B026/S1

[drc]

B026/S1 is an explosive rule uncovered by Extrementhusiast and further explored by lots of other people. The two basic spaceships are two c/2 p4 diagonals:

Code: Select all

x = 13, y = 4, rule = B026/S1
8bo2$3bo4bo3bo$obo8bo!

As well as a p8 variant:

Code: Select all

x = 8, y = 8, rule = B026/S1
7bo$6bo2$6bo2$bobo$o$6bo!

There's also a replicator that travels at the same speed, but period 16:

Code: Select all

x = 2, y = 2, rule = B026/S1
bo$o!

Replicators can be combined to achieve lower periods:

Code: Select all

x = 28, y = 29, rule = B026/S1
o$bo2$3bo$4bo7$11bo$12bo3$15bo$16bo7$23bo$24bo3$26bo$27bo!

p16 double rake along with a reflection reaction:

Code: Select all

x = 5, y = 39, rule = B026/S1
3bo$obo31$bo5$4bo$3bo!

p68 quad rake:

Code: Select all

x = 7, y = 5, rule = B026/S1
6bo$bo3bo$o$3bo$obo!

A puffer:

Code: Select all

x = 7, y = 12, rule = B026/S1
o4$b2o2$6bo$3bobo$bo2$bo$o!

There's also this arbitrarily large period spaceship:

Code: Select all

x = 48, y = 36, rule = B026/S1
15bo$14bo2$12bo$11bo7$4bo$3bo2$bo$o12$20bo$19bo2$19bo2$47bo$46bo2$46bo
!

5-cell breeder:

Code: Select all

x = 9, y = 5, rule = B026/S1
8bo$7bo2$3bo$obo!

p2 and p16:

Code: Select all

x = 36, y = 3, rule = B026/S1
o6bo5bo5b3o7bo2bo2bo$5bo6b3o4b3o$13bo5b3o!

Rake-type thing:

Code: Select all

x = 17, y = 14, rule = B026/S1
o8$12bo$11bo$14bo$13bo$16bo$15bo!

Extrementhusiast found a gun:

Code: Select all

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

-
There has also been interest in 1-cell thick soups, which do not explode. They cannot explode because they are bound to move only on one axis, and do not move much on that axis. However, this movement can support spaceships! Two have occurred naturally, 2c/10 and 2c/24:

Code: Select all

x = 35, y = 6, rule = B026/S1
obo2b5o3b7o5$7o2bobo2b3o2bo2bo3b3o2bo2bo!

Unnaturally, there are 2c/8, 2c/12, 2c/14, and 2c/16 spaceships:

Code: Select all

x = 614, y = 16, rule = B026/S1
o3b3o3bo2bobo2bo3bo2b11o2bo2b3o4b2o5$o3b3o3bo2bo2bo2bo2b3o3b7o2bobo2b
3o2bo2bo2bo2bo4b7o3bo3bo3b5o2bobo2bo3b5o2bobobobo2b5o3b6o3b5o3bo2bobob
obo2bo3b6o2bobo2bo4bo2bobobo2bo2bobobobo2bo3bo2bobobo2b3o2bobobo2b3o3b
3o3b3o2bo2bo3bo3b3o3bo3bo3b3o2bobobo2bo2bobobo2bo3bo3b3o3b3o3bo2bo2bo
3bo2bo2bo2bo2bo2b10o3b3o2bobo2b2o2bobobo2b3o2bo2bo3b3o3bo3bo2bobo2b11o
3b5o2bo2b15o2bo2b7o3b5o2bobobobobobobo2bo2bo3b3o3b5o2bobo2bo2bobobo2b
5o3b3o2bobo2bo2bo2b6o2bo2bo2bo2bo3b3o2bobobo2b6o3b7o3b7o2bobobobo2b3o
3bo2bobobo2b2o5$o3b3o3bo2bo2bo3b7o3b5o2bobo2bo3bo2bo2bo3b2o2bobobo2b3o
2bo2b3o3bo2bo2bo2bo3bo2bobo2bo3b3o3b2o3bo3b7o3b3o2bo2b9o2bobo2bo3bo3b
5o3bo2bobobo2bo2bobo2bo2bo2b3o3b3o3b3o2bobo2b11o2bo2bo2bo2b3o2bo2b3o2b
o2bo3b3o2bobo2b3o3b5o2bobobobobobobobo2b5o3b5o2bo2bo2bo2b3o2bobo2bo3b
3o3b3o3b5o3b5o2bo2b7o3bo2bo2bo2bo2b3o3b5o2bo2b11o3b3o2bo2b5o3bo5$2o3b
3o2bobobobo2bo2bo2bo3b7o3b7o2bo2b7o3bo3bo2bo!

There's also a tagalong for the 2c/10:

Code: Select all

x = 16, y = 23, rule = B026/S1
11bo3bo4$o12bo$o12bo$o12bo3$o12bo3$o12bo4$o12bo3$o12bo3$o12bo!

-
All of this and more can be found here, I reiterated some of the discoveries but please do consider reading through.

[AforAmpere]

2c/6, found with gfind:

Code: Select all

x = 14, y = 72, rule = B026/S1
$2bo3bobo3bo$5bo3bo$2bobo5bobo$5b5o$3b3o3b3o$6bobo$2b2obo3bob2o$2b3o5b
3o$3b2o5b2o$3b2o5b2o$2b2obo3bob2o$2b4o3b4o$2b4o3b4o$2b3o5b3o$2b3o5b3o$
2b4o3b4o$3b2o5b2o$3b3o3b3o$2b3o5b3o$2b3o5b3o$2b4o3b4o$2b11o$3b3o3b3o$
3b9o$3b3o3b3o$3b9o$3b3o3b3o$3b9o$2b4o3b4o$2b11o$2b4o3b4o$2b4o3b4o$2b4o
3b4o$2b4o3b4o$2b4o3b4o$2b11o$2b4o3b4o$2b11o$3b2obobob2o$3b3o3b3o$3b3o
3b3o$3b2o5b2o$2b4o3b4o$2b4o3b4o$2b11o$2b4o3b4o$3b3o3b3o$3b3o3b3o$2b11o
$2b4o3b4o$3b9o$3b3o3b3o$3b9o$3b3o3b3o$2b4o3b4o$2b4o3b4o$3b9o$3b3o3b3o$
3b9o$3b3o3b3o$3b3o3b3o$3b3o3b3o$3b3o3b3o$3bobo3bobo$bo3bo3bo3bo$bo3bo
3bo3bo2$bobo7bobo2$6bobo!

[AbhpzTa]

Single-replicator version of Extrementhusiast's p32 gun:

Code: Select all

x = 24, y = 24, rule = B026/S1
22bo$21b3o$22bo3$9bo5bo3$18bo2$12bo$13bo8$o4$4bo!

[muzik]

Infinitely extensible one-dimensional 2c/10 tagalong:

Code: Select all

x = 69, y = 15, rule = B026/S1
3o2bo2bo3bo2bo2bo3bo3bo3b3o3bo2bo2b5o2bobo2b5o3b7o7$26bo3b3o3bo2bo2b5o
2bobo2b5o3b7o7$49bobo2b5o3b7o!

I'm still surprised that the 2c/10, 2c/24 and tagalong 2c/10 are the only natural spaceships so far found in 1x256 - one would think some from the 2c/8, 2c/16 and 2c/18 would have turned up by now, since they're not that long or complex.

[muzik]

A new natural 4c/20:

Code: Select all

x = 43, y = 1, rule = B026/S1
o3bo3b3o2bo2b5o2bobo2b5o3bo2bo2bo!

Only just slightly smaller than the currently undiscovered 2c/8 as well, so here's hoping that comes up soon.

[muzik]

Signal through dots:

Code: Select all

x = 857, y = 75, rule = B026/S1
108bo2$104bo7bo2$100bo15bo2$96bo23bo199bo2$92bo31bo191bo7bo2$88bo39bo
183bo15bo2$84bo47bo175bo23bo199bo2$80bo55bo167bo31bo191bo7bo2$76bo63bo
159bo39bo183bo15bo2$72bo71bo151bo47bo175bo23bo199bo2$68bo79bo143bo55bo
167bo31bo191bo7bo2$64bo87bo135bo63bo159bo39bo183bo15bo2$60bo95bo127bo
71bo151bo47bo175bo23bo2$56bo103bo119bo79bo143bo55bo167bo31bo2$52bo111b
o111bo87bo135bo63bo159bo39bo2$48bo119bo103bo95bo127bo71bo151bo47bo2$
44bo127bo95bo103bo119bo79bo143bo55bo2$40bo135bo87bo111bo111bo87bo135bo
63bo2$36bo143bo79bo119bo103bo95bo127bo71bo2$32bo151bo71bo127bo95bo103b
o119bo79bo2$28bo159bo63bo135bo87bo111bo111bo87bo2$24bo167bo55bo143bo
79bo119bo103bo95bo2$20bo175bo47bo151bo71bo127bo95bo103bo2$16bo183bo39b
o159bo63bo135bo87bo111bo2$12bo191bo31bo167bo55bo143bo79bo119bo2$8bo
199bo23bo175bo47bo151bo71bo127bo2$5bo206bo15bo183bo39bo159bo63bo135bo
2$o215bo7bo191bo31bo167bo55bo143bo2$220bo199bo23bo175bo47bo151bo2$424b
o15bo183bo39bo159bo2$428bo7bo191bo31bo167bo2$432bo199bo23bo175bo2$636b
o15bo183bo2$640bo7bo191bo2$644bo199bo2$848bo2$852bo2$856bo!

Can't seem to find a clean 90 degree turn reaction.

[muzik]

Pathological object:

Code: Select all

x = 256, y = 1, rule = B026/S1
oobbooooooobbbobboboobooooooboboboobbbobooooooobobbobbbboobbobboobbooobbboobbooobbboobobobbboboboooooobbobboooboooooobboobobbboooobobobooboooobboboobbobobbooooobobbobobobbboobooooobbobboobbobbbbobooobobobobobobobobbobobbbboboooobbooobobooobbboooooboooobobo!

[muzik]

Yet another new natural xq10:

Code: Select all

x = 256, y = 1, rule = B026/S1
ooooooobbboobbbbobbbbbbboobbbobbbboooooooobobobbbobbbooboobbboooboobboboooooobbbbbbbooobobooboobobbobbooooobbobooobobooboobooobbbbobboobbobbbbobbooooooobbboobobbbbooooobobobooooboooobbobbbbboooobbboboboooobobbbobbbooboooooboboobbbbbbboobbobobboooobbobobooo!

[muzik]

Mixed rake:

Code: Select all

x = 7, y = 12, rule = B026/S1
5bo3$4bo3$5bo$o$bo3bo$6bo$3bo$4bobo!

[muzik]

Yet another natural 2c/10:

Code: Select all

x = 256, y = 1, rule = B026/S1
boboobbobobobooobbooobobbobbobobobobobboobooobobobbooooobbbobboboobooboooobbooboobbbobbbooboobooboobobbobobbbooobboobooobobboooboobbbbooooboobbobboooooooobbobbobbbobooboboboobobboboooooooobobbobooboobooobbooooooooboobbobbooboobooobooboobobboobooboobbobobbo!

Come on - we need more people giving this rule their all on apgsearch!

[Gamedziner]

Come on - we need more people giving this rule their all on apgsearch!

It's a very explosive rule.

[muzik]

Come on - we need more people giving this rule their all on apgsearch!

It's a very explosive rule.

Hence why I search it on 1x256.

[AlephAlpha]

3-cell puffer:

Code: Select all

x = 3, y = 7, rule = B026/S1
bo$2bo5$o!

[KittyTac]

Come on - we need more people giving this rule their all on apgsearch!

It's a very explosive rule.

Hence why I search it on 1x256.

Wait, you can search bounded grids?

[Majestas32]

No, it's just that one can apgsearch 1D soups (since this rule in 1D emulates a 1D next-nearest-neighbors rule which is not explosive)

[AlephAlpha]

Another breeder:

Code: Select all

x = 39, y = 39, rule = B026/S1
bo$o25$37bo$36bo2$36bo4$38bo3$27bobo$26bo$33bo!

[muzik]

Am i the only one who can't apgsearch this on the latest apgsearch?

[AlephAlpha]

Tagalong gun:

Code: Select all

x = 67, y = 28, rule = B026/S1
21bo3$24bo28bo$46bo3$43bo$15bo$16bo4$o5$58bo$57bo$bo3$4bo$66bo3$63bo!

[77topaz]

A p16 dot puffer, made by the interactions of two p16 rakes and a p4 spaceship:

Code: Select all

x = 26, y = 41, rule = B026/S1
3bobo$6bo14bobo$24bo$19bo$24bo$17bo$8bobo11bo$7bo9bo2$19bo$18bo8$22bob
o$25bo$20bo$25bo2$13bo3bo5bo$18bo2$14bobo3bo$19bo$12bo5bo2$10bo$15bo$
10bo$11bobo4$5bo3$o!

EDIT: A symmetrical, more complex variant, consisting of four interacting rakes:

Code: Select all

x = 35, y = 35, rule = B026/S1
11bobo$14bo8bobo$11bo14bo$12bobo8bo$24bobo2$14bobo$13bo$2bo19bo7bobo$
33bo$30bo$31bobo$8bo17bo$4bo5$28bo2$o27bo2bobo$27bo6bo$31bo$32bobo3$
22bo4$21bo2$26bo2$14bo!

[AlephAlpha]

A 90-degree reflector:

Code: Select all

x = 53, y = 57, rule = B026/S1
31bo3$28bo5$37bo$36bo$21bo$28bo2$46bo5bo$31bo15bo$22bobo$21bo25bo2$27b
o13bo$42bobo$27bo23bo$26bo2$48bo2$16bo$17bo5$8bo3$11bo21$obo$3bo!

A glider duplicator:

Code: Select all

x = 71, y = 42, rule = B026/S1
3bo63bo3$o69bo5$9bo51bo$8bo53bo4$18bo33bo$19bo31bo2$19bo31bo2$13bo43bo
$14bobo37bobo$23bo23bo3$20bo29bo$13bo43bo16$11bobo$14bo!

A puffer:

Code: Select all

x = 19, y = 18, rule = B026/S1
4bo11bobo$3bo11bo5$6bo4$bobo$o$4b2o$o2$2bo2$12bo!

[AlephAlpha]

Sierpinski triangle:

Code: Select all

x = 37, y = 18, rule = B026/S1
bo11bobo$o11bo2$6bo2$22bo11bobo$21bo11bo2$27bo6$3bo$2bo2$2bo!

[AlephAlpha]

A p4 rake:

Code: Select all

x = 7, y = 9, rule = B026/S1
4bo$3bo3$4bobo3$bo$o!

A very simple c/4 spaceship:

Code: Select all

x = 6, y = 7, rule = B026/S1
o2$3bo2$5bo2$2bo!

[Rocknlol]

Two collections of one-dimensional ships in B026/S1 (including ships that have been posted previously.)

I created an (admittedly amateurish) gfind clone for one-dimensional rules, specifically the rule that this rule emulates. The first file contains ships I was able to find on a breadth-first search i.e. the shortest ships of their speed assuming my code is bug-free (it isn't.) The second file contains ships I could only find on a depth-first, so there are probably shorter ships of each speed out there.

If there's interest, I'll release the code, but it's really very unpolished so if someone does want it there might be some lag between that and me posting it.

[LaundryPizza03]

2 c/4 diagonal spaceships:

Code: Select all

x = 37, y = 20, rule = B026/S1
o3b2o20bobo$o2bobo17bo6bo$2b3o4b2o13b6obo$obobo3bobo13b2o2b3obo$2b2o6b
o11bobob6o$4b5obo13bobo3b2o$4b2o3bo12bob3obobob2o$5b5obo12b3o$2bobob5o
2bo9bob4o5bo$4bo11bo7bob2o6bo$6bo5b3o10bo2bo5b2o$11b4o13bo5bo$12bo17b
4ob2o$9bobo5bo14bob3o$9bob2o21b3o$19bo$14bobo2bo$15b3o2$15bo3bo!

EDIT: 2c/6 diagonal partial:

Code: Select all

x = 28, y = 28, rule = B026/S1
5bobo2$3b3o$2bo4bob2o$2bo3bobo5bo$obo3b3o$4b4obo5bo$o2bob3obo4bo$4b2o
2b5o$3bo2b4o2b2o2bo3bo$3bo4bobobo$8bo2bo2bobobobo$8b3obo8bo$9bo$4bo2bo
3bo5bo5bo3bo$6bo12bob2obo$9bobo4b2o3b2o$14bob5o$11bo5b4o3bo$15bob2o$9b
obo5b2o$12bo2b2o4bo$15b2o$14bo$15bo2bo3$14bo!

[FWKnightship]

16c/64d rake:

Code: Select all

x = 52, y = 49, rule = B026/S1
4bobo$bo6bo$2b6obo$2b2o2b3obo$obob6o$2bobo3b2o$ob3obobob2o$2b3o$bob4o
5bo$2bob2o6bo$3bo2bo5b2o$6bo5bo$8b4ob2o$10bob3o$12b3o13$28bo$27bo$30bo
$29bo$32bo$31bo16$51bo!