Here's a puzzle that's maybe really more of an optimization problem.
With the new 0-degree Snark recipe, simeks' single-channel construction arm is now capable of bending itself around an arbitrary number of corners, then un-bending those corners again if needed. It can also throw off target blocks to either side, and shoot *WSSes in all directions -- and even Corderships and loafers and so on, if those are needed.
There appear to be universal elbow operations even when individual gliders are required to be separated by up to 213 ticks. This allows an interesting trick to be done with Guam's one-bit-spark-to-2G converter
, which recovers in 164 ticks.
Starting with an empty universe, we can change the state of 35 cells at T=0, as follows:
x = 66, y = 65, rule = LifeHistory
#C [[ THUMBNAIL THUMBSIZE 2 ]]
Then, as long as we have complete control of a single cell (the red cell above) we can send out single-channel recipes that can build any pattern that can be constructed with a finite number of gliders.
We can even promise to turn on the cell no more than once every 164 ticks, since we can't really do that anyway, or even only at most once every 213 ticks
if we didn't mind taking twenty times as long to get constructions done. Otherwise we can leave the cell alone, never turning it OFF.
-- Okay, so that's 36 cells we have to touch, 35 at T=0 and one more that we have to be able to modify indefinitely to allow for universal construction. The questions are
1) Can we get to universal construction with fewer T=0 cells and only one permanent-control cell?
2) If we have permanent control over any cells we touch, how many do we need to achieve universal construction?
The upper bound for the answer to #2 seems to be 4 cells, because you can produce gliders on demand, if you have control over three cells in a banana-spark shape (among others). And then you can lie in wait for a glider out along the output channel, and convert a glider into an elbow -- and then you never need to use that fourth cell again.
The lower bound is pretty definitely 3 cells, for obvious reasons. I strongly suspect that universality can be achieved with only three controllable cells, but I'm not sure I want to try to prove it.
2b) Are there arrangements of three cells where you only need to be able to turn the cells ON or leave them alone to make a stream of single-channel gliders? The banana-spark glider generation method I found needed four ticks, and I had to turn two different cells OFF in different generations.