Knightships in Life-like CA (examples inside!)

[velcrorex]

I found some.

Three Period 5 knightships in B36/S345

Code: Select all

x = 159, y = 40, rule = 345/36
125boo$123b6o$122boob4o$68boo53b5obo$3boo61b6o53bobboo$b6o58boob4o51bo
bbobbo$oob4o59b5obo50bo5bo$b5obo60bobboo50b3oboboo$3bobboo58bobbobbo4b
o50bobboo$bobbobbo4bo53bo5bobb6o48bo$bo5bobb6o50b3oboboobboobo48booboo
$b3oboboobboobo56bobbo54boboo$6bobbo62bobo54b4obbo$7bobo12boo47boo13b
3o42bo4bo$6boo11b3obbo47boo11b4o45b4obb3o$7boo10boboboboo46bobobbo5b3o
47bo4b3o$8bobobbo4b5obb3o45bobooboo3boobobbo44bob4obb3o$8bobooboo3boo
3bo3b3o44boobb3obobobobbo44boob4oboo$9boobboo3bo3boo5b4o42bo3bobboobob
obbo3boobo41boo3boboo$10bo4bo7bo5boobboo46bobobb3o4b5obo44boobo$14boo
7b3obobobbo47boobo7bobboboboo43b3o3bo$27b3o3boo46b3obb3o3boboo3bo44b4o
$28boo59boboobo48b4o4bo$26boobo3bobo55boboobobbobo3boo37bobboobo$26boo
bo4bo56b4ob6o3boo40boboobo$26boobobboboo57booboboob4oboboobo33b7o$29bo
b5obobo3bo50b4obboob3o4booboo32boobboo$31boobooboboobb3o48b10obbobbob
oobobo30boboboo$36bobboob3obbo48bo3boo8boo3bobo34boo$40boo4boboo50boo
12boo34b3o$38boob3oboobobbo61b3obbo30boobbobo$39bobbo5b4o66bo31bo4bo$
39b6obb4o64b5o30boobboobo$41boobo3bob4oboboo57boo32b3oboboo$42b3o3bo3b
oobb4o56bobbo31b6o$47bobo3bobb3o58boo36boo$44bo6boboboobo58bo39boo$51b
8obbo56b3obo$54bobobobo57boboo$58bo!

Two period 5 knightships in B36/S0345

Code: Select all

x = 111, y = 50, rule = 0345/36
7$44boo$4boo37b4obobo$3b4obobo31booboobboo$bbooboobboo32b3oboo$3b3oboo
34b7obo$3b7obo31bobobobboobboo$3bobobobboobboo28bobobb7obo$4bobobb7obo
27bo3b3obboobo$5bo3b3obboobo34bobo$12bobo35bo$10bo38boo$9boo38b3o$9b3o
39bobbooboo$11bobbooboo32b5obbo$11b5obbo32b3obobboo$11b3obobboobo31bob
3o$13bob6o36b4obo$17b3o41b4o$18bobobbo34boo3boobbo$21b3o34boob6o$21boo
bo35boobo$60bobo$20booboboo4b3o27b9o$20b6o4b3o29b4o4bo$23boboboobobo
29boob3obb3obb3o$25bo38bobbobb3obobo$25booboo35bobo4bobobobboo$28bo39b
oo8bobo$28boo$29boboo$30bo$30bo!

[Sokwe]

Astounding! As far as I know, these are the first knightships to be found in this manner. I've been quite busy lately, and so shelved my earlier project in this area. I still intend to eventually perform a more organized search over a large number of rules, as you suggested in an earlier post.

Two questions:

• Do you have a method for choosing rules that seem to have a high potential for small p5 knightships?
• What other rules have you seen that look promising?

[velcrorex]

My basic idea was to use narrow searches to tell me information about what might be in a wider search. I use WLS. So, I pick a rule pretty much at random and search for a narrow knightship. I keep the width small enough where the search will finish in 5 seconds or less for the average rule. I keep checking random rules and watch the search until I see something promising. Promising meaning not necessarily a search that takes significantly longer, but a search that has a longer partial. Then I'll make incremental changes to the rule to find the rule which produces the longest partial pattern. Even these searches don't take very long. Then, once I have a good rule, I'll widen the search and give the rule the full attack.
For the full attack I still use WLS. I'll make a board 80x40 or bigger and set all the cells to off except for a channel of empty cells from corner to corner and use the knightship sort order.
I've also tried searching for p3 or p4 knightships in the B2 rules, without any luck.

I found another small knightship, this time in B357/S346

Code: Select all

x = 34, y = 19, rule = 346/357
bbo$boo6boo$oobb3ob4o$boboo3b4obboo$bb3ob3obooboboo$7bo4boboo$5bo5b3o
bboo$10b4oboobboo$11b3obbobbobo$11boobob4o$13b3oboboboobo$15bobo3b5o$
15bo4b3obobbo$20boobboboobo$24bobboobbo$23bobbobb3o$26b7o$32bo$29boobb
o!

As for other promising rules, I would search in the rules from B35/S346 to B3578/S034678. I'm sure there's more to be found. You can also use the steps above to find other rules.

[p46beth]

This is quite impressive. To my knowledge no other knightships in life like rules are known aside from the gemini-based knightship in B3/S23.

All the knightships you have found seem to have relatively similar shapes.

This raises the question of whether this rough shape somehow makes knightships more likely, or whether this is just an artifact of your search method (the latter possibility is more likely).

[velcrorex]

There are other ships which move at strange angles on David Eppstein's CA site. Though I believe these were found by trying every possible pattern in a small space and seeing what developed, not a direct search for a knightship of a given period and direction.

The knightships I found all have a slanted shape due to the way I searched for them. I don't think there's anything preventing a knighship from having a different shape, they just may be harder to find in other shapes.

[velcrorex]

Found a p6 Knightship-wickstretcher in b3/s345, thought it belonged in this thread.

Code: Select all

x = 12, y = 10, rule = 345/3
5b3o$4b4o$3bo$b3obbo$oob3o4boo$oo3b3obboo$boboobb4o$bobbobboboo$3b3o4b
oo$10boo!

[velcrorex]

I searched all the B3 rules for p5 knightships. At width 10 there is only the following ship:

Code: Select all

x = 17, y = 10, rule = B3578/S235
11boboo$10bo4bo$11bobo$bboboo3bobbobboo$booboobboo$b3obobo$ob4obboobbo
$3obo3bo3bo$b3oboboboo$bboboo!

It also works in B3578/S2358

[Sokwe]

I searched all the B3 rules for p5 knightships. At width 10 there is only the following ship...

I'm somewhat surprised that this was the only p5 knightship at width 10. What program did you use to perform the search? Also, did you test both possible translations, or just the one that travels 2 cells in the "long" direction (i.e. slide = 1 and offset = 2 in afind)?

[velcrorex]

I used gfind with some of Paul Tooke's edits to search for knightships. I wrote my own program to run gfind over all the possible rules, instead of typing in all possible rules manually. I only searched in the one direction, 2 cells in the long direction, 1 cell in the short width 10 direction. The search took roughly a day.

[velcrorex]

A couple new p5 knighships in B3/S0346. Unlike the other rules in which I've found knighships, this one is not explosive.

Code: Select all

x = 33, y = 34, rule =  B3/S0346
5bo$7boo$4bobboo$5boboo$$4bobo$3boboo$3bobo$6boo$3b5o19bo$3boobbo18bo$
7boo17boo$6boo17boo$6bo18bo$7bo18bo$o5boobo9bo5boobo$bo18bo$7bo18bo$b
4obboo11b4obboo$5bob3o14bob3o$4boobbo14boobbo$4bobo4bo11bobo4bo$5boo3b
obbo10boo3bobbo$7boobobo13boobobo$7boob3o13boob3o$10b3o16b3o$10b3o16b
3o$11bo18bo$7bo18bo$5bo5bo12bo5bo$8b4o15b4o$6boo3bo13boo3bo$7b4o15b4o$
8boo17boo!

Another p5 in B36/S34578.

Code: Select all

x = 16, y = 16, rule = B36/S34578
6bo$bbob5o$4obbo3bo$obbooboboo$obbobobobo$3obbobo$5obbobo$b4obo$3boboo
bo$6bo3bo$6b3obo$9boo$9boo$10boo$11b3obo$11boboo!

For completeness I post the p6 knightship in B3/S345 from this thread.

Code: Select all

x = 23, y = 12, rule = B3/S345
4b3o$4b3o10b3o$bbo9boo4b5o$bbobboo3b3obobboobbo$bo4bo3boob3obobobo$oo
4b3obbobo5bo$boo4bo$bob4obb3o3bo$bbobb4obbobbo$bb3obboboobbobo$3b3obbo
3bobbo$15bo!

[towerator]

Is it me, or are explosive rules more favourable to knightsips?

[velcrorex]

Is it me, or are explosive rules more favourable to knightsips?

So far the majority of the knighships I've found have been in explosive rules. I don't know what proportion of all rules are explosive, and I don't know if spaceships in general are more favorable in explosive rules or if this is a particular property of knightships. I'm also not sure if there's a good measure of explosiveness of a rule and if that measure would correlate to the existence of knightships (or spaceships in general.)

In other news, two related and very long p5 knightships, this time in B3/S1346. I'm still running this search, so there may be more at this width.

Code: Select all

x = 33, y = 170, rule = B3/S1346
oo20bo$b3o18bo$bobbo20bo$4bo18boobo$4boo17bobbo$bboo20bobbo$bbobbo18bo
bo$7bo15bobobo$3bobbo21bo$5boobo15b3o$8bo14bobo3bo$4bo3bo13bobbobo$5b
3o15bo4boo$4b3o15boobbobo$3boo19bobbobo$4boo16b3obobboo$bbo3bo17boo3bo
$bb4o17boo3boo$4bo3bo15bobbo$5boo13bo5bo$6bo13bo8boo$bboobbo3bo9bo5b3o
$bbobbob4o8boobobbo3boo$b4obbobbo13bobobbo$5bo3bo12bobboobo$bbooboboob
o11bo3bobbo$8bo17bo3b3o$b3o3bo15bo3bo3bo$bbobobboo15b3obboo$5bobo18bo
bboo$3boobo17bobboo$3b5o18bo$4bo3bo16boo$4b4obo14bobbo$5boobobo13bobob
o$7b3o15boboo$5b3oboo8boo5bo$5boboboo10bo5b3o$3b4o4bo9boo5bo$6boobbo
10bo6b3o$7boboo11boo4bo$7bobbo9boo8b3o$6boboo14b3obobobo$5bobb3o11b3ob
oo3bo$4bobobo16bo4boo$3bobo3bobboo7b6oboo$5bobbooboo7bo5bo$3boo3bo3bo
8b5o3bo$4bobboobbo8bobbobobobo$bb3obo3boo9boo3bo$5bob4o9boo4boo$5bobo
bboo12boboo$5b3o14bo$8boo3bo8bobboo$6b3ob3o14bo$5bo3bo3bo9boboobo$6b4o
boo10boo$3boo5boo$bbobbob4o15bobbo$3bobobboo16bob3o$4bobobo13b3obboo$
4boo17bob6o$3booboo18bob3o$bb3o20boobbo$bobo3bo19bo$bbob6o14boobo$4bob
o16bobboobo$5bobobo12bob3ob4o$9bo12bo4b5o$4bobbo15boobbobobo$3bo4bobo
10bobobbob4o$3b3obo13b3obo3boo$6bobboo11bobob3o$obobobo4bo11boobobbo$
bbobbo4bo14booboo$boboobob3o13bobb6o$bbobbobobbo15booboboo$bbobo3boo
18bo$6bobbo13boobbooboo$6bo17bo5boo$4boobooboo13boboboo$4bobobbo14bo4b
o$8bo13boobbobo$7bo15bo$7boobo10bo4bo$10bo10bob4o$8boboo14bo$4bo3b4o
11b6o$boobo5bobo9boo4bo$bbo6boboo12b4o$bbobboob3o14bobbo$4bobobboboo
10bobb3o$6boobboo10bob3o$3bobobboo13bobobobo$6booboo14boobo$4boobboo
10b4o4bo$5b3o13bobb3obboo$3b3obbobo11booboob3o$3b3obobo10boobb3obbo$bb
oo5bo11b9o$4bobboo15b4o$5boob3o14bob3o$3bobb5o13bobobobo$4booboobo17b
oo$3boo4boo15bo$7bobo16bobo$7boo19boo$6b3o17boobo$3boo25bo$b3ob3o14boo
7bo$obobobobo14bo3bo3bo$4bo16bobbobboobo$bb4obo13boobob3o$bo3bob3o13bo
bobbobo$bo3booboo13boboobb3o$bb3o3bo18boobo$bbobb6o14boobbo$3bob3oboo
13bobb3o$9bo12bobboo$8boo12boo3b3o$8bobo12b4oboo$8bobo11bob3o$6bo3bo
11bob4obo$6bobbo13b3ob3o$b3o6boo10bo3booboo$bobo5bo13boobobboo$3bo3bob
oo12b4oboo$3bo3booboo16boo$3bob4oboo16bo$5boo4boo13boo$7boboboo9boo3bo
$5boo4boo7boobb3o$7b3oboo6bobobobobo$6boo3bo8booboboo$7bobboo10b3o$bbo
bboobbo12bobobobo$bobo4bo13boboobbo$bo3boobobbo8b4o5bo$3boboobo12bobbo
4bo$3b4obb3o10b3obobbo$6boboo15boobo$5bobo3boo14b3o$bobo4b5o13boo$boob
oobobboo14boobbo$5bob3o15boo$4boo15bo3bo4bo$3boo16bo6b3o$3bo18boo3boob
o$23bo4b3o$21bo8bo$22bobobbobo$23boo3bobbo$32bo$24boobbo3bo$24bob3oboo
$25boobobo$24boboobo$24boboobo$22boo4bo$20bo3boobbo$21bobbo5bo$23bobo
bb3o$25boboobbo$24b3o3boo$24bob3oboo$21b3obbo3boo$22bobobbobo$22b4obo$
22b3o$23bo!

[eran911]

I've found ( ) a common naturally appearing oblique (engine-like) puffer in the rule B368/S237
(here in code)

Code: Select all

x = 57, y = 69, rule = B368/S237
21bo23bo$21bo$5bo4bobobobobo4bobobobo14bobo2$5bo8bo8bo19bo3bo2$5bo8bo
8bobobobo12bo5bo2$5bo8bo14bo11bobobobobo2$5bo8bo14bo10bo9bo2$5bo8bo8bo
bobobo9bo11bo3$2bobobo4bobobo6bo3bobobobo8bo5bo4bobobo$o38bo$6bo8bo5bo
4bo14bo4bo5bo2$4bo6bobobo4bo5bo14bo3bobobo2bobo$56bo$2bo12bo3bo6bo14bo
3bo3bo$56bo$obobobo4bobobo2bo7bobobobo8bo3bobobo2bobo27$25b3o$22bo2bo$
21b4obo$20b2o$25b2o$19bo5bo$17b2ob2o2bo2bo$17b5o3bobo$18bob2o4bo6b2o$
18bo2bo11b2o$18b3o$19bo5b2o$25b2o9b2o$27b2o6bo2bo$24bo11b2o$23bo5bo$
23bo2bo3bo3bo$26bo2bo4bo$27b3o4bo!

if it isn't newly discovered let me know.

[velcrorex]

This is new to me anyway. Very cool. I wonder if several of these could be combined to produce a ship.

[c0b0p0]

As I mentioned in the Shoots and Roots thread, I found a slow, sparky, and natural knightshoot in B36/S24567 (shown here eating a blinker):

Code: Select all

x = 25, y = 38, rule = B36/S24567
22b3o17$14bob2ob2o$14b7obo$13b9o$11b4obobob3o$10b4ob7o$10b6obobob2o$
10bob11o$9b4obobobob2o$7b3obob9o$8b6obobob2o$8bob11o$7b4obobobob2o$5b
3obob9o$6b6obobob2o$6bob11o$2o3b4obobobob2o$obob2obob9o$2bob6obobob2o$
2bobob11o$b2ob3obobobob2o$5bo!