## B2ce/S0 (Simplest Interesting Rule?)

For discussion of other cellular automata.

### B2ce/S0 (Simplest Interesting Rule?)

This rule has only 3 transitions, but it's actually both interesting and explosive. A lot of the rule's growth looks like this:
`x = 4, y = 4, rule = B2ce/S0o\$3bo2\$3bo!`

You'll often see these 4c/10 dot puffers form, which have fuses that can burn its exhaust:
`x = 9, y = 5, rule = B2ce/S05bobo2\$o3bo3bo2\$5bobo!`

`x = 49, y = 43, rule = B2ce/S06bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5bobo\$46bo\$o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5bobo\$46bo3\$4bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo18\$6bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5bobo\$46bo\$o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5bobo\$46bo3\$6bobobo3bo3bo3bo3bo3bo3bo3bo3bo!`

AforAmpere found a nice c/2 that can be infinitely extended:
`x = 3, y = 23, rule = B2ce/S0bo\$2bo\$bo\$o\$o\$bo\$2bo\$bo3\$bo\$2bo\$bo\$o\$o\$bo\$2bo\$bo\$o\$o\$bo\$2bo\$bo!`

It's not too common naturally, sadly.

Here are some p2s and p4s. I don't know if p3 exists in this rule:
`x = 75, y = 11, rule = B2ce/S0o3bo4bo2bo12bo3bo10bo10bo4bo9bo4bo\$bo4bo7bo4bo2bo8bo5bo4bo10bo6bo7bo\$35bo12bo9bo\$6bo7bo4bo2bo8bo10bo3bo6bo9bo4bo5bo\$4bo4bo2bo13bo2bo5bo4bo10bo6bo7bo5bo\$25bo11bo8bo8bo4bo\$48bo17bo5bo\$63bo4bo5bo2\$68bo\$66bo4bo!`
she/they // Please stop using my full name. Refer to me as dani.

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

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Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA

### Re: B2ce/S0 (Simplest Interesting Rule?)

Is there a way to stabilize this rule while still keeping it interesting?
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

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Location: r cis θ

### Re: B2ce/S0 (Simplest Interesting Rule?)

6c/22d puffer if not known:
`x = 6, y = 4, rule = B2ce4i5n/S04y7eob3o\$5bo\$obo2bo\$4bo!`

a wider 4c/10 puffer:
`x = 14, y = 17, rule = B2ce4i5n/S04eyz7e13bo\$8bo3bo\$4bo4\$o7bo3bo2\$o7bo2\$o7bo3bo4\$4bo\$8bo3bo\$13bo!`
Failed Replicator!
`x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8bo\$obo\$bobo\$2bo!`

(That I wish was not failed D:)

jimmyChen2013

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### Re: B2ce/S0 (Simplest Interesting Rule?)

Hdjensofjfnen wrote:Is there a way to stabilize this rule while still keeping it interesting?

`x = 9, y = 9, rule = B2ce/S01c2a2bobobo8\$o7bo!`

EDIT:
`x = 7, y = 9, rule = B2ce/S01c2a3bo\$o5bo2\$o5bo\$3bo4\$3bo!`

EDIT: 9c/20 and 4c/10, respectively
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1139
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: B2ce/S0 (Simplest Interesting Rule?)

I think you make a good case for this being the simplest rule (in terms of number of transitions) which has interesting behaviour.

danny wrote:I don't know if p3 exists in this rule

I didn't find any after running several LLS searches. If p3 oscillators do exist in this rule then they are quite large.

I did find a p5 though:
`x = 10, y = 8, rule = B2ce/S05bo\$bo\$7bo\$obo\$7bobo\$2bo\$8bo\$4bo!`

Hdjensofjfnen wrote:
Hdjensofjfnen wrote:Is there a way to stabilize this rule while still keeping it interesting

`x = 9, y = 9, rule = B2ce/S01c2a2bobobo8\$o7bo!`

Only S1c of those two additional transitions is required to stabilise the rule. B2ce/S01c is apgsearchable.
It does have p3 (and p5) oscillators:
`x = 41, y = 31, rule = B2ce/S01c5bo24bo4bo\$3bo29bo\$6bo26bo2bo\$bobo\$7bo22bo2bo3bo\$o4bo3bo\$7bo25bo2bo\$bobo29bo\$6bo23bo4bo\$3bo\$5bo10\$5bo32bo\$3bo30b2o\$4bobo29bo2bo\$bobo30b2o\$2bo4bo23bobo6bo\$o30bobobobo\$2bo29bo\$4bo30bo\$30bo\$32bo\$34bo!`
The latest version of the 5S Project contains over 150,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

Posts: 1165
Joined: August 9th, 2013, 12:45 am

### Re: B2ce/S0 (Simplest Interesting Rule?)

This fuse:
`x = 129, y = 5, rule = B2ce/S014bo\$o\$4bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo\$o\$14bo!`

Burns p6s:
`x = 8, y = 9, rule = B2ce/S03bo2\$o3bo2\$4bo2bo2\$o3bo2\$3bo!`

There's a related p8 too which seems quite sparky:
`x = 10, y = 7, rule = B2ce/S05bo\$o8bo\$6bo2\$6bo\$o8bo\$5bo!`

EDIT: Failed replicator:
`x = 1, y = 8, rule = B2ce/S0o2\$o3\$o2\$o!`

Another p8:
`x = 9, y = 9, rule = B2ce/S0o3\$bobo2\$3bo2\$5bo\$8bo!`

she/they // Please stop using my full name. Refer to me as dani.

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

Posts: 953
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA

### Re: B2ce/S0 (Simplest Interesting Rule?)

A 4c/8 puffer:
`x = 39, y = 44, rule = B2ce/S011\$30bo\$28bo\$28bobo2\$31bo2\$31bo2\$28bobo\$28bo\$30bo5\$6bo\$8bo4bobo10bo\$12bobobo3bo7bo\$7bo2bo7bo3bo3bo2bo\$14bobo11bo\$5bo6bo2bob2obo\$8bo12bo8bo\$6bo3bo3bo3bo\$8bo12bo8bo\$5bo6bo2bob2obo\$14bobo11bo\$7bo2bo7bo3bo3bo2bo\$12bobobo3bo7bo\$8bo4bobo10bo\$6bo!`

Edit1:
A 2c/4 puffer:
`x = 28, y = 38, rule = B2ce/S06\$9bo4bo5bo4bo\$8bobo2bobo3bobo2bobo\$11b2o9b2o\$16bobo2\$16bobo2\$15bo3bo\$14bo5bo\$13bobo3bobo\$9bobo2bo5bo2bobo2\$10b2o3bo3bo3b2o\$14bobobobo\$14bo5bo\$15bo3bo3\$13bo3bo3bo\$12bo2bo3bo2bo\$13bo7bo2\$12bo9bo\$15bo3bo\$11bo11bo2\$12bo9bo\$15bo3bo2\$17bo\$15bo3bo!`

2718281828

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### Re: B2ce/S0 (Simplest Interesting Rule?)

A 2c/4 ship:
`x = 29, y = 17, rule = B2ce/S07\$10bobo2bobo\$6bobo10bobo2\$7b2o10b2o!`

2718281828

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Joined: August 8th, 2017, 5:38 pm

### Re: B2ce/S0 (Simplest Interesting Rule?)

And much nicer, c/7:
`x = 19, y = 12, rule = B2ce/S04bo9bo\$bo5bo3bo5bo2\$9bo\$2bo5bobo5bo\$4bobo5bobo\$9bo2\$3bobo7bobo\$o6bo3bo6bo2\$2bo2bo7bo2bo!`

I, think I agree the most interesting rule with 3 transitions.

2718281828

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