## B026/S1

For discussion of other cellular automata.

### 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:
`x = 13, y = 4, rule = B026/S18bo2\$3bo4bo3bo\$obo8bo!`

As well as a p8 variant:
`x = 8, y = 8, rule = B026/S17bo\$6bo2\$6bo2\$bobo\$o\$6bo!`

There's also a replicator that travels at the same speed, but period 16:
`x = 2, y = 2, rule = B026/S1bo\$o!`

Replicators can be combined to achieve lower periods:
`x = 28, y = 29, rule = B026/S1o\$bo2\$3bo\$4bo7\$11bo\$12bo3\$15bo\$16bo7\$23bo\$24bo3\$26bo\$27bo!`

p16 double rake along with a reflection reaction:
`x = 5, y = 39, rule = B026/S13bo\$obo31\$bo5\$4bo\$3bo!`

`x = 7, y = 5, rule = B026/S16bo\$bo3bo\$o\$3bo\$obo!`

A puffer:
`x = 7, y = 12, rule = B026/S1o4\$b2o2\$6bo\$3bobo\$bo2\$bo\$o!`

There's also this arbitrarily large period spaceship:
`x = 48, y = 36, rule = B026/S115bo\$14bo2\$12bo\$11bo7\$4bo\$3bo2\$bo\$o12\$20bo\$19bo2\$19bo2\$47bo\$46bo2\$46bo!`

5-cell breeder:
`x = 9, y = 5, rule = B026/S18bo\$7bo2\$3bo\$obo!`

p2 and p16:
`x = 36, y = 3, rule = B026/S1o6bo5bo5b3o7bo2bo2bo\$5bo6b3o4b3o\$13bo5b3o!`

Rake-type thing:
`x = 17, y = 14, rule = B026/S1o8\$12bo\$11bo\$14bo\$13bo\$16bo\$15bo!`

Extrementhusiast found a gun:
`x = 29, y = 13, rule = B026/S1bo\$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:
`x = 35, y = 6, rule = B026/S1obo2b5o3b7o5\$7o2bobo2b3o2bo2bo3b3o2bo2bo!`

Unnaturally, there are 2c/8, 2c/12, 2c/14, and 2c/16 spaceships:
`x = 614, y = 16, rule = B026/S1o3b3o3bo2bobo2bo3bo2b11o2bo2b3o4b2o5\$o3b3o3bo2bo2bo2bo2b3o3b7o2bobo2b3o2bo2bo2bo2bo4b7o3bo3bo3b5o2bobo2bo3b5o2bobobobo2b5o3b6o3b5o3bo2bobobobo2bo3b6o2bobo2bo4bo2bobobo2bo2bobobobo2bo3bo2bobobo2b3o2bobobo2b3o3b3o3b3o2bo2bo3bo3b3o3bo3bo3b3o2bobobo2bo2bobobo2bo3bo3b3o3b3o3bo2bo2bo3bo2bo2bo2bo2bo2b10o3b3o2bobo2b2o2bobobo2b3o2bo2bo3b3o3bo3bo2bobo2b11o3b5o2bo2b15o2bo2b7o3b5o2bobobobobobobo2bo2bo3b3o3b5o2bobo2bo2bobobo2b5o3b3o2bobo2bo2bo2b6o2bo2bo2bo2bo3b3o2bobobo2b6o3b7o3b7o2bobobobo2b3o3bo2bobobo2b2o5\$o3b3o3bo2bo2bo3b7o3b5o2bobo2bo3bo2bo2bo3b2o2bobobo2b3o2bo2b3o3bo2bo2bo2bo3bo2bobo2bo3b3o3b2o3bo3b7o3b3o2bo2b9o2bobo2bo3bo3b5o3bo2bobobo2bo2bobo2bo2bo2b3o3b3o3b3o2bobo2b11o2bo2bo2bo2b3o2bo2b3o2bo2bo3b3o2bobo2b3o3b5o2bobobobobobobobo2b5o3b5o2bo2bo2bo2b3o2bobo2bo3b3o3b3o3b5o3b5o2bo2b7o3bo2bo2bo2bo2b3o3b5o2bo2b11o3b3o2bo2b5o3bo5\$2o3b3o2bobobobo2bo2bo2bo3b7o3b7o2bo2b7o3bo3bo2bo!`

There's also a tagalong for the 2c/10:
`x = 16, y = 23, rule = B026/S111bo3bo4\$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.
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

drc

Posts: 1664
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Location: creating useless things in OCA

### Re: B026/S1

2c/6, found with gfind:
`x = 14, y = 72, rule = B026/S1\$2bo3bobo3bo\$5bo3bo\$2bobo5bobo\$5b5o\$3b3o3b3o\$6bobo\$2b2obo3bob2o\$2b3o5b3o\$3b2o5b2o\$3b2o5b2o\$2b2obo3bob2o\$2b4o3b4o\$2b4o3b4o\$2b3o5b3o\$2b3o5b3o\$2b4o3b4o\$3b2o5b2o\$3b3o3b3o\$2b3o5b3o\$2b3o5b3o\$2b4o3b4o\$2b11o\$3b3o3b3o\$3b9o\$3b3o3b3o\$3b9o\$3b3o3b3o\$3b9o\$2b4o3b4o\$2b11o\$2b4o3b4o\$2b4o3b4o\$2b4o3b4o\$2b4o3b4o\$2b4o3b4o\$2b11o\$2b4o3b4o\$2b11o\$3b2obobob2o\$3b3o3b3o\$3b3o3b3o\$3b2o5b2o\$2b4o3b4o\$2b4o3b4o\$2b11o\$2b4o3b4o\$3b3o3b3o\$3b3o3b3o\$2b11o\$2b4o3b4o\$3b9o\$3b3o3b3o\$3b9o\$3b3o3b3o\$2b4o3b4o\$2b4o3b4o\$3b9o\$3b3o3b3o\$3b9o\$3b3o3b3o\$3b3o3b3o\$3b3o3b3o\$3b3o3b3o\$3bobo3bobo\$bo3bo3bo3bo\$bo3bo3bo3bo2\$bobo7bobo2\$6bobo!`
I and wildmyron 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
- Finish a rule with ships with period >= f_e_0(n) (in progress)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

### Re: B026/S1

Single-replicator version of Extrementhusiast's p32 gun:
`x = 24, y = 24, rule = B026/S122bo\$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).
AbhpzTa

Posts: 473
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: B026/S1

Infinitely extensible one-dimensional 2c/10 tagalong:
`x = 69, y = 15, rule = B026/S13o2bo2bo3bo2bo2bo3bo3bo3b3o3bo2bo2b5o2bobo2b5o3b7o7\$26bo3b3o3bo2bo2b5o2bobo2b5o3b7o7\$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: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

A new natural 4c/20:
`x = 43, y = 1, rule = B026/S1o3bo3b3o2bo2b5o2bobo2b5o3bo2bo2bo!`

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: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Signal through dots:
`x = 857, y = 75, rule = B026/S1108bo2\$104bo7bo2\$100bo15bo2\$96bo23bo199bo2\$92bo31bo191bo7bo2\$88bo39bo183bo15bo2\$84bo47bo175bo23bo199bo2\$80bo55bo167bo31bo191bo7bo2\$76bo63bo159bo39bo183bo15bo2\$72bo71bo151bo47bo175bo23bo199bo2\$68bo79bo143bo55bo167bo31bo191bo7bo2\$64bo87bo135bo63bo159bo39bo183bo15bo2\$60bo95bo127bo71bo151bo47bo175bo23bo2\$56bo103bo119bo79bo143bo55bo167bo31bo2\$52bo111bo111bo87bo135bo63bo159bo39bo2\$48bo119bo103bo95bo127bo71bo151bo47bo2\$44bo127bo95bo103bo119bo79bo143bo55bo2\$40bo135bo87bo111bo111bo87bo135bo63bo2\$36bo143bo79bo119bo103bo95bo127bo71bo2\$32bo151bo71bo127bo95bo103bo119bo79bo2\$28bo159bo63bo135bo87bo111bo111bo87bo2\$24bo167bo55bo143bo79bo119bo103bo95bo2\$20bo175bo47bo151bo71bo127bo95bo103bo2\$16bo183bo39bo159bo63bo135bo87bo111bo2\$12bo191bo31bo167bo55bo143bo79bo119bo2\$8bo199bo23bo175bo47bo151bo71bo127bo2\$5bo206bo15bo183bo39bo159bo63bo135bo2\$o215bo7bo191bo31bo167bo55bo143bo2\$220bo199bo23bo175bo47bo151bo2\$424bo15bo183bo39bo159bo2\$428bo7bo191bo31bo167bo2\$432bo199bo23bo175bo2\$636bo15bo183bo2\$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: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Pathological object:
`x = 256, y = 1, rule = B026/S1oobbooooooobbbobboboobooooooboboboobbbobooooooobobbobbbboobbobboobbooobbboobbooobbboobobobbboboboooooobbobboooboooooobboobobbboooobobobooboooobboboobbobobbooooobobbobobobbboobooooobbobboobbobbbbobooobobobobobobobobbobobbbboboooobbooobobooobbboooooboooobobo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Yet another new natural xq10:
`x = 256, y = 1, rule = B026/S1ooooooobbboobbbbobbbbbbboobbbobbbboooooooobobobbbobbbooboobbboooboobboboooooobbbbbbbooobobooboobobbobbooooobbobooobobooboobooobbbbobboobbobbbbobbooooooobbboobobbbbooooobobobooooboooobbobbbbboooobbboboboooobobbbobbbooboooooboboobbbbbbboobbobobboooobbobobooo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Mixed rake:
`x = 7, y = 12, rule = B026/S15bo3\$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: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Yet another natural 2c/10:
`x = 256, y = 1, rule = B026/S1boboobbobobobooobbooobobbobbobobobobobboobooobobobbooooobbbobboboobooboooobbooboobbbobbbooboobooboobobbobobbbooobboobooobobboooboobbbbooooboobbobboooooooobbobbobbbobooboboboobobboboooooooobobbobooboobooobbooooooooboobbobbooboobooobooboobobboobooboobbobobbo!`

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!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

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

It's a very explosive rule.
`x = 81, y = 96, rule = LifeHistory58.2A\$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!`
Gamedziner

Posts: 790
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### 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!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

3-cell puffer:

`x = 3, y = 7, rule = B026/S1bo\$2bo5\$o!`
Last edited by AlephAlpha on January 12th, 2018, 10:13 am, edited 1 time in total.
AlephAlpha

Posts: 32
Joined: October 6th, 2017, 1:50 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?

KittyTac

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

### 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)

Majestas32

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

### Re: B026/S1

Another breeder:

`x = 39, y = 39, rule = B026/S1bo\$o25\$37bo\$36bo2\$36bo4\$38bo3\$27bobo\$26bo\$33bo!`
AlephAlpha

Posts: 32
Joined: October 6th, 2017, 1:50 am

### 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!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: B026/S1

Tagalong gun:

`x = 67, y = 28, rule = B026/S121bo3\$24bo28bo\$46bo3\$43bo\$15bo\$16bo4\$o5\$58bo\$57bo\$bo3\$4bo\$66bo3\$63bo!`
AlephAlpha

Posts: 32
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

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

`x = 26, y = 41, rule = B026/S13bobo\$6bo14bobo\$24bo\$19bo\$24bo\$17bo\$8bobo11bo\$7bo9bo2\$19bo\$18bo8\$22bobo\$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:
`x = 35, y = 35, rule = B026/S111bobo\$14bo8bobo\$11bo14bo\$12bobo8bo\$24bobo2\$14bobo\$13bo\$2bo19bo7bobo\$33bo\$30bo\$31bobo\$8bo17bo\$4bo5\$28bo2\$o27bo2bobo\$27bo6bo\$31bo\$32bobo3\$22bo4\$21bo2\$26bo2\$14bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: B026/S1

A 90-degree reflector:

`x = 53, y = 57, rule = B026/S131bo3\$28bo5\$37bo\$36bo\$21bo\$28bo2\$46bo5bo\$31bo15bo\$22bobo\$21bo25bo2\$27bo13bo\$42bobo\$27bo23bo\$26bo2\$48bo2\$16bo\$17bo5\$8bo3\$11bo21\$obo\$3bo!`

A glider duplicator:

`x = 71, y = 42, rule = B026/S13bo63bo3\$o69bo5\$9bo51bo\$8bo53bo4\$18bo33bo\$19bo31bo2\$19bo31bo2\$13bo43bo\$14bobo37bobo\$23bo23bo3\$20bo29bo\$13bo43bo16\$11bobo\$14bo!`

A puffer:

`x = 19, y = 18, rule = B026/S14bo11bobo\$3bo11bo5\$6bo4\$bobo\$o\$4b2o\$o2\$2bo2\$12bo!`
AlephAlpha

Posts: 32
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

Sierpinski triangle:

`x = 37, y = 18, rule = B026/S1bo11bobo\$o11bo2\$6bo2\$22bo11bobo\$21bo11bo2\$27bo6\$3bo\$2bo2\$2bo!`
AlephAlpha

Posts: 32
Joined: October 6th, 2017, 1:50 am

### Re: B026/S1

A p4 rake:

`x = 7, y = 9, rule = B026/S14bo\$3bo3\$4bobo3\$bo\$o!`

A very simple c/4 spaceship:

`x = 6, y = 7, rule = B026/S1o2\$3bo2\$5bo2\$2bo!`
AlephAlpha

Posts: 32
Joined: October 6th, 2017, 1:50 am