B3/S013

[Extrementhusiast]

This is a rule that quickly settles into single dots, dominoes, duoplets (small diagonal strokes), and oscillators. I would also like to have a census of this, partly because even 1000 by 1000 random soups typically stabilize within 500 generations, and usually less than that. I currently have oscillators of periods 1 (still lifes), 2, 4, 7 (!), 10, and 12.

SL: 99.999% chance of seeing at least one of these, infinite amount possible because of extension (one resembles a snake)
P2: extremely common in many forms, infinite amount possible because of extension
P4: very common in five basic forms, infinite amount possible because of extension
P7: extremely rare, seen only once
P10: one form, somewhat rare (looks a bit like a toad)
P12: one form, quite common (a pre-loaf)

[Lewis]

Is this the P7 you found?

Code: Select all

x = 5, y = 5, rule = B3/S013
bo$4bo$bo2bo$3bo$o!

I found it a while ago in the rule b378/s013 and it works in this rule too.

[velcrorex]

There's also a little ship:

Code: Select all

x = 5, y = 4, rule = B3/S013
2o2$2b3o$3bo!

[mvr]

Here's a P3:

Code: Select all

x = 5, y = 7, rule = B3/S013
3b2o$2bo$2b2o$o3bo$b2o$2bo$2o!

[Extrementhusiast]

Oh yeah, I put it in the pattern collection once but I unfortunately didn't save it. I have everything duplicated now.

@Lewis: Yes, that was the p7 I found.

[Sokwe]

There's also a little ship

David Eppstein's database calls that the sidewinder. Here are two c/4 diagonal spaceships that are not the sidewinder:

Code: Select all

x = 112, y = 56, rule = B3/S013
107bo$48bo58b3o$48bo57bobob2o$48bo2b2o52bo2bo$49bo3bo50b3o2bo$46bo4b2o
51b2o2bo2bo$47b2o54bo4bo$46bo4bobo49b2obo2bo$50bo55b2o$42bob2obobo49bo
b2o2bo$41b4o53b4o$42b2o55b2o$41bobobo52bobobo$38bo56bo$38b3ob2o51b3ob
2o$36b2o2b3o50b2o2b3o$34bo2b2o2bo49bo2b2o2bo$33bobo54bobo$33bobo3bo50b
obo3bo$33bo3bobo50bo3bobo$31bo4b2o50bo4b2o$30bo4b2o50bo4b2o$25bo2bobo
5bo45bo2bobo5bo$25bo4b2o4bo45bo4b2o4bo$23bobo4b2o3bo44bobo4b2o3bo$22bo
3bo5b2o45bo3bo5b2o$22bo10bo45bo10bo$21bo2bo6b2o45bo2bo6b2o$20b3obo5bo
46b3obo5bo$21bo8bo2bo44bo8bo2bo$19bo8b2o2bo43bo8b2o2bo$20bo9bo46bo9bo$
17b2obo2bo2b2obo44b2obo2bo2b2obo$16bo3b2ob3o3bo43bo3b2ob3o3bo$14bo3b3o
2b2o46bo3b3o2b2o$14bo4b2o2bo2bo44bo4b2o2bo2bo$17bob2o2bo50bob2o2bo$11b
2o10bo44b2o10bo$10bo3bob3o3bo44bo3bob3o3bo$10bo3bo5b3o44bo3bo5b3o$7b2o
6bo2bo45b2o6bo2bo$8bob2obo2bobo46bob2obo2bobo$5bobo3bob2o3bo43bobo3bob
2o3bo$12bo3bo52bo3bo$4bo7b2o2bo44bo7b2o2bo$3bo9b2o45bo9b2o$4bo8bobo45b
o8bobo$2b2obo8bo44b2obo8bo$o2b3o7bo43bo2b3o7bo$bobobobob2o2bo44bobobob
ob2o2bo$bobo3b2o2bo46bobo3b2o2bo$b6o2bo48b6o2bo$bo4bo2bo48bo4bo2bo$2b
2o4bo50b2o4bo$3bo56bo$5b2o55b2o!

This rule also supports some small c/5 spaceships:

Code: Select all

x = 46, y = 21, rule = B3/S013
37bo3bo$35b3o3b3o2$38bobo$37b2ob2o$21bo2bo12b2ob2o2$18bo8bo8bobobobo$
19b3o2b3o$19b3o2b3o9bobobobo$22b2o12bo5bo$20b2o2b2o9b3o3b3o$2bobo2bobo
9bo6bo9bo5bo$21bo2bo14bo$2o2bo2bo2b2o7b2ob2ob2o6bobobo3bobobo$b2o6b2o
8bo6bo8bo7bo$18b3o4b3o11bo$2bo6bo28bobo$2ob2o2b2ob2o7bo6bo$2bo6bo8b3o
4b3o11bo$2bo6bo9bo6bo11b3o!

Like many (or most?) rules that contain spaceships, this rule seems to contain many small c/5 spaceships while containing no small 2c/5 spaceships. Maybe someone more ambitious than I can find a 2c/5 spaceship. I also believe a width-13 or width-14 bilaterally-symmetric c/6 spaceship exists, but I have not yet done a search for it.

Also, here are some oscillators of periods 5, 6, 7, 8, and 11:

Code: Select all

x = 63, y = 35, rule = B3/S013
53bobob2obobo$5b2o$26bo12b4o10bo8bo$3bo4bo6b2ob2o9bo$5b2o7bo5bo5bo3bo
8bo2bo10bo8bo$16bobo9bo10bo2bo10bo8bo$4bo2bo7bo3bo$4bo2bo18bo2bobo7b4o
10bo8bo2$53bobob2obobo$14bo$15bo$17b3o$5b2o35bo$15b3o20bobo$bob2o2b2ob
o8bo22bo$20bo18bo$5b2o34bobo$39bo5$6bo$2bo2bo$4bo5bo$6bo$9bo$o2bob2o3b
o$bo3b2obo2bo$2bo$5bo$bo5bo$6bo2bo$5bo!

[Extrementhusiast]

Interesting how one of the oscillators resembles Kok's galaxy. Did you find these by computer search?

[Sokwe]

Did you find these by computer search?

The oscillators were found by random agar search with various symmetries. The spaceships were found using gfind.

Here's a c/6 orthogonal spaceship:

Code: Select all

x = 13, y = 30, rule = B3/S013
3bob3obo$5bobo2$5bobo$obo2bobo2bobo$5bobo$5b3o$3bo5bo$2bo7bo$2bo7bo$3b
obobobo$5bobo$o11bo$bo9bo$b2ob2ob2ob2o$2bo7bo2$4bo3bo$5bobo$obo2bobo2b
obo$bo4bo4bo$o5bo5bo$bo9bo2$b3o5b3o$3b3ob3o3$4bo3bo$4bo3bo!

Here are the thinnest and shortest orthogonal spaceships of different speeds (There are no c/5 spaceships with a height of 7, but I haven't tried 8):

Code: Select all

x = 129, y = 35, rule = B3/S013
54bo2$54b3o$53bo$53bo2$40b2o12b3o$58bo$37bobo17b2o$36bobo19bo$40bo17bo
$38bo$37b2obo14b2o2bo$36bobo15b2o$39b2o13bob2o$22bo17bo15b3o$19bo2bo
15b2o17bo$18bobo19bo16bo$19bobo17b2o16b2o$19b2o2bo$18b2obob3o11b3o18b
2o$19bobo2bo12bo20b2o$58bo$5b2o12bo3bo12b3o17bo$5bo13bo3bo13b2ob3o15bo
$3b2o16bo35bo$4b2o2b2o10b3o33b2o17b2o2bo$2bo5bo10bo3bo13bo2b3o33bo4bo$
3bob2o13bobo16b2o17bo19b2ob3o$3bo2bo13bobo16bo13b2o3bo19bo3bo9bo13bo$
19bo3bo14bo2b2o13bo33bo17bo$4bobo30b2ob2o14bo19bobo11bo4bo2bobo2bo4bo
6bobo8bobo$2bo5bo9b2o3b2o30bobo16bo5bo11b3obo5bob3o9b3o2b2o2b3o$3ob3ob
3o10bo16bobo15bo15b3ob3ob3o7bob3ob3ob3ob3obo7b2o8b2o$bo3bo3bo10bobo13b
3o17bo16bo3bo3bo13bo7bo16bo2bo!

These are the smallest known spaceships of each speed (by minimum number of cells):

Code: Select all

x = 91, y = 30, rule = B3/S013
81bob3obo$83bobo2$83bobo$78bobo2bobo2bobo$83bobo$83b3o$81bo5bo$80bo7bo
$80bo7bo$81bobobobo$83bobo$78bo11bo$79bo9bo$79b2ob2ob2ob2o$80bo7bo2$
82bo3bo$83bobo$78bobo2bobo2bobo$79bo4bo4bo$13b2o2bo44bobo2bobo8bo5bo5b
o$14bo4bo59bo9bo$16b2ob3o11bo26b2o2bo2bo2b2o$16bo3bo11b2o27b2o6b2o8b3o
5b3o$31bo49b3ob3o$2o12bobo13bo4bo5bobo8bobo7bo6bo$12bo5bo8bobo3b2o7b3o
2b2o2b3o6b2ob2o2b2ob2o$2b3o5b3ob3ob3o8bo2bo9b2o8b2o8bo6bo12bo3bo$3bo7b
o3bo3bo10bo15bo2bo12bo6bo12bo3bo!

Also, here's a 2c/6 spaceship:

Code: Select all

x = 9, y = 22, rule = B3/S013
3b4o2$3bo3$3b3o$2bobobo$2bo3bo$ob2ob2obo$3bobo$2b5o$2bo3bo$2bobobo$obo
bobobo$o7bo2$obo3bobo$3bobo2$2b5o$4bo$3b3o!

[Lewis]

Here's a new (smallest possible?) P3:

Code: Select all

x = 6, y = 6, rule = B3/S013
o$bo$3bo$2bo$4bo$5bo!

It was found naturally in a random soup.

[Lewis]

Here's a collection of all the oscillators posted so far along with some I found myself (both P9s and the last P3):

Code: Select all

x = 117, y = 95, rule = 013/3
bob2obo$o6bo4b2o4bobobo3b4o4b4o$11bo5bo2b2o$7bo20b4o2b4o$7bo$
11b2o5bob2o54bob2obo$o2b2o2bo4b2o3bo2bobo52bo6bo$27bob2o7bo62b
o$o25bo11bo36bo6bo14bobo$o11bobo7bo4bobo4b2ob2obo34bo6bo3bob2o
bo9bo$11bo3bo4bobo7bo5bo49bo4bo6bo$o6bo4bobo6bo14bo38bo2b2o2b
o3bo4bo8bobo$bob2obo12b2o65bob2obo6bo$75bo6bo$75bo6bo2$bob2ob
o68bo6bo$o6bo68bob2obo2$7bo$7bo6b2o4b4o4bo$13bo6bo2bo5bo75bo7b
o$3b2o2bo5b2o3bobo2bobo5bo44bob2obo$11bo3bo2bobo2bobo4bo44bo6b
o23b2o3b2o$7bo4b2o6bo2bo8bo69bo6bo6bo$7bo5bo6b4o9bo41bo6bo21b
o3bobo3bo$11b2o62bo6bo6bobo2bobo7bo9bo$o6bo82bo4bo10bo5bo$bob
2obo68bo2b2o2bo4bo2bo4bo2bo6bo7bo$90bo4bo10bo5bo$82bo6bobo2bo
bo7bo9bo$82bo21bo3bobo3bo$o6bo94bo6bo6bo$o6bo13b2o5bo46bo6bo23b
2o3b2o$13bobo4bo2bo3bo2b2o44bob2obo$o6bo7b2o3b4o3bo2b2o73bo7b
o$o6bo2$o2b2o2bo$21bo48bo5bob2obo$7bo5bo6bo2bo47bo3bo6bo$7bo4b
o2b2o3b2obo5b2ob2o$13bo8b2o3bobo2bo38bo3bo6bo$7bo63bo3bo6bo$7b
o$71bo3bo6bo6b2obo$92bo$71bo3bo6bo8bo$71bo3bo6bo$bob2obo$o6bo
63bo3bo6bo$71bo4bob2obo$o38bo$o13b2o19bo2bo$37bo5bo$o2b2o2bo4b
o4bo6b2o13bo$14b2o26bo$7bo12bob2o2b2obo3bo2bob2o3bo$7bo5bo2bo
17bo3b2obo2bo28bo4bo$13bo2bo7b2o9bo38bo4bo$o6bo30bo47bobob2ob
obo$bob2obo27bo5bo33bo4bo$39bo2bo31bo4bo6bo8bo$38bo$74bo4bo6b
o8bo$86bo8bo$bob2obo67bo4bo$o6bo66bo4bo6bo8bo2$o21bo51bo4bo6b
obob2obobo$o12b2ob2o5bo50bo4bo$12bo5bo6b3o$o2b2o2bo6bobo$13bo
3bo5b3o$o6bo19bo$o6bo20bo2$o6bo63bo5bob2obo$bob2obo65bo3bo6bo
2$72bo10bo$72bo10bo$bob2obo83bobo$o6bo64bo3bo2b2o2bo$92bo$7bo
11bo52bo3bo$7bo4bo9bo49bo3bo$15bo3bo3bo$7bo4bo2bo5bo50bo3bo6b
o$14bo57bo4bob2obo$7bo3bo7bo2bobo$7bo2$7bo$7bo!

I started a census for this rule. So far, the total object cound is 1097065. Here are the most common oscillators (of periods other that 2 and 4):
P12 : 2422
P10 : 90
P7 : 4
P3: 3 (the one I posted)
c/4 Diagonal Glider : 1

[Ntsimp]

Here's a p14:

Code: Select all

x = 5, y = 10, rule = B3/S013
bo2bo$bobo$o3bo2$b3o$b3o2$o3bo$bobo$bo2bo!

[Ntsimp]

Also a p16 and a p18:

Code: Select all

x = 20, y = 10, rule = B3/S013
$3bo2bo$3bobo8b2o$3bobo5bo6bo$5bo6b6o$4bo6bobo2bobo$10b2o6b2o$4b2o5b8o
$4bo!

[knightlife]

A new p4 and a bunch of extendable p4 examples:

Code: Select all

x = 67, y = 22, rule = B3/S013
15bo2bo2bo11bo2bo2bo2bo10bo2bo2bo2bo2bo$b2o10bob2ob2ob2o8bob2ob2ob2ob
2o7bob2ob2ob2ob2ob2o$bo$o$4o11bo2b2obo11bo2bo2b2obo10bo2bo2bo2b2obo$
13bob2obo2b2o8bob2ob2obo2b2o7bob2ob2ob2obo2b2o3$15b2obo2bo11bo2b2obo2b
o10bo2bo2b2ob2obo$13bobo2b2ob2o8bob2obo2b2ob2o7bob2ob2obo2bo2b2o3$15b
2ob2obo11bo2b2ob2obo10bo2b2obo2bo2bo$13bobo2bo2b2o8bob2obo2bo2b2o7bob
2obo2b2ob2ob2o3$33b2obo2bo2bo10b2ob2obo2b2obo$31bobo2b2ob2ob2o7bobo2bo
2b2obo2b2o3$53b2ob2ob2obo2bo$51bobo2bo2bo2b2ob2o!

The triplets can be interchanged at will to create new p4 oscillators of any length and in some cases, wicks (when there is a repeating pattern). A couple of the p4 oscillators in the collection are small versions of this extendable type.

There are two triplets possible at each position, so it corresponds to a binary number. Therefore there are 2^(n-1) possible p4 oscillators for a given length with n triplets. The last triplet doesn't count because it behaves differently than the others and you end up with a different phase of the same oscillator.

I found that there are also extendable p2 oscillators of width 2 and any length:

Code: Select all

x = 16, y = 54, rule = B3/S013
2bo$2obo3$bob2o$obo3$ob2o$bo2b2o3$2o2bo$2b2ob2o3$2o2bobo$2b2obobo3$2o
2bobo$2b2obob2o3$ob2obobo$bo2bobob2o3$ob2o2b2obo$bo2b2o2bobo3$ob2obobo
bobo$bo2bobobobo3$bo2bobobo2bo$ob2obobob2obo3$bo2b2o2b2o2bo$ob2o2b2o2b
2obo3$2b2obobob2obobo$2o2bobobo2bobo3$2b2ob2obobobob2o$2o2bo2bobobobo
3$2b2o2b2o2b2o2b2o$2o2b2o2b2o2b2o!

For any given length n the oscillator has n cells and again they correspond to a binary number. But the endpoints do not move and a sequence of three or more cells in a row must be avoided to allow the oscillator to work.

The p2 oscillators can be extended easily in this way:

1) add a cell at one end and see if it works.
2) if it does not work then advance the pattern by one generation and try extending it again. This time it will work and furthermore there will be two possible positions for the new cell.

The possibilities are not a simple power of two because sequences of three or more cells in a row have to be avoided.

EDIT:
The p2 oscillators described above can be placed with mirror images to create new oscillators:

Code: Select all

x = 5, y = 18, rule = B3/S013
bobo$bobo$bobo$o3bo$o3bo$bobo$o3bo$bobo$2ob2o$bobo$bobo$2ob2o$bobo$bob
o$o3bo$o3bo$bobo$o3bo!

These oscillators can have stationary cells in the middle, increasing the possible ways to extend them.

[Extrementhusiast]

The "new" p4 you posted is actually known and also quite common. Hmm.

[knightlife]

The "new" p4 you posted is actually known and also quite common. Hmm.

I meant to say it is new to the collection by Lewis posted in this thread. It stood out when I was running random soups. I thought it was pretty cool compared to the other simpler p4's posted in the collection. Where can I find the other "common" oscillators for B3/S013?

EDIT: Never mind, I will check David Eppstein's web page.

[Paul Tooke]

Here are different (from the above) p11 & p14 oscillators and a p17:

Code: Select all

x = 40, y = 53, rule = B3/S013
o4bo$bo4bo2$bo4bo$bo4bo2$bo4bo2$bo4bo$bo4bo18bo8bo$22bo2bo2bobo$bo4bo
17bobo2bo2bo$bo4bo13bo8bo8$o3bo6bo$bo2bo6bo$26b3o2bo$bo2bo6bo14b3o$bo
2bo6bo14bobo$26bob2o$bo2bo2b2o2bo16bo$21b4o3bo$bo9bo9b2o$bo9bo9b6o$24b
o$bo9bo$bo9bo9bo8$o4bob2obo$bo2bo6bo2$bo9bo$bo9bo2$bo9bo23bobobo2$bo9b
o21bobo$bo9bo17bobo$25bobo$bo9bo$bo9bo9bobobo!

I tried quick searches for asymmetric c/2 & c/3 puffers. Thanks to the S01, the output is mostly dots and dominoes, but at least it provides evidence that this rule supports infinite growth, albeit linear. Here are examples of simple c/2 puffers of periods 4,6,8,10,12 &16. As with all of the examples below, it may be possible to graft the puffer engine onto a smaller, narrower or more conveniently shaped body.

Code: Select all

x = 125, y = 49, rule = B3/S013
2bo3bo3bo60bo3bo3bo12bo3bo3bo13bo3bo3bo$b3ob3ob3o58b3ob3ob3o10b3ob3ob
3o11b3ob3ob3o$3bo5bo62bo5bo14bo5bo15bo5bo$5bobo66bobo18bobo19bobo2$bo
3bo70bo18bo2bo20bo3bo$3ob2o4bo36bo3bo3bo20b2o17b2obo15bo4b2ob3o$2bo4bo
b3o34b3ob3ob3o21bo14bo5bo13b3obo4bo$4bo4bo38bo5bo21b3o13b2o2b2o17bo4bo
$6b2o42bobo22b2o20b2o18b2o$5b4o66b2o20b2o17b4o$4bo3bobo12bo3bo3bo14bo
3bo23bo2bo36bobo3bo$3o4bo14b3ob3ob3o12b3ob2o25bo13bo3bo2bobo17bo4b3o$
2b2o4bo2b2o11bo5bo16bo4bo20b2o2bo11b3ob3o2b3o11b2o2bo4b2o$9bo16bobo20b
o2b2o2bo15b5o14bo5b2o16bo$3bo6bo2bo41b3o17bo17bobobo13bo2bo$3b2o4b2o
11bo3bo28bo17bo23b2o$8b2obobo7b3ob2o26b3o15b2o3bo15bo2bobo14bo$2bo20bo
4bo23b2o3bo18b2o13b2ob2o3b2o11bo2bo$2bobo6bo13bo2b2o2bo19b3obo13bo4bo
15bobobo16b2o$4bo4b3o19b3o14bo2bo3bo13bo5bo17bo19b2o$ob2o27bo15b3o2bob
o16b2obo$bo8b3o17b2o17bo2b2o14bo4bo20bo17bo$3bo5bo19bo22bobo12b4o3b2o
18bo$2b2ob3o20b2obo19b4o14b2o5bo$b2o2bo2bo2b2o19bo18bob2o15bo5b2o$4b2o
5b3o15bob3o37bo$2bo3bo3b2obo15bobo37bo41bo$2b3o4bo44b2o14bobo22bo18bo$
4b2o6bo16bo24bo17bo38bo$2bobo6b2o17bo39bo41bo$2b3o24bo$71bo$28bo26bo
15bo$3bo91bo$111bo$3bo24bo85bo$55bo15bo39bo$3bo67bo40bo$28bo$3bo91bo$
55bo$3bo24bo42bo$71bo39bo$3bo110bo$28bo26bo55bo$95bo16bo$71bo$71bo!

The higher period c/2 puffers tthat I found at p24 & p48 were mostly LCMs of lower period engines. This messy p48 was the exception:

Code: Select all

x = 14, y = 33, rule = B3/S013
3b3ob3ob3o$5b2obob2o$7bobo$7bobo$8bo$8b3o$6bo2bobo$4bob2o2b2o$3o6bo$2b
2o$9b2o$3bo6bo$3b2o2bobo$6b3ob2o$6bobo3bo$5b2obo3b2o$4bo3bo$3o5b3o$2b
2o6b2o$10b2o$3bo5bo2bo$3b2o6b3o$11bo$5bo4b2o$3bobo3bo$3bo$4bo5bo$3bo6b
2o$3b2o4bo$2bo6bo$5bo2bo2$7bo!

Puffer searches usually throw up some higher period spaceships. Here are some representative samples of p4,p6(x2) and p10 spacehips;

Code: Select all

x = 97, y = 48, rule = B3/S013
3bo3bo3bo29bo3bo3bo34bo3bo3bo$2b3ob3ob3o27b3ob3ob3o32b3ob3ob3o$4bo5bo
31bo5bo36bo5bo$6bobo35bobo40bobo2$8bo3bo27bo3bo41bo2bo$3bo4b2ob3o25b3o
b2o41bob2o$2b3obo4bo29bo4bo38bo5bo$4bo4bo33bo2b2o2bo36b2o2b2o2bo$6b2o
41b3o34b2o6b3o$5b4o40bo38bo5bo$3bobo3bo78b2o$6bo4b3o34b2o43b2o$b2o2bo
4b2o35bo2bo42bo$4bo43b2o35b3ob3obob2o$o2bo83b2obobo$89bobobo$89bobo3bo
$90bo3bo$88bo$89bo2b2obo$90b2o$87b2o4bo$83b3o5bobo$85b2ob2obo2bo$89bob
obobo$89bob3o$88bo$89b4obo$42bo3bo3bo39bo3bo$41b3ob3ob3o39b3o$43bo5bo$
45bobo44bo$91b3o$47bo$47b2o$49bo$47b3o$46b2o$46b2o$45bo2bo$46bo$45bo2b
2o$46b5o$47bo$50bo$49bobo$50bo!

At slower speeds, puffers are less easy to find and I've only come up with two results at c/3. Here is a p9 c/3 'dot puffer':

Code: Select all

x = 10, y = 40, rule = B3/S013
3b3o2bo$3o2bo2b2o$2bo4bo$7bo$bobo2bo$bo5bo$2bo4b2o$3b2o$bobo3bobo$2b2o
3b2o$6bobo$4bo$4bo$3b3o$2bo$2b2ob2o$7b2o$3b2o$b2o$3b3o$3bo$4bo$3bo$4bo
$5bo3$5bo3$5bo3$5bo3$5bo3$5bo!

... and here is a p3 c/3 wickstretcher:

Code: Select all

x = 9, y = 21, rule = B3/S013
3bobo$4bo$b2o3b2o2$bo5bo$bo5bo2$2b2ob2o$o2bobo2bo$bo2bo2bo$2b2ob2o2$2b
o3bo$2b2ob2o$3b2o3bo$o2bobobo$bo4bobo$o6bo$o$bo4b3o$bo!

Paul