B2ce/S0 (Simplest Interesting Rule?)

[dani]

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:

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

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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:

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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:

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

[Hdjensofjfnen]

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

[jimmyChen2013]

6c/22d puffer if not known:

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x = 6, y = 4, rule = B2ce4i5n/S04y7e
ob3o$5bo$obo2bo$4bo!

a wider 4c/10 puffer:

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

[Hdjensofjfnen]

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

I answered my own question.

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

[wildmyron]

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

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!

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

I answered my own question.

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:

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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!

[dani]

This fuse:

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

Burns p6s:

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x = 8, y = 9, rule = B2ce/S0
3bo2$o3bo2$4bo2bo2$o3bo2$3bo!

There's a related p8 too which seems quite sparky:

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x = 10, y = 7, rule = B2ce/S0
5bo$o8bo$6bo2$6bo$o8bo$5bo!

EDIT: Failed replicator:

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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!

Sadly it's not XOR

[2718281828]

A 4c/8 puffer:

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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:

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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]

A 2c/4 ship:

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

[2718281828]

And much nicer, c/7:

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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.