Rhombic wrote:Gamedziner wrote:The problem there is that the two tracks would eventually converge.

Well yeah, but isn't that how 31/240 etc work? you set up something to delete the last B-heptomino and connect a synthesis at a translation.

Your understanding of the prior work seems wrong, the crawlers are not deleted in any of the fast ships. The only one where an crawler seems to be deleted and resynthesized is the HBK, since the glider is destroyed and rebuilt. But I argue that the glider isn't even the "crawler" in the HBK, but rather the "crawlee."

A reaction shifting two tracks relative to one another isn't a dealbreaker, but it makes things harder for sure. You probably want to work with non-mirrored track pairs in trying to patch this up.

What qualifies as a promising reaction?

The ideal is the following. Have some pair of objects at t=0, let's call them C1 and C2. C1 is the crawler and can be arbitrarily complex, C2 the "crawlee" and needs to be a regular pattern (periodic or periodic-with-offset like a spaceship).

At time t=T, the universe again consists of C1 and C2, but C1 is displaced by vector V1 with components (A1, B1), and C2 displaced by V2 with components (A2, B2), and possibly advanced by G2 generations. Examples:

C1 = Pi

C2 = Blinker

T = 45

V1 = (0, 17)

V2 = (0, -11)

G2 = 1

`x = 5, y = 17, rule = B3/S23`

2bo$2bo$2bo12$b3o$o3bo$2ob2o!

C1 = Herschel

C2 = Block

T = 240

V1 = (0, 31)

V2 = (0, -22) or (-8, -4)

G2 = 0

Extra block and 2 gliders

`x = 10, y = 26, rule = B3/S23`

8b2o$8b2o22$3o$bo$b3o!

C1 = Herschel

C2 = Glider

T = 79

V1 = (23, 5)

V2 = (-27, -29)

G2 = 1

Extra glider

`x = 16, y = 18, rule = B3/S23`

15bo$13b2o$14b2o13$3o$bo$b3o!

C1 = Herschel

C2 = Glider

T = 72

V1 = (27, 1)

V2 = (-22, -38)

G2 = 0

Extra bunch of junk

`x = 14, y = 28, rule = B3/S23`

11bobo$11b2o$12bo23$3o$bo$b3o!

C1 = Half-Bakery

C2 = Glider

T = Anything more than 62

V1 = (6,3)

V2, G2 = Depends on T

`x = 16, y = 14, rule = B3/S23`

b2o$o2bo$bobo$2bob2o$3bo2bo$4bobo$5bo5$13b2o$13bobo$13bo!

In all of these cases, the spaceship speed is V1 divided by T. C1 objects are not created or destroyed at any point in the ship. The challenge is for objects of type C2 to be created at the front and destroyed at the back. The displacement and phase shift of the second object simply tells where the next crawler must be for the reaction to repeat, which is important for the construction aspect but doesn't say much about the possibility/impossibility of the ship except for maybe giving a good idea about coset problems.

If C1 reappears but C2 is incompletely formed, it is usually really hard to do anything to salvage the crawler. If there is way too much junk, it's again usually really hard. If there is no junk at all, it depends on whether anything good comes out of rubbing multiple copies together.

If the goal is to dig up a ton of promising reactions, going into slightly more complex Cs would be a way to go. Either use multiple still lives and oscillators together as C2 (but bear in mind that the chance of having C2 fully rebuilt at any later T is way lower), or more exotic C1 (combinations of active objects, or just more odd ones).

Physics: sophistication from simplicity.