## B2ce/S0 (Simplest Interesting Rule?)

For discussion of other cellular automata.
dani
Posts: 1002
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

### 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:

Code: Select all

x = 4, y = 4, rule = B2ce/S0
o\$3bo2\$3bo!
You'll often see these 4c/10 dot puffers form, which have fuses that can burn its exhaust:

Code: Select all

x = 9, y = 5, rule = B2ce/S0
5bobo2\$o3bo3bo2\$5bobo!

Code: Select all

x = 49, y = 43, rule = B2ce/S0
6bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5bo
bo\$46bo\$o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo\$46bo\$3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo5bobo\$46bo3\$4bobo3bo3bo3bo3bo3bo3bo3bo3bo3bo18\$6bo3bo3bo3b
o3bo3bo3bo3bo3bo3bo3\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5bobo\$46bo\$o3b
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo\$46bo\$3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
5bobo\$46bo3\$6bobobo3bo3bo3bo3bo3bo3bo3bo3bo!
AforAmpere found a nice c/2 that can be infinitely extended:

Code: Select all

x = 3, y = 23, rule = B2ce/S0
bo\$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:

Code: Select all

x = 75, y = 11, rule = B2ce/S0
o3bo4bo2bo12bo3bo10bo10bo4bo9bo4bo\$bo4bo7bo4bo2bo8bo5bo4bo10bo6bo7bo\$
35bo12bo9bo\$6bo7bo4bo2bo8bo10bo3bo6bo9bo4bo5bo\$4bo4bo2bo13bo2bo5bo4bo
10bo6bo7bo5bo\$25bo11bo8bo8bo4bo\$48bo17bo5bo\$63bo4bo5bo2\$68bo\$66bo4bo!
she/her
moose#0915

Hdjensofjfnen
Posts: 1516
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

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

Is there a way to stabilize this rule while still keeping it interesting?
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o\$6bo\$o3b3o\$2o\$bo!

jimmyChen2013
Posts: 134
Joined: December 11th, 2017, 3:28 am

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

6c/22d puffer if not known:

Code: Select all

x = 6, y = 4, rule = B2ce4i5n/S04y7e
ob3o\$5bo\$obo2bo\$4bo!
a wider 4c/10 puffer:

Code: Select all

x = 14, y = 17, rule = B2ce4i5n/S04eyz7e
13bo\$8bo3bo\$4bo4\$o7bo3bo2\$o7bo2\$o7bo3bo4\$4bo\$8bo3bo\$13bo!
Failed Replicator!

Code: Select all

x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo\$obo\$bobo\$2bo!
(That I wish was not failed D:)

Hdjensofjfnen
Posts: 1516
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

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

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

Code: Select all

x = 9, y = 9, rule = B2ce/S01c2a
2bobobo8\$o7bo!
EDIT:

Code: Select all

x = 7, y = 9, rule = B2ce/S01c2a
3bo\$o5bo2\$o5bo\$3bo4\$3bo!
EDIT: 9c/20 and 4c/10, respectively
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o\$6bo\$o3b3o\$2o\$bo!

wildmyron
Posts: 1398
Joined: August 9th, 2013, 12:45 am

### 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:

Code: Select all

x = 10, y = 8, rule = B2ce/S0
5bo\$bo\$7bo\$obo\$7bobo\$2bo\$8bo\$4bo!
Hdjensofjfnen wrote:
Hdjensofjfnen wrote:Is there a way to stabilize this rule while still keeping it interesting

Code: Select all

x = 9, y = 9, rule = B2ce/S01c2a
2bobobo8\$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:

Code: Select all

x = 41, y = 31, rule = B2ce/S01c
5bo24bo4bo\$3bo29bo\$6bo26bo2bo\$bobo\$7bo22bo2bo3bo\$o4bo3bo\$7bo25bo2bo\$bo
bo29bo\$6bo23bo4bo\$3bo\$5bo10\$5bo32bo\$3bo30b2o\$4bobo29bo2bo\$bobo30b2o\$2b
o4bo23bobo6bo\$o30bobobobo\$2bo29bo\$4bo30bo\$30bo\$32bo\$34bo!
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

dani
Posts: 1002
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA
Contact:

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

This fuse:

Code: Select all

x = 129, y = 5, rule = B2ce/S0
14bo\$o\$4bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo\$o\$14bo!
Burns p6s:

Code: Select all

x = 8, y = 9, rule = B2ce/S0
3bo2\$o3bo2\$4bo2bo2\$o3bo2\$3bo!
There's a related p8 too which seems quite sparky:

Code: Select all

x = 10, y = 7, rule = B2ce/S0
5bo\$o8bo\$6bo2\$6bo\$o8bo\$5bo!
EDIT: Failed replicator:

Code: Select all

x = 1, y = 8, rule = B2ce/S0
o2\$o3\$o2\$o!
Another p8:

Code: Select all

x = 9, y = 9, rule = B2ce/S0
o3\$bobo2\$3bo2\$5bo\$8bo!
she/her
moose#0915

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

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

A 4c/8 puffer:

Code: Select all

x = 39, y = 44, rule = B2ce/S0
11\$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:

Code: Select all

x = 28, y = 38, rule = B2ce/S0
6\$9bo4bo5bo4bo\$8bobo2bobo3bobo2bobo\$11b2o9b2o\$16bobo2\$16bobo2\$15bo3bo\$
14bo5bo\$13bobo3bobo\$9bobo2bo5bo2bobo2\$10b2o3bo3bo3b2o\$14bobobobo\$14bo
5bo\$15bo3bo3\$13bo3bo3bo\$12bo2bo3bo2bo\$13bo7bo2\$12bo9bo\$15bo3bo\$11bo11b
o2\$12bo9bo\$15bo3bo2\$17bo\$15bo3bo!

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

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

A 2c/4 ship:

Code: Select all

x = 29, y = 17, rule = B2ce/S0
7\$10bobo2bobo\$6bobo10bobo2\$7b2o10b2o!

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

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

And much nicer, c/7:

Code: Select all

x = 19, y = 12, rule = B2ce/S0
4bo9bo\$bo5bo3bo5bo2\$9bo\$2bo5bobo5bo\$4bobo5bobo\$9bo2\$3bobo7bobo\$o6bo3bo
6bo2\$2bo2bo7bo2bo!
I, think I agree the most interesting rule with 3 transitions.