## B026/S1

For discussion of other cellular automata.
drc
Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### B026/S1

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:

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``````x = 13, y = 4, rule = B026/S1
8bo2\$3bo4bo3bo\$obo8bo!
``````
As well as a p8 variant:

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``````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:

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``````x = 2, y = 2, rule = B026/S1
bo\$o!
``````
Replicators can be combined to achieve lower periods:

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``````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:

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

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``````x = 7, y = 5, rule = B026/S1
6bo\$bo3bo\$o\$3bo\$obo!
``````
A puffer:

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``````x = 7, y = 12, rule = B026/S1
o4\$b2o2\$6bo\$3bobo\$bo2\$bo\$o!
``````
There's also this arbitrarily large period spaceship:

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``````x = 48, y = 36, rule = B026/S1
15bo\$14bo2\$12bo\$11bo7\$4bo\$3bo2\$bo\$o12\$20bo\$19bo2\$19bo2\$47bo\$46bo2\$46bo
!
``````
5-cell breeder:

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``````x = 9, y = 5, rule = B026/S1
8bo\$7bo2\$3bo\$obo!
``````
p2 and p16:

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``````x = 36, y = 3, rule = B026/S1
o6bo5bo5b3o7bo2bo2bo\$5bo6b3o4b3o\$13bo5b3o!
``````
Rake-type thing:

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``````x = 17, y = 14, rule = B026/S1
o8\$12bo\$11bo\$14bo\$13bo\$16bo\$15bo!``````
Extrementhusiast found a gun:

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``````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:

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``````x = 35, y = 6, rule = B026/S1
obo2b5o3b7o5\$7o2bobo2b3o2bo2bo3b3o2bo2bo!
``````
Unnaturally, there are 2c/8, 2c/12, 2c/14, and 2c/16 spaceships:

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``````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.
\100\97\110\105

AforAmpere
Posts: 1111
Joined: July 1st, 2016, 3:58 pm

### Re: B026/S1

2c/6, found with gfind:

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``````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!
``````
Wildmyron and I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule

AbhpzTa
Posts: 494
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: B026/S1

Single-replicator version of Extrementhusiast's p32 gun:

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``````x = 24, y = 24, rule = B026/S1
22bo\$21b3o\$22bo3\$9bo5bo3\$18bo2\$12bo\$13bo8\$o4\$4bo!``````
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Infinitely extensible one-dimensional 2c/10 tagalong:

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``````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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

A new natural 4c/20:

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``````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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Signal through dots:

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``````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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Pathological object:

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``````x = 256, y = 1, rule = B026/S1
oobbooooooobbbobboboobooooooboboboobbbobooooooobobbobbbboobbobboobbooobbboobbooobbboobobobbboboboooooobbobboooboooooobboobobbboooobobobooboooobboboobbobobbooooobobbobobobbboobooooobbobboobbobbbbobooobobobobobobobobbobobbbboboooobbooobobooobbboooooboooobobo!``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Yet another new natural xq10:

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``````x = 256, y = 1, rule = B026/S1
ooooooobbboobbbbobbbbbbboobbbobbbboooooooobobobbbobbbooboobbboooboobboboooooobbbbbbbooobobooboobobbobbooooobbobooobobooboobooobbbbobboobbobbbbobbooooooobbboobobbbbooooobobobooooboooobbobbbbboooobbboboboooobobbbobbbooboooooboboobbbbbbboobbobobboooobbobobooo!``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Mixed rake:

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``````x = 7, y = 12, rule = B026/S1
5bo3\$4bo3\$5bo\$o\$bo3bo\$6bo\$3bo\$4bobo!
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Yet another natural 2c/10:

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``````x = 256, y = 1, rule = B026/S1
boboobbobobobooobbooobobbobbobobobobobboobooobobobbooooobbbobboboobooboooobbooboobbbobbbooboobooboobobbobobbbooobboobooobobboooboobbbbooooboobbobboooooooobbobbobbbobooboboboobobboboooooooobobbobooboobooobbooooooooboobbobbooboobooobooboobobboobooboobbobobbo!``````
Come on - we need more people giving this rule their all on apgsearch!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Gamedziner
Posts: 796
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: B026/S1

muzik wrote:Come on - we need more people giving this rule their all on apgsearch!
It's a very explosive rule.

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``````x = 81, y = 96, rule = LifeHistory
58.2A\$58.2A3\$59.2A17.2A\$59.2A17.2A3\$79.2A\$79.2A2\$57.A\$56.A\$56.3A4\$27.
A\$27.A.A\$27.2A21\$3.2A\$3.2A2.2A\$7.2A18\$7.2A\$7.2A2.2A\$11.2A11\$2A\$2A2.2A
\$4.2A18\$4.2A\$4.2A2.2A\$8.2A!
``````

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Gamedziner wrote:
muzik wrote: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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AlephAlpha
Posts: 39
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

3-cell puffer:

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``````x = 3, y = 7, rule = B026/S1
bo\$2bo5\$o!``````
Last edited by AlephAlpha on January 12th, 2018, 10:13 am, edited 1 time in total.

KittyTac
Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: B026/S1

muzik wrote:
Gamedziner wrote:
muzik wrote: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
Posts: 524
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

### Re: B026/S1

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
Posts: 39
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

Another breeder:

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

muzik
Posts: 3787
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Am i the only one who can't apgsearch this on the latest apgsearch?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AlephAlpha
Posts: 39
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

Tagalong gun:

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

77topaz
Posts: 1497
Joined: January 12th, 2018, 9:19 pm

### Re: B026/S1

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

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``````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
Posts: 39
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

A 90-degree reflector:

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``````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:

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

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

AlephAlpha
Posts: 39
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

Sierpinski triangle:

Code: Select all

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

AlephAlpha
Posts: 39
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

A p4 rake:

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``````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
Posts: 96
Joined: April 15th, 2012, 9:06 am

### Re: B026/S1

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.
Attachments
B026_S1_ships_1.rle