Why so few c4+ rakes?

[Platypus5]

I am trying to construct "battleships" using the game of life. Pretty mature and productive, huh? Anyway, as I browsed for rakes (guns) and simple puffers ("shield generators") to make new warships out of, I noticed that starting at c4 orthogonal, the number and diversity of the rakes and puffers available went down dramatically.

Why is that? Where can I find the few C4 rakes? (Pitting c3 ships against each other gets boring)

[Dr. Monstaa]

Perhaps because rakes need to go slow enough to generate gliders. If you look at the tail end of the rake (the "glider engine") you'll see that most of them encase an area and reveal the glider rather than force it out of the back. Don't quote me on this but that's my explination.

[Wojowu]

I don't think your explanation is good, because most (expect of Cordership based ones) puffers and rakes I've seen are c/2 which is maximal possible speed in Conway Life. Now I am working on puffers, and I prefer to use c/2 spaceships/puffers/rakes, because they are smallest and simplest and there is most of them I think there is few c/4 rakes because no one had idea how it would be built

[HartmutHolzwart]

I'm not sure whether you did get the point in rake building. Reading David Bells articles gives you an impression on how the first c/3 rakes were built.

From there on you should read through the old "Game of Life News" to see the development.

Jason Summers page also contains downloads for 2c/4 and 2c/5 rakes collections.

Cheers,
Hartmut

[Dr. Monstaa]

I don't think your explanation is good, because most (expect of Cordership based ones) puffers and rakes I've seen are c/2 which is maximal possible speed in Conway Life. Now I am working on puffers, and I prefer to use c/2 spaceships/puffers/rakes, because they are smallest and simplest and there is most of them I think there is few c/4 rakes because no one had idea how it would be built

I said don't quote me didn't I? Anyway I didn't mean it for all of them seeming as the thread name is why so few c4+ rakes. Think you make a good point though, I guess this thread's creator was looking at patterns with large bounding boxes, which really aren't renowned for they're speed.

Where can I find the few C4 rakes?

I say look for smaller rakes.

[Wojowu]

Can you see quote in my previous post? No? I just commented your post. I haven't quoted. But "few" means that there is not many rakes, it is not related to size of bounding box. And in topic name there is "c4+". That means "speed c/4 or bigger" and I think here author means c/4 and slower spaceships, like c/5, c/6, 2c/7. And you said rake must be slow enough to shot gliders

[p46beth]

Okay, let's not turn this into a typical forum argument of nitpicking each others' posts. Wojowu is correct--faster rakes (i.e. c/2) are easier to construct, not harder.
The reason there are so few rakes slower than c/4 is just that--they are rarer, larger, and harder to build.

[Sokwe]

There are very few known puffer engines for speeds below (slower than) c/3 (except for c/12 diagonal). For c/4 orthogonal, there are only four distinct puffer engines (two of which only produce blocks), and for c/4 diagonal, there is only one known puffer engine known.

Code: Select all

#C Respective credits:
#C diagonal: Hartmut Holzwart
#C orthogonal: David Bell, Matthias Merzenich, Matthias Merzenich, Paul Tooke
x = 351, y = 91, rule = B3/S23
339bobobo$338b7o$338bo5bo$339bo3bo$339bo3bo$337b2o5b2o$339bo3bo$337b2o
bobob2o$336bobobobobobo$334b3obobobobob3o$334b2o2bobobobo2b2o$334b2ob
2obobob2ob2o$337b2obobob2o$340bobo2$336b2obo3bob2o$335bobob5obobo$335b
o5bo5bo$334b2o3bo3bo3b2o$334bo4bo3bo4bo$338bo5bo$340bobo$335b2ob3ob3ob
2o$335b2o9b2o$338bob3obo$341bo$338b7o2$340bobo$341bo$333b3o2bo5bo2b3o$
334bo2b9o2bo$56b3o277bo3bobo3bo$338bo5bo$56bo2bo278bo5bo$55bo3bo279bo
3bo$55b2o283b3o$54bobob2o276b2o7b2o$55bo2bobo274bobo2bobo2bobo$59b3o
272b2o4bobo4b2o$57b2o2bo272b2o4bobo4b2o$54bobobo2b2o$54bobo4bo272b2ob
2o5b2ob2o$54b2o276b2o4bo5bo4b2o$57bo274b3o2b2ob3ob2o2b3o$57bo275bobob
2o2bo2b2obobo$53b3ob2o4b3o267b2o3bo5bo3b2o$53b3o8bo3bo269b7o$54bob2o8b
3o269bo5bo$55b2o10bo2bo267b3ob3o$56bo9bo2b5o260b3obo5bob3o$55bo2b2o7b
3o210bo3bo50b2o2b5o2b2o$57b2o8b2ob2obo206bo3bo49bobo2bo3bo2bobo$57bo
13b2o206bobobobo48bo3bo5bo3bo$57bo13bo262bo2b2o5b2o2bo$57bo11b2o207bo
7bo47bo13bo$55bo2bo10b3o203bob2o2bobo2b2obo45b2ob3ob3ob2o$56b3o9bo2bo
203bobo2b2ob2o2bobo43b2obob2o3b2obob2o$58bo215bob2obobobobob2obo41bobo
13bobo$48b3o16b2o263bo3b2o7b2o3bo$49bo8b2o220bo3bo$69bo263bo2bo9bo2bo$
47b4o7b3o6bobo206b2ob2o3b2ob2o52bo$15b3o28bobo2bo18bo205b2o9b2o46b2o3b
3o3b2o$15bo30bo5bo17bo208b2o3b2o48bobo3b3o3bobo$16bo30bo3b2o6b2o6b2o
211bo3bo48b2obo9bob2o$18b2o38bo2bo5b3o209bo5bo50b3o2bo2b3o$19bo28bob3o
bo4b2o4b2o65bo60bo59b3o13bo8bobo3bobo8bo13b3o21b2o2b2o2bo2b2o2b2o$47b
2ob3obo9bo3bo61b2obobob2o6bo34bo6b2obobob2o56bob2o12b4o5b4o3b4o5b4o12b
2obo21b2o2b7o2b2o$16bo28b2o5bobo4b2o4bo3bo63bobob2o4b5o2bo24bo2b5o4b2o
bobo58bo3b4o9bo2b2o3bo2bo5bo2bo3b2o2bo9b4o3bo20b2o11b2o$13b4obo26b2o
12b2o7bo61b3o2bo3bo2bo4bo2b2obo18bob2o2bo4bo2bo3bo2b3o54b2o3bo4b4o3b4o
2bo2bob2o5b2obo2bo2b4o3b4o4bo3b2o24b2ob2o$13bo4bo27bob2o37b2o14b3o14b
2o8b2o2bo3b3o4bo4bob2o18b2obo4bo4b3o3bo2b2o8b2o14b3o14b2o11bo4bo5b4ob
3o4bo4bo7bo4bo4b3ob4o5bo4bo23bobobobo$14bo4b2o25b2ob2o35bob2o12bob3ob
2o9bobo8bo6bob2o3bob3obo3bo16bo3bob3obo3b2obo6bo8bobo9b2ob3obo12b2obo
17bo4bobo3bo9b2o5b2o9bo3bobo4bo28b2ob2ob2ob2o$16bo2b3o24bob3o34bo5bo
10bo5b2o8b2o3b3o2bobo6bo3b2o4bob2o3bo16bo3b2obo4b2o3bo6bobo2b3o3b2o8b
2o5bo10bo5bo14b2o7b2obo3b3o17b3o3bob2o7b2o26b5ob5o$2b2o16b2o24bobobo8b
2o24b4o2b2o10b4obob2o6b2o2b4o2bo8bo3b2o3bo3b4ob2ob4o2b4ob2ob4o3bo3b2o
3bo8bo2b4o2b2o6b2obob4o10b2o2b4o19b2o4bo10bo9bo10bo4b2o30bobo7bobo$2bo
bo12b2ob2o37b2o22bo2b4ob8ob2o3bo6bo9bo3bo2b2o15bo5b5ob4o2b4ob5o5bo15b
2o2bo3bo9bo6bo3b2ob8ob4o2bo35bo7bo48bo5bo5bo$2bo14b2ob2o26b2o34bo3bo2b
ob2o3bob2o10b2obo3bo5bo29bo2b2obo2bob2o2bo29bo5bo3bob2o10b2obo3b2obo2b
o3bo30b2o4bo7bo4b2o42b3o3bo3b3o$5bo9b2o3b2obobo22b3o38b2o3bo4b3o10b4o
42b2obo2bob2o42b4o10b3o4bo3b2o34bo2bo15bo2bo39bo4bo2bo2bo4bo$5b2o7b2o
4bo3bo22bo3bo42b2obo15b2o2bo90bo2b2o15bob2o40bobo2b2o7b2o2bobo39bo4bo
7bo4bo$5b2o8b2ob3o6bo19bo3bo7b2o97bo3b2o3bo103b2o2b3obo5bob3o2b2o39bo
15bo$4b2o6b5ob2o6bobo18bo11b2o98b8o104b2o2bo3bo5bo3bo2b2o42bo9bo$2ob2o
6b2o3bob2o7bo19bo228bobo7bobo45b3ob3ob3ob3o$o4bo7bob2o31bo2bo122bo11bo
148bobo2bobo2bobo$ob4o10bo31bo124b3o9b3o84b6o9b6o41bo5bobo5bo$4b2o44b
2o7b2o101b2o9b3o9b3o87bob2o2b3o2b2obo44b2obob2ob2obob2o$4b2o5b2o3bo12b
o29b2o101b2o111bobo9bobo49b2ob2o$4b2o5bo3b2obo9bobo19b2o121b4ob2ob2ob
4o84b2obo2b2o5b2o2bob2o39b4o3bobobo3b4o$6bo4bobo3bo10bobo20bo119bobo5b
obo5bobo81b2o3bo2b7o2bo3b2o38b2o5bo3bo5b2o$5b2o3b2obo15bo144b2o3bobo3b
2o87b2o13b2o43b2o11b2o$5bo45b2o6b2o109bo2bo2b3o3b3o2bo2bo143b2obob5obo
b2o$6bo52b2o109bobo15bobo90b3o52b3o5b3o!

Of these five engines, only the latter two of the orthogonal ones can be used to construct rakes. All of the known c/5 orthogonal and c/5 diagonal puffers are engineless, and work by circulating gliders and/or *WSSs (all slower known puffers are based on Gemini or switch engines).

It seems that one of the primary reasons that it is difficult to find slow puffer engines is that the output of a potential puffer catches up to the supporting part. For example, if one removes one of the block-predecessors from the bottom of Hartmut Holzwart's c/4 line ship, the extra stuff created at the back starts to destroy the line at about generation 8. In contrast, c/2 line puffers do not tend to have this problem:

Code: Select all

x = 156, y = 32, rule = B3/S23
34b3o27b3o13b3o27b3o$33bo3bo25bo3bo11bo3bo25bo3bo$32b2o4bo11bo11bo4b2o
9b2o4bo11bo11bo4b2o$31bobob2ob2o3b4ob2ob2ob4o3b2ob2obobo7bobob2ob2o3b
4ob2ob2ob4o3b2ob2obobo$30b2obo4bob2ob4o7b4ob2obo4bob2o5b2obo4bob2ob4o
7b4ob2obo4bob2o$29bo4bo3bo4bo2b2obobob2o2bo4bo3bo4bo3bo4bo3bo4bo2b2obo
bob2o2bo4bo3bo4bo$6bo17bo16bo4bo7bo4bo27bo4bo7bo4bo25bo17bo$5b3o15b3o
3b2o7b2o6bo7bo6b2o7b2o3b2o7b2o6bo7bo6b2o7b2o12b3o15b3o$3b2ob3o13b3ob2o
100b2ob3o13b3ob2o$4bo2bob2o4bo4b2obo2bo18b2o7b2o35b2o7b2o27bo2bob2o4bo
4b2obo2bo$b2obo4bobob2ob2obobo4bob2o17bo5bo39bo5bo26b2obo4bobob2ob2obo
bo4bob2o$b2obobo2bobo7bobo2bobob2o15bo2bo3bo2bo35bo2bo3bo2bo24b2obobo
2bobo7bobo2bobob2o$bo8b3obobob3o8bo16bo2bobo2bo37bo2bobo2bo25bo8b3obob
ob3o8bo$2o7b2o9b2o7b3obo15bobo43bobo24bob3o7b2o9b2o7b2o$33b2o12bobobob
o39bobobobo21b2o$31b2obo11b2obobob2o37b2obobob2o20bob2o$34b2o9bo3bobo
3bo35bo3bobo3bo18b2o$33bo88bo$35b3o7b2ob2ob2ob2o35b2ob2ob2ob2o16b3o$7b
3o15b3o9b2o78b2o9b3o15b3o$6bo3bo13bo3bo9bo7bo3bo3bo37bo3bo3bo16bo9bo3b
o13bo3bo$5b2o4bo11bo4b2o8b2o6bo3bo3bo7b3o9b3o9b3o3bo3bo3bo4b3o8b2o8b2o
4bo11bo4b2o$4bobob2ob2o3b3o3b2ob2obobo8bo21bo3bo7bo3bo7bo3bo14bo3bo7bo
8bobob2ob2o3b3o3b2ob2obobo$3b2obo4bob2ob3ob2obo4bob2o6bobo5b2o5b2o5b2o
3b2o5b2o3b2o5b2o3b2o5b2o5b2o3b2o5bobo6b2obo4bob2ob3ob2obo4bob2o$2bo4bo
3bo4bobo4bo3bo4bo6b3o3b4o3b4o3b2obobob2o3b2obobob2o3b2obobob2o3b4o3b2o
bobob2o3b3o6bo4bo3bo4bobo4bo3bo4bo$14bo5bo20b2ob2o2b2ob2o2b2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2b2ob2ob2ob2ob2ob2o20bo5bo$2b2o7b2o9b2o
7b2ob3o5bobo4bobo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4bobo3bobo3bobo5b
3ob2o7b2o9b2o7b2o$36bo82bo$34bo6b2ob2o2b2ob2o2b2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2o2b2ob2ob2ob2ob2ob2o6bo$34bob2o80b2obo$39b78o$38bo78b
o!

Another factor that can affect the number of known puffers for a particular speed is the minimum necessary period. With our current search methods, as the period of the object increases, the size of the object that one can reasonably search for becomes smaller. Therefore, it is generally easier to find puffers at lower periods simply because one can search a larger area.

In the case of the speed 2c/5 orthogonal, there are a large number of known puffer engines despite the relatively high base period (5). This is not too surprising, as 2c/5 is relatively fast, and so puffers are not destroyed by their own output, but it is an interesting case, because, from what I've seen of other rules, it is not typical to have a large number of relatively small 2c/5 spaceships and puffers. In many (most?) B3 rules, the smallest c/5 spaceships tend to be smaller than the smallest 2c/5 spaceships, but this seems to be reversed in Life.

[Tropylium]

In the case of the speed 2c/5 orthogonal, there are a large number of known puffer engines despite the relatively high base period (5). This is not too surprising, as 2c/5 is relatively fast, and so puffers are not destroyed by their own output, but it is an interesting case, because, from what I've seen of other rules, it is not typical to have a large number of relatively small 2c/5 spaceships and puffers. In many (most?) B3 rules, the smallest c/5 spaceships tend to be smaller than the smallest 2c/5 spaceships, but this seems to be reversed in Life.

Are you sure about that? Taking a look at the B3 "interesting rules" listed in Eppstein's SS database, I find:

(2c/5 smaller: 6)
— 2 rules with small 2c/5 ships (PseudoLife, B35/S236)
— 2 rules with medium-sized 2c/5 known (Life, Coagulations)
— 1 rule with a medium-sized 2c/5 and a large c/5 known (Day & Night)
— 1 rule with a large 2c/5 known (2×2)

(c/5 smaller: 8+5)
— 2 rules with medium-sized c/5s known (Amoeba, B36/S124)
— 5 rules with a medium-sized c/5 and a large 2c/5 known (HighLife, Move, Stains, B36/S245, B368/S12578)
— 1 rule with a large c/5 known (3-4 Life)
— 5 rules with some c/5s and nothing faster than c/3 known (Bacteria, Blinkers, Bugs, Holstein, Slow Blob)

6 vs. 13 would be a good case, but the last 5 seem to be rather examples of rules not supporting any very fast spaceships. The lack of any truly small (< 10×10) c/5 ships also stands out here…

All of the "best" 2c/5 rules seem to be B3+x/S23+y, tho, with fairly similar engines even (basically c/2 engines with one-step delay). So perhaps given more rules, c/5 might still end up more numerous…

(On another note tho, I'm reasonably sure Life's smallest non-traditional spaceships have not yet been found; there may well be a small glide-reflectiv 4c/10 or 2c/10, for example.)

[Sokwe]

@Tropylium
Looking at David Eppstein's database as a whole, there are far fewer known rules with 2c/5 spaceships than there are with c/5 spaceships. Also, I have searched for new spaceship speeds in many Life-like rules, and, in my experience, 2c/5 spaceships tend to be somewhat rare, and those that I tend to find are quite large compared to c/5 spaceships in the same rule.

Edit: Specifically, David Eppstein's database identifies 2546 rules with known c/5 spaceships and only 557 rules with known 2c/5 spaceships. The "best looking" rules for 2c/5 spaceships seem to be B3/S23 - B35678/S235678. Note that in this set of rules, there are more rules with known 2c/5 spaceships (153) than with known c/5 spaceships (55). There is also a sizable set of rules with a small 2c/5 ship.

The lack of any truly small (< 10×10) c/5 ships also stands out here

There may be no such "small" ships in David Eppstein's "interesting rules", but that's a rather biased sample. Here are two small c/5 ships in other rules: glider 897, glider 2290.

Edit 2:

the last 5 seem to be rather examples of rules not supporting any very fast spaceships...

There are 1314 rules with a known c/2 ship (i.e. the speed limit is definitely greater than 2c/5) and a known c/5 ship, but without a known 2c/5 ship. By contrast, there are 307 rules with a known 2c/5 ship, but without a known c/5 ship. This does not account for the size of the ships, but it does indicate that c/5 ships seem to be easier to find (with current methods) even in rules where the speed limit is known to be greater than 2c/5. Since most of these ships are long and thin, this indicates that c/5 ships are found at smaller widths than 2c/5 ships. This does not account for minimum length at a particular width, which might be an important factor if the trends in minimum height with respect to width are significantly different for c/5 and 2c/5.

[Tropylium]

@Tropylium
Looking at David Eppstein's database as a whole, there are far fewer known rules with 2c/5 spaceships than there are with c/5 spaceships.
(…)There are 1314 rules with a known c/2 ship (i.e. the speed limit is definitely greater than 2c/5) and a known c/5 ship, but without a known 2c/5 ship. By contrast, there are 307 rules with a known 2c/5 ship, but without a known c/5 ship.

Is it possible to get a list of all spaceships of a given velocity from there?

There may be no such "small" ships in David Eppstein's "interesting rules", but that's a rather biased sample.

So it seems. Not sure why should that be the case, however, the small c/5 examples you posted cover both exploding and stable rules…

And of course, it does make sense that a faster velocity is less likely to be abundant; it sets stricter limits on the structure of the engine, especially in B3 rules where it's fairly close to the maximum velocity possible.

[Sokwe]

Is it possible to get a list of all spaceships of a given velocity from there?

David Eppstein has written a program (see here) to search his database e.g. for rules with a known spaceship of a particular velocity. The database can be downloaded here (3.3 MB).