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B0/D8 rulespace

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B0/D8 rulespace

Postby Tropylium » October 7th, 2011, 5:57 am

These don't tend to gather that much attention, so here's a general megathread.

A few discoveries in the vicinity of B01345/S234:

• A domino in B0134567/S2345 turns out to be a "chaotic replicator"; it's neither a 2ⁿ sawtooth nor a self-standing wickstretcher. It does have a definite period and speed, however (4c/8 namely). I am not sure if gaps appearing in the replicator stream have an upper size limit or not.

In 4-divisible generations, the pattern settles down to rectangles of width 2 and odd length. The maximum size of these rectangles seems to grow over time, and as a rectangle's center leaves a blank space, this seems like an easy metric to track:
—g0: 1 (= domino)
—g4: 5
—g20: 7
—g28: 9
—g40: 13
—g64: 19
—g220: 21
—g244: 49

Moreover, it is not even trivial to see that this pattern even remains a replicator indefinitely, as a rectangle of 2×4, were one to occur, will explode…

• I reported in the alternating rules topic a rule which explodes only along even mirror axes. I seem to have found a plain example of the same: B013458/S02345. For instance:
x = 348, y = 2, rule = B013458/S02345
o10bo333bobo$o10bo!

The seed on the left keeps growing until it collides with the "pseudoblinker" at generation 35951. After this, action starts winding down, tho this does take until generation 86992 to be completed.

Overall this is a stabilizing rule. Those ubiquitous p2 "pods" grow from a single domino; any number of other more or less rectangular p2s are possible. Note also the butterfly-like p18 and the two p4s you can see in the ash of the methuselah above.

There's also a c/10 ladder and c/10 and c/6 wicks:
x = 32, y = 25, rule = B013458/S02345
31bo$b28o$bo$b28o$31bo4$21bo$b20o$b20o$b20o$b20o$21bo4$b5o$b5o$b5o$6o$
6o$b5o$b5o$b5o!

Alas, the first two are of different thicknesses, so no spaceship…

• Speaking of ladders, I find B013456/S234 a fairly interesting rule. It is chaotically exploding, but in an unusual fashion — it leaves perfectly still sparse ash behind, much like your usual stabilizing rule. All growth seems to occur due to the ubiquitous c/4 "shoots"; if perturbed, they burn cleanly at c/2 (at period 48). Once this reaches the end, a number of things may happen to the shoot:
—dies out cleanly
—leaves some debris
—gives birth to one sideways shoot (plus a little debris?)
—gives birth to two sideways shoots
—is cleanly reborn and continues in both directions
—the back end stabilizes, the front end continues
—gives birth to a backwards shoot stabilized from the front

Also, a shoot's end hitting the stalk of another will, in addition to igniting the second one in both directions, create two new shoots alongside the first one.

I find this rule very interestign to watch. This is the smallest chaotic growth pattern I've found:
x = 14, y = 3, rule = B013456/S234
2o9b3o$2o9b3o$2o!

There's also a symmetric p280 burning reaction which generates a lot of junk; in the previous example, you can see one starting in the upper right around generation 13700 (terminates around gen 17600).

And here's a collection of other ladder shapes, with wider ones at c/8, c/16, and c/76, and a c/12 fuse for the basic shoot:
x = 54, y = 22, rule = B013456/S234
48b2o$48b2o$48b2o8$2o7b2o9b2o3b2o6b5o$2o7b2o7b11o4b2ob4o4b10o$3o6b2o7b
11o4b7o4b10o$9b2o7b11o4b7o4b10o$18b11o4b7o4b10o2$7b6o$7b6o$7b6o$7b6o$
8b4o$9b2o!
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Re: B0/D8 rulespace

Postby Extrementhusiast » October 7th, 2011, 10:15 am

B014/S1: Very interesting to watch. It's as if the rule is a collection of greyships!
x = 173, y = 102, rule = B014/S1
47b3o$47b3o$47b3o7$65b2o$65bo32bo$97b3o$95b5o$93b4obo$89bob4obo$90b3ob
o$88b3obo$86b3obo$85b2obo$86bo6$171bo$170b3o$166bob5o$167b3obo$165b3ob
o$163b3obo$161b3obo$159b3obo$157b3obo$155b3obo$153b3obo$151b3obo$149b
3obo$147b3obo$145b3obo$143b3obo$141b3obo$139b3obo$137b3obo$135b3obo$
133b3obo$131b3obo$129b3obo$2bo124b3obo$b3o121b3obo$2b3o118b3obo$3bo
117b3obo$120b2obo34bo$121bo35b2o$155b6o$153b8o$151b8o$149b8obo$147b8ob
o$145b8obo$bobo139b8obo$5o138b6obo$b3o141b2obo$146bo13$148bo$144b5o$
142b8obo$140b12obo$138b16obo$136b20obo$134b24obo$132b28obo$130b32obo$
128b36obo$126b40obo$124b44o$122b48o$122b48o$124b44o$126b40obo$128b36ob
o$130b32obo$132b28obo$134b24obo$136b20obo$138b16obo$140b12obo$142b8obo
$144b5o$148bo!
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Re: B0/D8 rulespace

Postby Tropylium » October 7th, 2011, 11:41 am

Wouldn't "whiteships" be more appropriate?

Checking a few close-by rules, B0148/S12 also has a "shoots" explosion structure leaving ash… tho these decay at 5c/36 or 3c/46, and gro at c/2, so the shoots are what dominates the population. Also, the ash is sufficiently sparse that I'm not sure areas of nothing but ash actually expand; the attracting phase may actually be low-density chaos, akin to eg. Star Wars.
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Re: B0/D8 rulespace

Postby Extrementhusiast » October 7th, 2011, 6:20 pm

B026/S1: Diagonals FTW!
x = 303, y = 164, rule = B026/S1
292bo7bo3$296bo$296bo$296bo$290bo5bo5bo$296bo$296bo$296bo3$292bo7bo25$
237bo$234bobo14$277bo$198bo77bo16$235bo5$238bo$237bo14$215bo$212bobo
19$195bo2$195bo3bo$198bo35$174bo4$175b2o2$180bo$177bobo$4bo170bo$3bo$
6bo168bo$5bo168bo$8bo$7bo2$3bo$obo!
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Re: B0/D8 rulespace

Postby ebcube » October 7th, 2011, 8:22 pm

You're not going to believe this. On the rule that Extrementhusiast just posted, there's a c/4 orthogonal spaceship. Of width 1. No, I'm not making it up. I found it with gfind.

x = 1, y = 50, rule = B026/S1
o4$o$o$o4$o3$o2$o3$o4$o3$o$o$o$o$o$o$o$o$o$o$o3$o3$o$o$o5$o$o!


Obviously, this rule emulates a 1D CA. But... wow.

EDIT: Also, gfind finds this really really thin and long c/4 and c/6 orthogonal spaceships. One of them is 5 cells wide by 224 (!) cells high.

x = 26, y = 224, rule = B026/S1
23bo3$23bo2$23bo$23bo$22bobo$21bobobo$22b3o$21b5o$22b3o$22b3o$21b5o$
21b5o$21b5o$22b3o$22b3o$22b3o$21b5o$22b3o$21b5o$22b3o$22b3o$21b5o$21b
5o$21b5o$21b5o$22b3o$22b3o$21b5o$22b3o$21b5o$21b5o$21b5o$22b3o$22b3o$
21b5o$22b3o$22b3o$21b5o$21b5o$21b5o$21b5o$22b3o$22b3o$22b3o$21b5o$22b
3o$22b3o$22b3o$21b5o$22b3o$22b3o$22b3o$21b5o$22b3o$21b5o$21b5o$22b3o$
21b5o$22b3o$22b3o$22b3o$22b3o$22b3o$21b5o$21b5o$22b3o$22b3o$22b3o$22b
3o$22b3o$22b3o$21b5o$22b3o$22b3o$21b5o$21b5o$22b3o$22b3o$21b5o$22b3o$
22b3o$21b5o$21b5o$22b3o$21b5o$22b3o$22b3o$22b3o$21b5o$21b5o$21b5o$21b
5o$22b3o$22b3o$21b5o$22b3o$22b3o$22b3o$22b3o$21b5o$21b5o$22b3o$22b3o$
21b5o$21b5o$22b3o$22b3o$21b5o$22b3o$21b5o$21b5o$21b5o$22b3o$21b5o$22b
3o$21b5o$21b5o$22b3o$22b3o$21b5o$22b3o$22b3o$21b5o$21b5o$21b5o$22b3o$
21b5o$21b5o$21b5o$22b3o$21b5o$23bo$22b3o$23bo$23bo$22b3o$22b3o$23bo$
22b3o$23bo$22b3o$21b5o$22b3o$23bo$21b5o$22b3o$21b5o$21b5o$bo20b3o$2o
20b3o$3o19b3o$b3o18b3o$3o18b5o$b3o18b3o$b2o19b3o$3o19b3o$4o18b3o$b3o
17b5o$4o18b3o$4o17b5o$4o18b3o$4o17bobobo$3o19b3o$3o20bo$4o19bo$b3o19bo
$3o20bo$4o19bo$3o20bo$b3o18b3o$b3o18b3o$4o19bo$3o20bo$3o19b3o$3o19b3o$
b3o19bo$4o18b3o$b3o18b3o$b3o18b3o$b2o19b3o$b2o20bo$b2o19b3o$3o20bo$b2o
20bo$4o18b3o$b3o18b3o$4o19bo$3o19b3o$4o18b3o$3o19b3o$b2o19b3o$b3o18b3o
$3o20bo$b2o19b3o$b3o18b3o$4o19bo$b2o20bo$b2o20bo$b3o19bo$4o18b3o$b3o
19bo$b2o20bo$b2o19b3o$b3o19bo$3o20bo$b3o19bo$b3o19bo$3o20bo$3o19b3o$4o
19bo$2bo19b3o$2bo19b3o$2bo20bo$b2o19b3o$b2o20bo$b2o20bo$b2o19b3o$b3o
19bo$2bo18bo3bo$2bo$2bo20bo!


EDIT2: More data. I've found a 1D c/6 spaceship. The CA it is emulating has a neighbourhood range of 3. Here is the spaceship of size 1x614:

x = 1, y = 614, rule = B026/S1
o4$o$o$o4$o3$o3$o3$o3$o$o$o4$o$o$o$o$o$o$o3$o2$o3$o$o$o3$o3$o3$o3$o5$o
$o$o$o$o$o$o4$o4$o4$o$o$o$o$o3$o2$o3$o4$o$o$o$o$o3$o2$o2$o2$o3$o$o$o$o
$o4$o$o$o$o$o$o4$o$o$o$o$o4$o3$o2$o2$o2$o3$o4$o$o$o$o$o$o3$o2$o3$o5$o
3$o2$o2$o3$o3$o2$o2$o2$o3$o4$o3$o2$o2$o3$o$o$o3$o2$o2$o3$o$o$o4$o$o$o
4$o$o$o3$o3$o4$o4$o$o$o4$o4$o4$o$o$o3$o2$o2$o3$o3$o2$o2$o3$o4$o4$o$o$o
4$o$o$o4$o3$o3$o4$o3$o3$o3$o3$o3$o$o$o$o$o$o$o$o$o$o4$o$o$o3$o2$o3$o$o
3$o2$o2$o3$o$o$o3$o3$o4$o$o$o4$o4$o3$o2$o3$o$o$o$o$o$o$o$o$o$o$o4$o$o$
o$o$o3$o3$o$o$o$o$o$o$o$o$o$o$o$o$o$o$o3$o3$o$o$o$o$o$o$o4$o$o$o$o$o3$
o2$o2$o2$o2$o2$o2$o3$o3$o4$o$o$o4$o$o$o$o$o3$o2$o3$o3$o2$o2$o3$o$o$o$o
$o4$o$o$o3$o2$o3$o3$o3$o$o$o$o$o$o3$o3$o3$o3$o4$o$o$o3$o2$o2$o3$o$o$o$
o$o$o4$o$o$o$o$o$o$o4$o$o$o$o$o$o$o3$o2$o2$o2$o3$o$o$o4$o3$o2$o2$o3$o$
o!


To search for these spaceships, use the arguments for gfind /oXnY/*Z/lW, where X is the desired speed (for example, enter 8 to search for c/8), Y is a even number (2 is good enough), Z is a low enough number (the spaceship above was found with Z=10) and W = X * Y * 4 * 2 (gfind won't try to find spaceships of width lower than 4). You will probably have to both invert the resulting spaceship and paste it on an odd generation.

EDIT3: 1D c/8 spaceship. It is considerably shorter than the previous spaceships. I think that spaceships of any (even) speed are possible, as well as oscillators of any (even) period

x = 1, y = 69, rule = B026/S1
o$o4$o$o$o3$o2$o2$o2$o3$o3$o3$o4$o$o$o$o$o$o$o4$o$o$o$o$o$o$o3$o3$o$o$
o$o$o$o$o4$o4$o3$o!


EDIT4: Not only even speeds! c/7 incoming:

x = 1, y = 436, rule = B026/S1
o4$o$o$o4$o3$o3$o4$o$o$o$o$o$o$o4$o$o$o$o$o3$o2$o3$o4$o3$o3$o4$
o$o3$o2$o2$o3$o$o$o3$o3$o$o$o4$o3$o3$o3$o4$o3$o2$o3$o4$o$o$o4$o$
o4$o4$o$o$o$o$o$o$o4$o$o$o3$o3$o$o$o$o$o$o$o$o$o3$o2$o3$o4$o4$o$
o$o$o$o4$o3$o2$o2$o3$o3$o2$o3$o3$o3$o$o$o4$o$o$o4$o$o$o3$o2$o3$o
$o$o$o$o$o$o$o$o$o$o3$o3$o3$o3$o$o$o3$o3$o$o$o3$o3$o4$o$o$o3$o2$
o3$o$o$o4$o$o$o$o$o3$o2$o2$o2$o2$o2$o2$o2$o3$o$o$o$o$o4$o$o$o$o$
o3$o3$o3$o3$o$o$o3$o2$o3$o4$o$o$o4$o$o$o4$o$o$o$o$o4$o$o$o$o$o3$
o3$o$o$o$o$o$o$o4$o3$o3$o3$o3$o$o$o4$o$o$o$o$o3$o3$o$o$o$o$o$o$o
$o$o$o$o4$o$o$o3$o3$o$o$o$o$o4$o!


Would it be possible to engineer ships of any speed?
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Re: B0/D8 rulespace

Postby Extrementhusiast » October 8th, 2011, 5:56 pm

*jaw drops*
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Re: B0/D8 rulespace

Postby ebcube » October 8th, 2011, 8:22 pm

My reaction exactly. I don't think a spaceship of width 1 in what is tecnically a 2D automaton had been found before. David Eppstein' smaller gliders list (from his CA database) lists a 2x2 diagonal glider as the smaller glider. Then again, 1x50 isn't exactly small, it's more like thin.

I should try to do a ruletable for the 1D automaton, but I'm not sure about how to emulate a range 3 CA.
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Re: B0/D8 rulespace

Postby Tropylium » October 9th, 2011, 10:31 am

ebcube wrote:I should try to do a ruletable for the 1D automaton, but I'm not sure about how to emulate a range 3 CA.

You needn't; the easiest way may be to just simulate both "phases".
Even generations > B1/S02
Odd generations > B/S02

Here are a few 1D oscillators BTW, of periods 16, 16, 24, 32, 24, 40, 48, and 104:
x = 39, y = 36, rule = B026/S1
16bo3b3o3bo5$12bo3bo3b3o5$12bo3bo3b3o3bo3bo5$8bo3bo3bo3b3o3bo3bo3bo5$
4bo3bo3bo3bo3b3o3bo3bo3bo3bo5$8bo3bo3bo3b3o3bo3bo5$4bo3bo3bo3bo3b3o3bo
3bo5$o3bo3bo3bo3bo3b3o3bo3bo!


Now taking bets on how long until someone puts together a puffer (or wickstretcher, or gun, or rake, or replicator…)
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Re: B0/D8 rulespace

Postby knightlife » October 9th, 2011, 12:34 pm

Growing rake fires salvos of increasing size (2^n):
x = 17, y = 14, rule = B026/S1
o8$12bo$11bo$14bo$13bo$16bo$15bo!


As for the 1D oscillators, continuing your last sequence by adding dots to the left makes a new oscillator (often):
x = 63, y = 1, rule = B026/S1
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b3o3bo3bo!


It only degenerated once to p2 before reaching p200.

EDIT:
Those "blinkers" are replicating.
Here is a p512:
x = 71, y = 1, rule = B026/S1
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b3o3bo3bo!


Just for fun, a p210624 according to oscar:
x = 211, y = 1, rule = B026/S1
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3b3o3bo3bo!
Last edited by knightlife on October 9th, 2011, 1:04 pm, edited 1 time in total.
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Re: B0/D8 rulespace

Postby ebcube » October 9th, 2011, 1:04 pm

The c/5 1D spaceship is surprisingly small:

x = 1, y = 19, rule = B026/S1
o3$o2$o2$o3$o$o$o$o$o4$o!


EDIT: And it has a 2D tagalong!

x = 16, y = 23, rule = B026/S1
11bo3bo4$o12bo$o12bo$o12bo3$o12bo3$o12bo4$o12bo3$o12bo3$o12bo!
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Re: B0/D8 rulespace

Postby Extrementhusiast » October 9th, 2011, 1:08 pm

Oh, my! This rule has far more potential than I ever imagined!

EDIT: Gun!
x = 29, y = 13, rule = B026/S1
bo$2bo25bo$27bo8$bo$o25bo$27bo!


And single dots can be used to eat the gliders:
x = 53, y = 53, rule = B026/S1
41bo$14bo10$o3$51bo6$13bo$14bo25bo$39bo4$26bo4$13bo$12bo25bo$39bo6$bo
3$52bo10$38bo$11bo!
Last edited by Extrementhusiast on October 9th, 2011, 1:19 pm, edited 1 time in total.
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Re: B0/D8 rulespace

Postby knightlife » October 9th, 2011, 1:16 pm

A small lightspeed spaceship traveling in an ocean of dots:
x = 205, y = 1, rule = B026/S1
o3bo3bo3bo3bo3bo3bo4b4o4b4o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo!

The dots are restored after it passes by.

EDIT:
A smaller one launches a 2D puffer:
x = 117, y = 10, rule = B026/S1
116bo2$o3bo3bo3bo3bo3bo3bo3bo4b4o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3$116bo4$116bo!
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Re: B0/D8 rulespace

Postby skomick » October 9th, 2011, 4:23 pm

SE glider bounces against SW glider. SW glider stays on path.
x = 30, y = 5, rule = B026/S1
3bo$obo25bo2$28bo$29bo!

Seirpinski triangle generator:
x = 25, y = 9, rule = B026/S1
bo15bo$o15bo$19bo$18bo$21bo$10bo9bo3bo$3bo7bo2$11bo!

Wickstretcher:
x = 10, y = 8, rule = B026/S1
5bo$4bo3$bo7bo$o$3bo3bo$obo!

Rake breeder:
x = 7, y = 7, rule = B026/S1
o$bo2$bobobo$6bo$3bo$4bobo!
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Re: B0/D8 rulespace

Postby knightlife » October 9th, 2011, 10:44 pm

Small diagonal spaceship is replicator based:
x = 13, y = 12, rule = B026/S1
8bo$9bo2$11bo$12bo4$o$bo2$bo!
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Re: B0/D8 rulespace

Postby Tropylium » October 10th, 2011, 7:07 am

A slightly larger replicator "bomber" spaceship:
x = 18, y = 23, rule = B026/S1
17bo$10bo$11bobo$16bo7$7bo2$5bo3$12bo2$10bo4$o$bo!


A few capped replicator guns:
x = 264, y = 44, rule = B026/S1
3bo3$o$77bo2$149bo$74bo2$146bo11$203bo2$245bo$200bo2$242bo11$37bo69bo
69bo39bo39bo$36bo69bo69bo39bo39bo3$43bo69bo69bo39bo39bo3$40bo69bo69bo
39bo39bo!


Basic p16 monorake, can be easily turned into a puffer engine:
x = 43, y = 95, rule = B026/S1
$3bo$obo9$24bo6$22bobo$25bo9bobo$34bo$39bo$34bo$41bo$36bo$41bo$24bo13b
obo2$30bo$16bo12bo$13bobo5$4bo$bobo9$24bo6$22bobo$25bo9bobo$34bo$39bo$
34bo$41bo$36bo$41bo$24bo13bobo2$17bo12bo$14bobo12bo16$25bo6$23bobo$26b
o9bobo$35bo$40bo$35bo$42bo$37bo$42bo$25bo13bobo2$31bo$30bo!


p24 puffer engine:
x = 8, y = 10, rule = B026/S1
obo$3bo$o$bobo3$4bobo$bo5bo$4bo$5bobo!


Chaotic salvos from colliding replicators:
x = 5, y = 7, rule = B026/S1
3bo$4bo4$o$bo!

BTW I notice some kind of a parity rule going on: colliding replicators of opposite "color" (in the chessboard sense) tend to create messy explosions, while those of the same color lead to more orderly results. Not always

skomick wrote:Wickstretcher

I think that's a dense backrake.
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Re: B0/D8 rulespace

Postby Tropylium » October 11th, 2011, 6:16 pm

A quick ruletable for the 1D subautomaton. State 1 is the "thin" phase, state 2 the "fat" phase.
n_states:3
neighborhood:Moore
symmetries:none
# 0 off
# 1 on, even phase
# 2 on, odd phase

var a={0,1,2}
var b={a}
var c={a}
var d={a}
var e={a}

0,0,0,a,b,c,d,e,1,2
0,1,0,a,b,c,d,e,0,2
0,0,1,a,b,c,d,e,0,2
0,1,1,a,b,c,d,e,1,2
0,2,0,a,b,c,d,e,0,1
0,2,2,a,b,c,d,e,2,1
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Re: B0/D8 rulespace

Postby knightlife » October 11th, 2011, 11:58 pm

This 15-cell precursor becomes a c/12 orthogonal spaceship, found by chance:
x = 33, y = 1, rule = B026/S1
o3bo3bo3bo3b9o3bo3bo!

One of the phases of the spaceship has a population of 15 cells as well.
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Re: B0/D8 rulespace

Postby ebcube » October 14th, 2011, 10:01 am

That's great!

I'm thinking about writing a small program to find 1D spaceships on this rule.
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Re: B0/D8 rulespace

Postby knightlife » October 16th, 2011, 10:18 pm

An exhaustive search for 1D spaceships reveals the 2c/10 spaceship is indeed the first to show up:
Small section of file:
x = 16, y = 141, rule = B026/S1
2obob7obo5$2obob7obobo5$2obob7ob2o5$2obob7ob3o5$2obob8o5$2obob8o2bo5$
2obob8obo5$2obob8ob2o5$2obob9o5$2obob9obo5$2obob10o5$2obob11o5$2ob2o5$
2ob2o10bo5$2ob2o9bo5$2ob2o9b2o5$2ob2o8bo5$2ob2o8bobo5$2ob2o8b2o5$2ob2o
8b3o5$2ob2o7bo5$2ob2o7bo2bo5$2ob2o7bobo5$2ob2o7bob2o5$2ob2o7b2o5$2ob2o
7b2obo5$2ob2o7b3o5$2ob2o7b4o5$2ob2o6bo!

The precursor is just 16 bits long although the actual spaceship cycles through 18-18-19-19-20 on even tics.
This doesn't prove it is the smallest 1D spaceship just yet, but it most likely is the smallest.
To conclusively prove it is the smallest the search must continue through 20 x 1 size.
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Re: B0/D8 rulespace

Postby Osiris » October 18th, 2011, 3:23 pm

B016/S12:
A self-complementary rule, the behavior of a pattern in an even generation is the same as that of the negative pattern in an odd generation and vice versa.
It has this replicator:
x = 3, y = 4, rule = B0168/S12
bo$obo$obo$bo!

The spaceship database at http://fano.ics.uci.edu/ca/ lists two spaceships (one of which is not directly displayed in the database):
x = 7, y = 18, rule = B0168/S12
bo4bo$obo$obo$bo7$4bo$3bo$bobo$o$o$bobo$3bo$4bo!


I got very close to making a greyship:
x = 29, y = 34, rule = B016/S12
b2o$o2bo2$b2o3b2o18b2o$b2o2bo2bo16bo2bo$b2o$b2o3b2o3b2o8b2o3b2o$b2o3b
2o2bo2bo6bo2bo2b2o$b3ob3o18b2o$b3ob3o3b2o3b2o3b2o3b2o$b7o3b2o2bo2bo2b
2o3b2o$b8ob3o8b3ob3o$b8ob3o3b2o3b3ob3o$b12o3b2o3b7o$b13ob4ob8o$b13ob4o
b8o$b27o$b27o$b27o$b27o$b27o$b27o$b27o$b2o2b19o2b2o$bob2ob17ob2obo$b2o
2b19o2b2o$bo4b2o2b9o2b2o4bo$bo4bob2ob7ob2obo4bo$6b2o2b9o2b2o$6bo4b2o2b
3o4bo$6bo4bob2ob2o4bo$6bo4b2o2b3o$11bo4b2o$11bo4b2o!
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Re: B0/D8 rulespace

Postby ebcube » October 18th, 2011, 6:22 pm

Osiris wrote:B016/S12:
A self-complementary rule, the behavior of a pattern in an even generation is the same as that of the negative pattern in an odd generation and vice versa.


If I recall correctly, that property is common to every B0/D8 rule.

I've been trying to make a greyship with your attempt with no luck yet. Because of the property you mention, you can insert an inverted odd-pattern spaceship or replicator inside your greyship (whiteship?); this could be used to perturb the "tail" (or a similar tail) that your attempt leaves behind and destroy it.
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Re: B0/D8 rulespace

Postby Extrementhusiast » November 20th, 2011, 9:20 pm

On a different note, B0123/S35 has a common diagonal wickstretcher:
x = 100, y = 100, rule = B0123/S35
4ob3o2bo3bo2bo3b6o2bob2o5b2obo5bob3o2bob2o7bobo3bo2bobob2obobob2ob4o5b
obo$bo5bo2bo3b2o2b3o4b2ob4ob2ob2obobob2ob2o9bo4bo2bo2bobobo2b2o2b4o2bo
bobo2b2o$4ob5o7b2obob2o2b2o2b4o3b7o2b3obo4b3ob3ob2ob3o3bo6bo3bo2bo2b2o
2bo$bobo2bo2bobobobobob2obob2obo5bo2bo7b6o2bobo7b2o3b7o3bo2b2o3bo3bo2b
o3bob2o$b2ob2o2b2ob5ob2obobobo4b2obobo2b3ob2o4b3o6bob5ob2o2bo3b2o2bobo
2b2obobo3b3ob4obo$b2o2b3o2b2ob2ob2ob3obob4o8bo3bo2b2o2bob3o3b3o2b3o3b
2o4b2o2b4obobo3bob5ob2o$2bo3b2o2bobo2bo2bobob2o5bobob3o2b2ob2o2bo9bob
2ob3o2bo6b2o2bob3ob2obobob2obob2o3bo$4obo7b2o2b6ob5ob2o4bo2b8o2b7o3b2o
5b2o4bo2b2obob2obob2o2bobob2obo2bo$bobo2bo3b4o2b3ob2o3bob3obobobo2b3o
4bob3o2bo6bobo4b2obob4o2b4o6b6obob2o$3b2o3bo3bo2bob2obo2b3ob2o2bobo2b
2o2b4o4bobo2bo2bo3b4o2bobo2bo5b4o2bo6b3ob2o2b2o$2obo2bob5obo2bobob2ob
6ob2o2bo2bo2bob2o2bob3ob2o2b2o3bobob2o2b2ob5o2b2obo4b3o5b3o$3b3ob2ob3o
2b2ob4o3b3o2bo2b2obob2o3bob2o2bo2b5o2bob2o3b2o4bo4b2obo2bob7o2b2obo$2o
b3o2b2o2b4obobo2b3obob4obob3obob7obo5bo2b2o3b3o3b2o3bo3bo4b2obo2b2o2b
2ob3o$o2b3obo2b3o3bo4bob2ob2obo3b3obo2bo2bob8ob5ob7obo3b2obobo2b2ob3o
2bob2ob3ob3o$b2o2b3ob2o3bo3b3o3b6obob3o4b3ob2o2b2obo3bob2ob4ob2obobo3b
3o3bo2b2o2bo4b2ob2ob2o$2bo2b4obo2b7o2b7ob5obobo2b2ob5o3b4o2bob5o3b7obo
2bo5bob3obobo2bo$o3bobob7o3bo2bo2bob4o2b6o4bob2o3b5o3b2o7bo4bob3obo2b
3ob2obob2o3bo3b2o$2ob2o2b5obo3bo3bo5bob4o2b4obo2b2ob6o5b3o2bo4b2ob4o2b
3o2b3o2b3o2bob4o2bo$2o2b2o5b2o5b4ob2o2bobob2o2bobob2o5b3o3b2obo3bobob
3o2bobo6bob2o4bo2bob2ob2obobo$b3o3b2ob5ob2o5bo3b2o2b4o4bob2obob2ob5obo
2bo2b2o2b4o2bo6bo5bob2o2bob3obo$b5obobob5obo2bo6bo3b2ob2obobo3b2o3b4o
2bob3o2b3obobobo2bobo2bob2ob3ob2o3b2obob3o$2o3bo2b2ob3obo2bobob3o4b2ob
2ob2obo7b2obob2obobob7ob2ob2o2b2obo4b3o2bo7b4obo$o3bo2bobo4b8o2b2o2bob
ob3o4b4o3bob3ob3obo3b3o3bo3bobob2o4bo2b3ob3obobo3b3o$obob2ob2o2bo2b3ob
3o4b3ob5ob2obo3bob2ob4obobobob6obob4o5bo5b2ob2ob5o3b3o$bo2b2obob3o2bo
4bobobo5b2o2bob3obobobobobobo5b3o2b6obo2bobobo2b3ob2o3bo3bob5ob2o$obob
4ob4o2b3o4bobobo2b3o2bo4bo3b4o4bobobobo2bob3o3b5obo2b10obo3bobo$o2b2ob
o3b3o2b5o2b4obo2bo2bob4ob4o2bob2o2bo2b2ob3o6bob7ob2obo5b2o2b2ob2o2b3o$
3ob2o5b2o3b3obo2bob2o3bo2bo4b4obobob2o4bo2bob4o2b2o5bo7b2o4b2obo2bo2b
2obo$o2b3ob3o2bobo5bobo2bobo2bobo4b2ob2ob2ob3o2b2o4b2ob3o2bo2bo2bo2bo
3bo2bo2bo2bo2b4o2bo$2b3ob3obob2o2bo3bob6ob4o2bo2b3obob4obobobobo4b3o2b
4obo2b3o3b4ob3obobo2b4o2bo$b3obo2bo3bobobob2obo2b4o2bo3bo2bo2bo3b2obo
2bo2bob5o2bo3b3ob2o2bob3o6bo4b3o2bo$2obobobobo2b2obob8obob2ob4obob6o2b
obo3bob3ob3ob2obo2bob2o3bo3b2o4bobobo2b2o$o4bo2bo3bo7bobo3b3o5bo3b2o3b
2o2bobobo10b2o2b3ob3obob2o8b3ob2o3bo$bobob2ob6ob3ob2obo2b2o2b2o2b2o2bo
b2o6b3obob3o2bo3b2o4bo2bo2b4obo2bo4bobo3b2ob3o$2o4b3o2b8o4bo3bo5bob2o
4b2o2b2o2b3ob6obob5obob3o3bob3o3b7o3bobobo$o2bo2b2obo3bob4ob5o3bo3b2ob
o2bob3obob2o3bob4o2b2o4bobo2b2o4bob2o10bob3ob2obo$obo3bo3bo5bobob8ob2o
9bo2bo3b5obobo2bob2o5bobob2o2b2ob2o4b4obob2o3b3o$o2b2obob2o2b2o2bo2bo
3bo3bo3bo2bob2ob4o2b3obo2bob3o2b2o3b3obo4bobo2b2obo4b2o4bob3o$o2bob5o
2b2obob3o2bobo2bobo5b6ob4o2b5o2b2o7b2obo2bobo4b5o3b2ob3o2bo5bo$o2b2o5b
5ob3o2bobo3bo2b2ob2o2bobo2bo2bob2o2bo4bo3b2obo2b3ob5o2bo2b2obob4o2b2o
2b2obo$3o2b2ob2ob2o3bo2b4ob4o7bobo4b3obo2b2o5b3ob3ob2ob4o3b4o3b2ob4o5b
2obo$bo8bo3bo2bo2b2o2bobo2bobo2b3obo2b2obobo4bobobob3o3b2obo2b2ob2o4bo
b2o3bo2b4ob4o2bo$ob3ob3obob2obo5bo2bobobo3bobob7o2b6obo2bo3b2o2b7o2b4o
4bo5bobobob3ob4o$3o6b3o3bo4b3o2bo2bo3b2o6bobo3bo2b3o2bo4bobo3b2ob2o8bo
3b3obo2bo5bobo$bob4obobob3ob2obo3bobo3bobobobo2bob3obo3b2o3b2ob2o2b2o
2bob2o2bo4b6o5bo2b3o3bobobo$o3b3o2bo6b4obob2o4bo2bob4obobobobo2bob4o2b
3o3bo2bo3b3o3b3o4bo3b2ob2obob2ob2o$bobo5b2obobo3bo4bo5bob2obo2b3o3bobo
2b2ob3o3b3obobo3bo3bobo2bo2b2o2b3o2b2ob6obo$2o3bobob3obob5ob3o5b4ob2ob
o2b3obo6b3o2bobo3b3o3bobobobobob2o3bob2obob5obob2o$2b2o4bob3obo3b3o5b
3obobobob3ob3o2bo2b3obob3obobo3bo2bob4ob7obo6b3ob6o$2obob2ob3o3b2ob6ob
ob3o2b3obobobob2obo2b2o4b3ob2ob2o2bobob2ob2obo2b4o2bo2bob5o2bobobo$o2b
o2bo2b4obo2bo2b2o2b2o4bo5bobo2b2ob2obo5bo4b2o2b4o2bob10o2b2o2b2o5b3obo
bo$3b5ob2o2b4o2bobo2b3obob2o3b2o2bo2bo3b2ob5obobo4b2o5bo4bo4b7o6bob2o
2bo$4o10b3ob3o3bo3b5ob3o2b2ob4o2b2o2bo2b3ob2o2b2o2bo2b2obobo5bo3bobo6b
2obobo$bo3bob2obo3bo4bobo2bobobo4b2ob4ob2o4b2obobobobo4bob3o3bo3bob2o
6b2ob4o4bob3o$10bobo2bo6bob2ob3o3bobobob2obo2bobo3b3ob5o3b4o3b2o2bob2o
b3ob3ob2o2b2ob2ob2o$2obo4b2o5b3o2bo3bobobob3obo2b2o2bobo2bob2o2bob2ob
3ob3obob3o4b2o2b2o2bobo2bob2obobob2obo$ob2obo4b6obo6bo3b4obo2bob2obo2b
2obo2bo3b4obo2b2o3b4ob2obob3o3b3o6bob2ob3o$2ob3ob3o3b2obobobobo3bo2b2o
bo4b3obob2obob2ob2obob2o2b3ob5obo3bo3b9o3bob2o2b4o$ob4o2b4o3bob3o2bo2b
o5bo5b5ob5ob2ob5o3bobob3o3b3obo7bo2b5o2b5ob2o$2o2bo4bo3b2o7b3ob3o3bo3b
o2bob2o2b2o5b2o3b3o2b3o4bobo2b2ob2o2bo2bo3b4ob3o$bo3bo2b3o7b3obo3bo5bo
2b3obobo2bob2ob3o2b3o3b4obobo4bobobo4bo2b4o2b3ob2o3bo$o4b4obobo2b2obo
3bob3o2bob2obo2b2o2b5o2b2obob2ob5obo2bobo4bo2b3ob2o4bobob2o4b3obo$2ob
3o3bo2b5o4b3ob2o5b2ob4o2bo3b4o4bo3bobo4b3o5bob2o2bobo4bo6b4obo$bobobo
3bob5o2b3obo2b2o3b3o3bob2ob2o2b2o2b5o4b4o2bobo4b3ob6o7bo2b2ob6o$o2b2ob
2o4b4o4b3o2b4obob2o3b2o2bob3o3b2o2bo5bo2b2obob3o2b2o2b2o8bo2b2o7bo$b3o
2bobo2b10ob5ob2ob2o3bob2obobo2b2o2bo2bo2bob3ob4ob2ob2ob8o2b2o2bobobob
4o2bo$obo3b5ob2ob4ob2ob6o2bob3o2bo2b2obo5bobob6o2b4o2b3ob5o3bo3b3ob4ob
ob2obo$ob6obobobobo3bo3b2ob2ob3ob4ob3o2bob5o3bob2o5bo3b2o4bo2bo2b2o3bo
3b2ob2ob4o$obobo2bob3obobobo2bo5b4obo3bob2obobo2b3ob2ob2obobobo2b2o4b
4o2b2ob2ob2obo2bobo2bo2bo3b2o$bobob3o3bo4b3o2bo8b4o2bob2o2bobobob3ob3o
2b2o2bobo4bo3b4obo3bobo3b2o2b5o2b2o$b4o2b3ob3o8b4o2b2o2b2ob3o5b2o3b2ob
o3b2ob3o2b3obo3b3o2b2obo6b2obob2ob2o3bo$3o3bo2b2ob2ob2o2b2o2bo3b4o2b4o
3bo2bobo2b4ob3ob2o2b2obob2ob2o2b2ob4o2b2obob12o$3b7o2b2o2bob4o2b4o3b2o
bo2bo2bo2bo3b2o3b4o2b4o2bob2obob2ob3o2b2obo2b3ob4o$7obob6o2bobo3bo3bob
ob4obob4o2bo3bo6bo2bo6b5o4bo3b3o3b3obo2b3o2b3o$5bo4bobobo2bo2bob4o2bo
5bo2b4o2bo2b3o3bob2o3b4o2b2obobo3b8o4b2o2b2o4b2obo$ob2obob4o2b3o4bo2b
4ob3obo2b3o7bo4bo2b2o2b2o4bo3bo4b3obobobob4o2bo3b4ob3o$o4b4obo3b3obob
4o2b2ob2o4b6obobo7b5ob2o3b5o2b2ob4obob3o2bob3o4bob3o$2bobo6b5obo2bo2b
5obo3b2o3bob2obo2b2o2bob5o2b6o3bo3b4o3bobob4o5bob2o3bo$4o5b5o3bo2b2ob
2o3b4ob2o3bob3ob3ob2obo4b2o2b2o3b2o2bo2bo2bob3obo2bo2bob3ob2ob2obo$b5o
b3o2bob2o5b2ob5o2b2o3bo4b2o3b2o3bob2o2b2obo2b2o3b3o3bo2b3obo5b2ob4o2bo
bo$5b3ob2o9bo6b2o2b2o3bo2b2ob2o3b4obob2obo2bob5ob3obobobo8bo2bo2bo5b2o
$5ob2obo4b3ob2o2bobo2b3o2bobob2obobob2obob2o3bo2bob2o2bo2b2o3b3obob2ob
3o5b3o3bobo$bobobo5bo2bobo2bobobo2bobobo2b3o5b6ob2o2bo5bob2obo2bo4b2o
2b6ob2o2b3ob2o2b2o3bo$4ob2obo2bobo4bo5b2ob4obo3b5o3bob2obobob4ob2o5b2o
bo6b4o4b3ob2obob2ob5o$3o2bo4b4o2b3o3b2o3b2obo4b3o2bobob2obo7bobob4o2bo
bo2b5obo3b5obo2b2obo2b3obo$o2b2obob2o2b2o2bo4b3obo2bo2b2ob4ob6ob3ob3ob
o2b2obobob3obo2bob5o2bo2b2o3b2o8b2o$4obob3o2bo2bobo4b4o6b2obo4b2o2bo2b
ob2ob2o3b3ob2o6bob2obo4b2o2b3o2bo2b2o2b2o2bo$3b2o3b2obob2ob4ob4obob2o
2bo5bobob2ob3o3bobob3obo6b2obobob2o2b2o3b2o4bob2obo4b2o$4bob3o6bobo2b
5obo2b7o3b8obobobob2o3bob2ob2obobobobo2bo4bobob2ob2obo2bobob2o$bobob2o
3b3o2b3o7b2ob5o2b4ob8ob9obobo4b2o2b2ob4o3bob6ob11o$2b3ob2ob2ob3ob2o2b
2o2bo2bo2b2ob4obo4bobobo3bo2b2ob2ob4obobob3ob2obobobob2o5b2o3bo3bo$8bo
b2o8bo3b3obobob2o4bob2ob3o2b2obo3bob9obob3o2b3o3b4obo3b2obo6bo$2o2bo2b
3o2b3ob2obo5bo6b4o2b2o2bobobo2b3o3b4obo4b6obobo3b3ob3o2bo4bo2bobobo$2o
2b2o3b2o4b2obobo3b2o2bo3b3o5b2o4bobo3bob2o4bo3b3o2b2o3b2o4b7ob2obo6b2o
$bob2o3bob4o4bo2b9o7bo4bobob2obob2o4b2o2b2obo2b2ob2o5b2obo8bo2b2o2bob
2o$2bo2bo2b2o5b2o3bo2b2ob2o2b3obob5ob2obo2bo3b2obob4o2bo4b2ob2obobo2b
2o2b2ob3o3b4obobo$2b2o4b3o3bo6bobo2b2o7bo2b6o5bo6bob2o2b3obobo2b6o3b3o
4b3o2bob5o$bobo7bobo2b2obobobobo2bo2b2o2bobob2o2bo2b4o4b2o4b4o2b2o2b3o
2b6obo2b2ob2obo2bobo$b4o2bo2b2obo3b3o2b4o2bo3b2o2bo2b2o2b3obo3b4o3bo2b
o2bob2o3bo6b2o3bo2bo2bob2ob2o2bo$2b3o2bo2bo6b4ob2o2bo3b3o2bob4o3b7ob3o
bo2b2obo3b2obo2bo6b4ob2ob2o2bo2bob2o!

That is a soup that produces it.
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Re: B0/D8 rulespace

Postby Wojowu » November 21st, 2011, 10:10 am

x = 14, y = 12, rule = B0123/S35
5o2bobobobo$b2o2bob2o3b2o$ob11o$bob2o2bobobo$2b2ob3o4b2o$2bobobob2obo$
obo2b6o2bo$2b2obo2b6o$2bo3bo3b2o$obobo3b5o$3o3bo3b2obo$2bo2bob3o2b2o!

Same wickstretcher with smaller soup
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Re: B0/D8 rulespace

Postby Extrementhusiast » November 21st, 2011, 8:02 pm

B013/S4 has many spaceships:
x = 25, y = 88, rule = B013/S4
6b2o$4bo3b2o$5b3o$4bo3b2o$6b2o10$3bo$3b2o17bobo$4bo17bobo9$b3o$b3o$5o$
b3o$b3o8$18b3o$16bo$18b3o22$17b2o$16b2obo$16b2obo$17b2o14$15bo$16b2o$
15bo$15b3o$14bo$14bo$15b3o$15bo$16b2o$15bo!


B023/S23 is also interesting:
x = 69, y = 60, rule = B023/S23
22bo2$23bo$25bo18$49bo2$49b3o5$67bo$66bobo$29bo37bo2$30bo14$48b3o$49bo
$49bo$48b3o6$bo2$obo58bo2$3o63bo!


B0/S24 has three natural puffers:
x = 94, y = 31, rule = B0/S24
o4bo38bo6bo$2b2o42b4o$6o38bo6bo$2b2o42b4o43bo$2b2o40bo6bo39bo$2b2o40b
2o4b2o$2b2o$2b2o$2b2o40bo6bo41bo$2b2o40b2o4b2o$2b2o$2b2o87bo$2b2o40bo
6bo39bo$2b2o40b2o4b2o$2b2o3$91bo3$93bo$93bo5$93bo3$91bo$91bo!
I Like My Heisenburps! (and others)
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Re: B0/D8 rulespace

Postby Tropylium » April 8th, 2012, 10:36 am

B0/S8 with added S7 tends not to produce very well-behaved rules (leading to B1-ish explosions), but B012/S017 seems to have a selection of reasonably nice things…
1D lightspeed "blinker" replicator:
x = 1, y = 3, rule = B012/S017
o$o$o!

3 related spaceships:
x = 9, y = 20, rule = B012/S017
5bo$5bo$5bo$o$o7bo$o7bo$o7bo3$7bo$8bo$8bo$8bo3$7bo$8bo$8bo$8bo$7bo!

Sierpinski generator:
x = 11, y = 8, rule = B012/S017
7bo$7bo$7bo$2bo$b2o7bo$2bo7bo$2bo7bo$o!

(really looks like it would be growing from nothing and travelling forward, but no, it's just a replicator puffer)
Some wickstretchers; note the c/6 "joint":
x = 14, y = 17, rule = B012/S017
4bo$3bo$2bo2bo$bo2b3o5bo$o2b4o6bo$ob10obo$o2b8o2bo$bo10bo$2bo8bo3$5bo
5bo$12bo$7b4obo$5bo2b2o2bo$6bo4bo$7bo2bo!


(Still, more of a curiosity for its rulespace area than an especially interesting rule, I think.)
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