A significant problem is that while the pi's are period 45 objects, the spaceship streams are period 450. Thinning the p45 rakes down to p450 is not so easy, and we need something reasonably efficient.
The approach that we have chosen is to (for each half) build a p450 stream of MWSSs that travel backward. The stream will be mostly period 45, but with every 10th MWSS missing. A p45 rake aimed at the MWSS stream can have 9 of every 10 gliders deleted by the MWSSs, and thus be thinned out to p450, provided everything is timed properly.
Middleweight spaceships are used because neither
LWSSs nor HWSSs are capable of deleting gliders in
enough different ways. Here are the ways that a
MWSS can delete a glider:
Unfortunately, since a backward spaceship stream like this has a fixed timing, it imposes serious restrictions on when and where the p450 gliders can be emitted. In fact, there is not enough flexibility to allow the gliders to be positioned so as to recreate the forward-traveling spaceships (which is their whole purpose). This is a problem!
To gain the required flexibility, we turn the gliders into stationary objects (blocks or blinkers), and then, at the right time, turn them back into gliders. This technique provides the extra degree of freedom that we need.
After some searching, I settled on width 25 for
this "catch and throw" concept.
At this width, there is one way to create a backward
glider from a block, and two ways to create a forward
glider from a blinker:
Now that we have we have a way to create p450 rakes, we need to figure out how to crash the emitted gliders together to construct the spaceships that comprise the fanout devices and the helix. So, let's look at some ways to construct spaceships from gliders, with the gliders all approaching from the same side.
Some of the spaceships that we need to construct are fairly close together, and our options for constructing them are very limited. Most of the spaceships could be constructed with smaller components, but to take advantage of that, we would have to go to the effort of building a larger set of components to use.
Another thing to be aware of is that we don't need to construct any heavyweight spaceships until it comes time to construct the helix. This occurs roughly 2/3 of the way down the Spaceship, and only on one side. So the initial blinker tracks don't even need to be able to support constructing HWSSs -- we can reconfigure one of them to do so when we need it.
[Keep in mind that the total cell population is probably the most important thing we should try to minimize. The lion's share of the population comes from the fanout devices, which become more fully populated as one approaches the front of the Spaceship. So the vertical lengths of the components near the front of the Spaceship have a bigger effect on the population than anything that goes on near the back of the Spaceship.]
Anyway, here are some one-sided spaceship constructions, which
should be sufficient for our purposes:
LWSS:
MWSS:
HWSS:
Now to start putting some of these pieces together.
Here are two of the
components that make up a p450 forward LWSS rake. By varying
the space between them, we can change the distance at which
the LWSSs are constructed.
Here's a diagram to help clarify the glider paths
in the above pattern:
This pattern requires blocks and blinkers to already exist
on the
tracks in the right places. How do they get there? We need two
more large components, one preceding the first half of the
forward spaceship rake to lay down blocks,
and one preceding the second half to lay down blinkers.
Here's a component that lays down the blocks needed by
the above LWSS rake:
[The above example pattern doesn't show one of the pairs of blinker trails in the middle. It must be present, though, because it shares a track with another component that needs it.]
A similar component will need to be built to lay down the blinkers used by the forward rake.
Actually, there probably needs to be two versions of each of these components. Because the period of the Spaceship is an even number (450), the backward MWSSs appear in a particular phase only at every other cell. The "odd-cell" versions should be only slightly different, but may need a different number of pi's used to reposition the blinkers.
[There's nothing that actually requires the period to be an even number, and an odd period like 495 would offer more flexibility in a few situations like this. It seems difficult to design the helix, though, and I don't think the advantage is big enough to warrant starting over with a different period.]
Here's a simpler LWSS rake:
However, this doesn't work fast enough to create some of the LWSSs in the helix. (Note that another rake, not shown, is needed to delete the extra loaf.)
Basically, that's it. There is one final step: at the very end of the Spaceship, we need to destroy any remaining blinker trails and backward MWSSs. This is very easy compared to most of the rest of the Spaceship -- gliders can readily be fired back at the blinkers to delete them, plus there are probably a lot of shortcuts that could be used instead.
With regard to actually constructing such a Spaceship, the next major thing that's needed is a way to automatically generate p450 forward LWSS, MWSS, and HWSS forward rakes at any given distance from the blinker tracks. For all intents and purposes, a computer program must be written to do this. The distinct components of pi's that make up the rakes could be built by hand, if necessary (though it would be quite a lot of tedious work, and it would be really nice if they could be computer-generated), and then the computer program could combine them.
Once this is done, we should know two things:
This information will allow us to put the finishing touches on the exact design of the Spaceship.
The next thing to do would be to build the front part of the Spaceship (manually), down to the point where the first two blinker trails are built. The details of how the gliders are repositioned, and how many extra forward spaceships are needed, will then be determined.
From there, basically just work from front to back. Each section we complete determines exactly how the next section needs to be arranged.
It's unclear whether it would be worthwhile to write any more computer programs for generating parts of the Spaceship (say, for constructing blinker trails). Combining all the segments and spaceship rakes, on the other hand, is probably best left to a computer program, due to the extraordinary size of the Spaceship, and the fact that an error made early on could invalidate everything that comes after. (Computer programs don't mind starting over.)