that would have taken a week of running batch jobs over night at that time. Perhaps the negative result can be confirmed more easily with modern tools.

I think there is still potential to get a reaction like this with some small, natural catalysts, let alone engineered and Bellman-derived catalysts. But unfortunately, the more helpers we add, the more diagonals we use up.

Some suggestive but ultimately useless reactions came up, such as this one:

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```
x = 12, y = 10, rule = B3/S23
2bo$obo$b2o6b3o4$6b2o$5bo2bo$6bobo$7bo!
```

It actually had a traffic light and excess beehive that I removed after inspection. One thing that is easy to filter for, but too restrictive, is collisions such that the target and ash have the same number of cells. There could be a multicycle component that varies in cell count (but as I said, I am pretty sure there is not, at least in a 15x15 box).

There were lots of collisions that produce multiple excess gliders and spaceships. Too many to try to count. Maybe these could be refactored into glider-producing collisions if the targets can be reset leaving a net positive.