Stepships - A new type of c/2 spaceship

[edwardfanboy]

I think I discovered a new type of c/2 spaceship I call a "Stepship". It is based on blinker puffer 1.
It uses the spark of the lowest HWSS as a blinker fuse.
Here is RLE code of the first 6 stepships.

Code: Select all

x = 180, y = 348, rule = B3/S23
2b3o$b5o$2ob3o22b6o$b2o25bo5bo$28bo$4bo24bo4bo$2bo28b2o$bo4bo$bo3bo3bo
3bo3bo3bo3bo3bo$b4o4bo3bo3bo3bo3bo3bo$9bo3bo3bo3bo3bo3bo3$4b4o$3b6o$2b
2ob4o$3b2o11$28b3o$27b5o$26b2ob3o22b6o$27b2o25bo5bo$54bo$30bo24bo4bo$
28bo3bo24b2o$27bo$27bo5bo3bo3bo3bo3bo3bo3bo$27b7o3bo3bo3bo3bo3bo3bo$
37bo3bo3bo3bo3bo3bo$4bo$2bo3bo$bo28b4o$bo4bo22b6o$b5o22b2ob4o$29b2o3$
2b2o28b2o$b2ob3obo$2b7o2b3ob3ob3ob3ob3ob3o$3b5o2$6b2o$4bo4bo$3bo$3bo5b
o$3b6o10$58b3o$57b5o$56b2ob3o22b6o$57b2o25bo5bo$84bo$60bo24bo4bo$58bo
3bo24b2o$57bo$57bo5bo3bo3bo3bo3bo3bo3bo$57b7o3bo3bo3bo3bo3bo3bo$67bo3b
o3bo3bo3bo3bo$34bo$32bo3bo$31bo28b4o$31bo4bo22b6o$31b5o22b2ob4o$59b2o
3$32b2o28b2o$31b2ob3obo$32b7o2b3ob3ob3ob3ob3ob3o$33b5o2$36b2o$6b2o26bo
4bo$5b2ob3o22bo$6b5o22bo5bo$7b3o23b6o3$6b5o$6bo6bo3bo3bo3bo3bo3bo2bo$
6bo6bo3bo3bo3bo3bo3bo3bo$7bo5bo3bo3bo3bo3bo3bo3bo$9bo3$8b2o$7b2ob4o$8b
6o$9b4o14$88b3o$87b5o$86b2ob3o22b6o$87b2o25bo5bo$114bo$90bo24bo4bo$88b
o28b2o$87bo4bo$87bo3bo3bo3bo3bo3bo3bo3bo$87b4o4bo3bo3bo3bo3bo3bo$95bo
3bo3bo3bo3bo3bo$64bo$62bo3bo$61bo28b4o$61bo4bo22b6o$61b5o22b2ob4o$89b
2o3$62b2o$61b2ob3o$62b4o3b3ob3ob3ob3ob3ob3o$63b2o2$66b2o$36b2o26bo4bo$
35b2ob3o22bo$36b5o22bo5bo$37b3o23b6o3$36b5o$36bo4bo3bo3bo3bo3bo3bo3bo$
36bo4bo3bo3bo3bo3bo3bo3bo$37bo2bo4bo3bo3bo3bo3bo3bo3$10b5o$10bo4bo22b
2o$10bo26b2ob4o$11bo3bo22b6o$13bo25b4o$12b3o$11b5o$10b2ob2obo$11b2o2b
2o2b3ob3ob3ob3ob3ob3o5$12b6o$12bo5bo$12bo$13bo4bo$15b2o15$118b3o$117b
5o$116b2ob3o22b6o$117b2o25bo5bo$144bo$120bo24bo4bo$118bo28b2o$117bo4bo
$117bo3bo3bo3bo3bo3bo3bo3bo$117b4o4bo3bo3bo3bo3bo3bo$125bo3bo3bo3bo3bo
3bo$94bo$92bo3bo$91bo28b4o$91bo4bo22b6o$91b5o22b2ob4o$119b2o3$92b2o$
91b2ob3o$92b4o3b3ob3ob3ob3ob3ob3o$93b2o2$96b2o$66b2o26bo4bo$65b2ob3o
22bo$66b5o22bo5bo$67b3o23b6o3$66b5o$66bo4bo3bo3bo3bo3bo3bo3bo$66bo4bo
3bo3bo3bo3bo3bo3bo$67bo2bo4bo3bo3bo3bo3bo3bo3$40b5o$40bo4bo22b2o$40bo
26b2ob4o$41bo3bo22b6o$43bo25b4o$42b3o$41b5o$40b2ob2obo$41b2o2b2o2b3ob
3ob3ob3ob3ob3o3$16b3o$15b5o$14b2ob3o22b6o$15b2o25bo5bo$42bo$18bo24bo4b
o$16bo28b2o$15bo4bo$15bo3bo3bo3bo3bo3bo3bo3bo$15b4o4bo3bo3bo3bo3bo3bo$
23bo3bo3bo3bo3bo3bo3$18b4o$17b6o$16b2ob4o$17b2o18$147b3o$146b5o$145b2o
b3o22b6o$146b2o25bo5bo$173bo$149bo24bo4bo$147bo28b2o$146bo4bo$146bo3bo
3bo3bo3bo3bo3bo3bo$146b4o4bo3bo3bo3bo3bo3bo$154bo3bo3bo3bo3bo3bo$123bo
$121bo3bo$120bo28b4o$120bo4bo22b6o$120b5o22b2ob4o$148b2o3$121b2o$120b
2ob3o$121b4o3b3ob3ob3ob3ob3ob3o$122b2o2$125b2o$95b2o26bo4bo$94b2ob3o
22bo$95b5o22bo5bo$96b3o23b6o3$95b5o$95bo4bo3bo3bo3bo3bo3bo3bo$95bo4bo
3bo3bo3bo3bo3bo3bo$96bo2bo4bo3bo3bo3bo3bo3bo3$69b5o$69bo4bo22b2o$69bo
26b2ob4o$70bo3bo22b6o$72bo25b4o$71b3o$70b5o$69b2ob2obo$70b2o2b2o2b3ob
3ob3ob3ob3ob3o3$45b3o$44b5o$43b2ob3o22b6o$44b2o25bo5bo$71bo$47bo24bo4b
o$45bo28b2o$44bo4bo$44bo3bo3bo3bo3bo3bo3bo3bo$44b4o4bo3bo3bo3bo3bo3bo$
52bo3bo3bo3bo3bo3bo$21bo$19bo3bo$18bo28b4o$18bo4bo22b6o$18b5o22b2ob4o$
46b2o3$19b2o$18b2ob3o$19b4o3b3ob3ob3ob3ob3ob3o$20b2o2$23b2o$21bo4bo$
20bo$20bo5bo$20b6o!

EDIT: At the top it used to say "x = 0, y = 0, rule = B3/S23".
EDIT: 137ben pointed out that there are infinity raised to the power of infinity stepships.

...Thus there are Inf^Inf different stepships.

[p46beth]

....Your rle code starts with "x=0, y=0". This means that it fits in a 0 by 0 rectangle, and so it does not come out in most life programs. Could you edit that to the correct size?

[edwardfanboy]

....Your rle code starts with "x=0, y=0". This means that it fits in a 0 by 0 rectangle, and so it does not come out in most life programs. Could you edit that to the correct size?

Fixed!

[LumpsOfMuck]

In the words of butthead: Ummm cool. I wonder if these could be used as glider reflectors or something. Idk, still cool either way

[p46beth]

This can be used to prove that the number of distinct nontrivial spaceships is uncountable. Each "step" can be extended arbitrarily to countably many blinkers, and arbitrarily many steps can be combined. Thus there are Inf^Inf different stepships, where Inf is the cardinality of the set of natural numbers.

[beebop]

I found an extensible one-time eater for a Stepship (order 6 shown). It consists of a 2-tub one-time blinkerpuffer1 eater and a 2-block 1-time HWSS eater to get that last HWSS. Each bp1 eater is translated (13, -1) from the previous one's position.

Code: Select all

x = 193, y = 77, rule = B3/S23
2o158b3o$2o157b5o$158b2ob3o22b6o$2o157b2o25bo5bo$2o184bo$162bo24bo4bo$
160bo28b2o$17bo3bo137bo4bo$16bobobobo136bo3bo3bo3bo3bo3bo3bo3bo$17bo3b
o137b4o4bo3bo3bo3bo3bo3bo$167bo3bo3bo3bo3bo3bo$136bo$134bo3bo$133bo28b
4o$133bo4bo22b6o$133b5o22b2ob4o$161b2o3$18bo3bo111b2o$17bobobobo109b2o
b3o$18bo3bo111b4o3b3ob3ob3ob3ob3ob3o$135b2o2$138b2o$108b2o26bo4bo$107b
2ob3o22bo$108b5o22bo5bo$109b3o23b6o3$19bo3bo84b5o$18bobobobo83bo4bo3bo
3bo3bo3bo3bo3bo$19bo3bo84bo4bo3bo3bo3bo3bo3bo3bo$109bo2bo4bo3bo3bo3bo
3bo3bo3$82b5o$82bo4bo22b2o$82bo26b2ob4o$83bo3bo22b6o$85bo25b4o$84b3o$
20bo3bo58b5o$19bobobobo56b2ob2obo$20bo3bo58b2o2b2o2b3ob3ob3ob3ob3ob3o
3$58b3o$57b5o$56b2ob3o22b6o$57b2o25bo5bo$84bo$60bo24bo4bo$58bo28b2o$
21bo3bo31bo4bo$20bobobobo30bo3bo3bo3bo3bo3bo3bo3bo$21bo3bo31b4o4bo3bo
3bo3bo3bo3bo$65bo3bo3bo3bo3bo3bo$34bo$32bo3bo$31bo28b4o$31bo4bo22b6o$
31b5o22b2ob4o$59b2o3$22bo3bo5b2o$21bobobobo3b2ob3o$22bo3bo5b4o3b3ob3ob
3ob3ob3ob3o$33b2o2$36b2o$34bo4bo$33bo$33bo5bo$33b6o!

[Tropylium]

This can be used to prove that the number of distinct nontrivial spaceships is uncountable. Each "step" can be extended arbitrarily to countably many blinkers, and arbitrarily many steps can be combined. Thus there are Inf^Inf different stepships, where Inf is the cardinality of the set of natural numbers.

Altho this was known anyway thanks to extensible spaceships (eg. the c/2 barge).

Most puffers can be turned into "stepships" in various ways, really:

Code: Select all

x = 244, y = 74, rule = B3/S23
156b2o$155b4o$155b2ob2o$157b2o15b2o$172b2ob2o$152b2o18b4o$152bo20b2o$
151bobo$151bo$151bo15b2o3bo$165b3o4b2o$144bobo17bo2bo5b2o$145b2o17bo7b
2o$145bo18b2o3$139bobo21bo2bo$140b2o25bo6b2o$140bo22bo3bo4b2ob2o$164b
4o4b4o$173b2o$134bobo24b2o$135b2o$135bo27bo$162bo2$129bobo$130b2o34b3o
$130bo37bo$167bo2$124bobo71b2o5b4o$125b2o44b3o22b2ob2o3bo3bo$125bo47bo
22b4o8bo$172bo24b2o5bo2bo$46b2o$46b2o71bobo73bo$120b2o54b3o15b2o8b2o$
46b2o72bo57bo14bo9bo2bo$45bo2bo6b4o118bo16b5o4bo2bo$44b6o9bo135b4o3b2o
b2o$48bo6bo2bob2o52bobo65bo15bo4b2o$44b4o6bo60b2o64bobo$45b2o7bo60bo
68bo$24b2o19bo8bo126b2o$23b2obo27bo3bobobo5b3o130b3o$21b2o2bo28bo3bo2b
o3bo4b2o37bobo75bo2bo12bo$bo18bob2obo28bo4bo6b3o2b2o37b2o79bo10bo$o12b
3o4bo2bo5bobob3o13bo7b2o10bo40bo76bo3bo$bo19bo7bo18b3o5b3o4b2o2bo13b2o
105b4o41b2o5b4o$17b2o18bo9b2obo12b2o5bo9b4o122b3o22b2ob2o3bo3bo$16bo2b
o10bo6bo8b2o18bo12b2obobo8b2o8b2o103bo22b4o8bo$17b2o18bo9b2obo12b2o5bo
9b3obo8b2o8b2o102bo24b2o5bo2bo$bo19bo7bo18b3o5b3o4b2o2bo14b2o26b2o5bo
2bo$o12b3o4bo2bo5bobob3o13bo7b2o10bo12bo26b4o8bo108bo$bo18bob2obo28bo
4bo6b3o2b2o12b2o22b2ob2o3bo3bo89b3o15b2o8b2o$21b2o2bo28bo3bo2bo3bo4b2o
12bobo24b2o5b4o91bo14bo9bo2bo$23b2obo27bo3bobobo5b3o15bo125bo16b5o4bo
2bo$24b2o19bo8bo175b4o3b2ob2o$45b2o7bo178bo4b2o$44b4o6bo35b2o17b2o105b
3o$48bo6bo2bob2o27bobo16b2o7b3o98bo$44b6o9bo31bo17bo2bo6bo97bo$45bo2bo
6b4o51bo6bobo120b4o$46b2o64b2o3b2o103bo2bo13bo3bo$95b2o129bo16bo$46b2o
48bo125bo3bo12bo2bo$46b2o48bo20bo2bo102b4o$97b2o22bo$117bo3bo$101b4o
13b4o$100bo3bo$104bo$100bo2bo!

(You may note in particular the replacement of one of the LWSSes of the 2nd engine with the glider stream from the 1st, which IMO makes this a little more "united" as a pattern)

[p46beth]

Altho this was known anyway thanks to extensible spaceships (eg. the c/2 barge).

The example you give is not sufficient. The extendable barge has only countably-infinite forms.

[Wojowu]

This can be used to prove that the number of distinct nontrivial spaceships is uncountable. Each "step" can be extended arbitrarily to countably many blinkers, and arbitrarily many steps can be combined. Thus there are Inf^Inf different stepships, where Inf is the cardinality of the set of natural numbers.

Truly saying there is only countably many stepships. We can consider each stepship with x steps as a finite string of natural numbers {a,b...,z} which has x elements, where a is length of first step, b is length of second step, etc.
Each of a,b,c... can be one of natural numbers, which size is N, and N is countable. So, there are N^x stepships of length x, which is also countable number for any x. Then, the whole number of stepships is an infinite sum: N^1+N^2+N^3+... which, by set theory, is equal to sum: N+N+N+...=N*N which, by set theory, is equal to N, which is countable, Q.E.D.
But we can reach uncountably many non-trivial spaceships IF and (as far as I know) only IF we consider infinite stepships. Then each stepship can be considered as infinite string {a,b,c...} and, using Cantor's diagonal argument we can prove that on any countable length list of strings don't contain at least one string:
Consider any infinite list of infinite strings:
1.{a,b,c,d,e...}
2.{f,g,h,i,j...}
3.{k,l,m,n,o...}
4.{p,q,r,s,t...}
5.{u,v,w,x,y...}
...
Then we can construct a string which isn't on list by taking numbers: a (first number in first string), g (second number on second string), m (third number on third string), etc. Now we can construct string:
{a+1,g+1,m+1,s+1,y+1...}
Now we can take an arbitrary number x, and we must prove string x. it isn't the same as our new string. It can't be, because our string is different from string x. on place x. If in string x. number x. is some z, then on x. place of our string is z+1. If we place our new string on first place on list, we can repeat diagonal argument infinitely many times, and we still can find one new string (using diagonal argument), so there are uncountably many such strings, and there are uncountably many infinitely long step ships, Q.E.D.

[Tropylium]

The extendable barge has only countably-infinite forms.

But we can reach uncountably many non-trivial spaceships IF and (as far as I know) only IF we consider infinite stepships.

Interesting points. Still, there are quite a few other ways of constructing families of 2^ℵ₀ infinite spaceships. For a simple example, consider the Fly tagalong. These may be chained either up or down; this means that fly chains infinite in one direction can be interpreted as a binary representation of a real number, and that any real number can be represented as an infinite fly chain.

It should be simple to see that the same result holds whenever there are multiple components that can be repeated infinitely and combined with each other. Examples perpendicular to the direction of travel are also possible, such as OWSS flotillae, or spiders connected with different types of pre-pulsar pushalongs.

[Macbi]

But we can reach uncountably many non-trivial spaceships IF and (as far as I know) only IF we consider infinite stepships.

In fact, there are only countably many finite objects in life (number each cell with a distinct prime, given an finite object in life, multiply the primes of its alive squares, this gives an injection into the naturals).

[Wojowu]

I've found new extensible spaceship!

Code: Select all

x = 107, y = 69, rule = B3/S23
14b2o72b2o$12bo4bo68bo4bo$18bo73bo$12bo5bo67bo5bo$13b6o68b6o$102b2o$
100bo4bo$106bo$100bo5bo$101b6o$96b3o$94b2ob2o$96b3o$101b6o$100bo5bo$
106bo$100bo4bo$102b2o$24b6o57b6o$23bo5bo56bo5bo$29bo62bo$23bo4bo57bo4b
o$25b2o61b2o$101b6o$100bo5bo$106bo$96b2o2bo4bo$96b3o$96b2o2bo4bo$106bo
$100bo5bo$101b6o$12b2o74b2o$10bo4bo70bo4bo$16bo75bo$10bo5bo69bo5bo$11b
6o70b6o$102b2o$100bo4bo$106bo$100bo5bo$101b6o$96b3o$94b2ob2o$96b3o$
101b6o$100bo5bo$106bo$100bo4bo$102b2o$b6o80b6o$o5bo79bo5bo$6bo85bo$o4b
o80bo4bo$2b2o84b2o$101b6o$100bo5bo$106bo$96b2o2bo4bo$96b3o$96b2o2bo4bo
$106bo$100bo5bo$101b6o$17b2o69b2o$15bo4bo65bo4bo$21bo70bo$15bo5bo64bo
5bo$16b6o65b6o!

Rightmost LWSSes have attached Schick engines which are stabilized by HWSSes right behind them to produce two lines of blocks. Blocks are later eaten by HWSSes on left, which can be shifted to the left or right as you want. We can also use MWSSes on left instant of them

[Pooping_Alien]

A new "step"!
Create a Schick engine with LWSS's for front.
Attach Coe engines (Coe ship's tagalong part) to both sides of Schick engine's loco.
Coe engine's domino spark acts just like that of a HWSS, so it can clear out blinkers.
The engine I described above is particularly wide so it should probably go as stepship's front, though it _can_ do cleanup.