AforAmpere wrote:Adjustable slope ships:Code: Select all`<snip (2,1) slope ship>`

Code: Select all`<snip (3,1) slope ship>`

Very nice! And so simple - I was evidently looking at this problem in a convoluted way.

The fastest I can make the (2,1) slope ship go is (4,2)c/52:

(2,1)c/(4n+2), p(8n+4), n>5:

`x = 14, y = 20, rule = B2ce3cen4eknt5kn6-ce7c8/S01c2-ck4ciknr5aknq6k7e8`

2bo$9bo3bo$bo8bo$obo6bo4$10bobo$11bo8$3bo$8bo3bo$9bo$8bo!

AforAmpere wrote:Are non-integer slopes possible in this rule? I can't seem to get them to work, but they might exist. All integer slopes are definitely possible:Code: Select all`<snip more oblique ships>`

Indeed, all rational slopes are possible. It would be nice to know what the minimum period for any particular slope is, and to write a script to generate the ship of any given slope. It may be worthwhile finding the slide-reflect reaction with the lowest possible repeat time first.

As for non-integer slopes you would need a totally different kind of construction. I can't remember where the discussion about this topic was (fairly recently too) but any pattern which meets the traditional definition of a ship in a regular Moore neighbourhood CA has a rational speed, almost by definition of what is a ship. I liked the idea for creating a pattern which moved with non-rational speed, but it can't be periodic and therefore must grow in size over time. I suppose it might be possible to use these dot movers to do the kind of computation which was discussed, and the construction may not need to be a UC, but it's certainly going to be a lot more complicated than a small rectangle.