toroidalet wrote: ↑September 14th, 2023, 3:33 am

By the way, I think it's very unlikely that a rule without any <4-cell objects would have adjustable things (except maybe guns). In order to make an adjustable thing, we would need to have at least two separate components. These must both consist of two cells (if one were 3, the other would be 1, implying the dot was a still life), and the only ways for a two-cell pattern to expand without S0 involve B2a (duoplet, domino, 2k-dots and hollow blinker/2i-dots). All of those except the hollow blinker are out for producing oscillators or spaceships. Since it is a high-period oscillators or counter in many B2a rules, there might be some way to put two hollow blinkers in the plane to make an adjustable oscillator, which would be quite impressive in and of itself.

I'm not good with B2a rules, so here's my answer in the non-relativistic realm:

If you include my restriction that there should be no other objects with minpop < 4, your 4-cell adjustable osc challenge is impossible.

I have worked out the possible transitions, and concluded that in a rule where no minpop <4 objects exist, B2e and S1c must coexist, B2c implies B2i (but B2i can exist without B2c), and S0 and S1e are impossible as they imply the dot and domino still-lifes, respectively. Taking 3-cell objects into account is far too difficult.

All sequences starting with 2 cells using the constraints above will die or form these objects:

Code: Select all

```
x = 1, y = 1, rule = B2ci3i/S
obo!
```

If this is what you mean by 4-cell adjustable things, then this is my answer. If you mean >4-cell adjustable things, this is getting less into the realm of rulegolfing and more into the realm of engineering. But I digress.

Here's my result:

**13** oscillators (p1, p2, p4, p6, p10)

Code: Select all

```
x = 22, y = 35, rule = B2-an3ceqry4c5a/S1c2-en3-n5a6a7c
2o4b2o4bo5b3o$2o5b2o4b2o4bo$13bo4$2bo12bo3bobo$2o5b2o4b2o$o5bo2bo2bo6b
obo5$bo$o$3bo$2bo3$bo$3bo2bobo$o6bo$2bo5bo4$obo$bobo5$2bo$o3bo$2bo!
```

EDIT: Why don't we just use EnumPattEvo, evolution mode, on an RLE of all 4-cell clusters? That will speed the process up!

EDIT2: Why don't we do this with LtL?