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As both these constellations are a self-sustainable for some generations and a bit faster than gliders, this could maybe give additional possibilities.

Why would you build helices based on gliders and not on *WSS?

May I suggest another approach toward Helices: If we could find some helix consisted of *WSS that burns faster than c/2 (it's possible as the universe is not empty) - This will allow universal helix of any allowed speed. Just burn with very fast speed, and wait for the next *WSS salvo to arrive.

A helix can only able to burn faster than c/2 if it is moving in reverse - either it is climbing very closely spaced ships moving away (this must be faster than c/2 if it works) or climbing backwards on an incoming stream of ships. It wouldn't be very useful for ships either way.

The idea was to have Herschels, Pis, or other objects climb *WSSes, instead of the normal gliders climbing *WSSes.

Sphenocorona wrote:It wouldn't be very useful for ships either way

If it climbs upstream why wouldn't it be useful?

If you worry about geometry - so it definitely can be useful for knight ships. I also think it's possible to have some "holes" inside the helix to make it sort of cris-cross geometry. There is no reason why it wouldn't be possible or useless. Obviously it would be always slower than c/2 at the end - but this is fast enough.

Sphenocorona wrote:The idea was to have Herschels, Pis, or other objects climb *WSSes, instead of the normal gliders climbing *WSSes.

Thx for the explanation. Didn't get it in the first read.

Sphenocorona wrote:The idea was to have Herschels, Pis, or other objects climb *WSSes, instead of the normal gliders climbing *WSSes.

I think that though this idea is worth trying I wouldn't put too much hope on it, and that's why. First of all, gliders in the burning helix reactions are not that slow, as you might think. In the following reaction the glider is as fast as c/2 Unfortunately this reaction can be chained only at the speed of 11c/24, which thus appears to be the greatest known theoretical asymptotic speed limit for caterpillar-like spaceships.

Secondly, gliders have a nice property compared to methuselahs: they are periodic and thus you can adjust their velocities accordingly, i. e. the above reaction can be also treated as 12c/28, 13c/32 and so on.

On the other hand, it might make sense to investigate methuselah-based reactions in the context of glider-based helices, but the latter are terra incognita in any aspect (and it's not even clear if they themselves have a practical application, because you can only achieve velocities slower (or equal) than c/4 with them, but those can be achieved perhaps easier by colliding *WSS into gliders.)

The only reason to follow this line would be that it might give more flexibility and thus more efficient helices for a given speed, either in terms of basic period or in number of *WSS needed for support.

Oh, before I forget: do we have something that could be used for 11c/24? That's blazingly fast for caterpillar technology, a true challenge...

HartmutHolzwart wrote:The only reason to follow this line would be that it might give more flexibility and thus more efficient helices for a given speed

Glider-*WSS reactions already give enough flexibility due to the trick I explained in the last post. Methuselah-*WSS would make sense only if one finds a reaction that can be chained at speeds faster than 11c/24. That's the limiting factor. (If you take a look closely, you'll see that most *WSS in the caterpillar or in the (13,1)c/31 helix are due to this reaction, and there is enough number of reactions that move at slower speeds.)

HartmutHolzwart wrote:Oh, before I forget: do we have something that could be used for 11c/24? That's blazingly fast for caterpillar technology, a true challenge...

11c/24 is an asymptotic limit, you would need an infinite number of *WSS to achieve that velocity

codeholic wrote:which thus appears to be the greatest known theoretical asymptotic speed limit for caterpillar-like spaceships.

Hmm why do we limit ourselves by two *WSS? if we add more *WSS, looking for "combined" G->*WWS->G reaction, wouldn't it might allow greater speeds?

Sadly, no. At least no reaction with 3 *WSS has been found that would allow greater velocity. (I admit though, that the search might be not perfect).

I wasn't thinking about higher speed, but e.g. at reaching 17c/45 with less *WSS because of some new intermediate step that allows to reach this speed with say x4 instead of x6.

Even if the number of *WSS needed would be more, we could save fom needing less *WSS for the fanout device.

The caterpillar is different from the waterbear or the centipede in this respect.

HartmutHolzwart wrote:I wasn't thinking about higher speed, but e.g. at reaching 17c/45 with less *WSS because of some new intermediate step that allows to reach this speed with say x4 instead of x6.

As I said, the length of the caterpillar's helix is mostly due to the 11c/24 reaction. You could make the helix shorter only if there were a faster (or comparable) reaction. But maybe if there were an appropriate turner, it could work, but I personally doubt that 4x is possible with a sequence of relatively small collisions.

I would also consider SL moving helix, for two reasons:

1. There were no well explored searches in this area.
2. After you find anything fast enough you can adjust the speed freely.

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I've made some very preliminary random search and come up with this 25c/103 helix (which gives a hope to find something faster):

this is still close to 1/4! Do expect to get much faster with this idea?

Coming back to glider helices: I understand that currently the main obstacle is that there are only relatively slow glider turners. And the search space for these is well explored. So no hope for pleasant surprises. Correct?