B2/S34 (MM's Spiralgraph)

[I6_I6]

I created this thread mostly to move discussion about the rule away from the Unnamed Life-Like Rules thread, but also because it's a decently interesting rule in its own right.

Previous discussion:

I was forcing my girlfriend to play with automata the other day and was decided to use B2/S34.
It seems to be unnamed. The only reference I can find to it is: viewtopic.php?f=11&t=1217&p=224693&hili ... 34#p224693

Is there a name somewhere?
If there's no name, can memberlist.php?mode=viewprofile&u=3922 make one up?
If they pass, can I make one up?

...

I think this is a rule which hasn’t been explored much before, because patterns are pretty explosive.
However you can put chaos in a square “cage” witch produces interesting results:

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 x = 12, y = 12, rule = B2/S34
bo2bo2bo2bo$12o$bo8bo$bo3bo4bo$2o6bob2o$bo4b2o2bo$bo4bo3bo$2o3bo2bob2o
$bo3bobo2bo$bo8bo$12o$bo2bo2bo2bo!

P1946

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 x = 15, y = 12, rule = B2/S34
bo2bo2bo2bo2bo$15o$bo11bo$bo8b2obo$2o4bo6b2o$bo2bobobo4bo$bobobobo5bo
$2o4bo4bob2o$bo2b2o2bobo2bo$bo11bo$15o$bo2bo2bo2bo2bo!

Yeah, I'm mostly playing with visual effects (I'm wondering if we need a separate Forum section for these types of users).
A lot of rules I explore don't have any academic value.
It's just fun to give them names.

B2/S34 is interesting in particular because it makes much more detailed patterns than Serviettes.

Here's the "default" Persian Rug pattern

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x = 10, y = 10, rule = B2/S34
oo$oo!

My girlfriend named the rule: MM's Spiralgraph
Let's add it to the full list of rules, when we get a chance

The elementary cellular automata W90 can be simulated, and at least 2 one-dimensional 4-state ones, see the following cages:

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x = 135, y = 55, rule = B2/S34
bo2bo2bo2bo2bo17bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo2bo3bo17bo3bo2bo2bo2b
o2bo2bo2bo2bo2bo3bo$15o15b15o11b25o15b35o$bo11bo17bo11bo13bo12bo2bo2bo
2bo17bo2bo2bo2bo13bo2bo2bo2bo$bo11bo17bo4bob2obobo13bob3o3bobo2bo2bo9b
o9bo9bo2bo5bo2bo2bobo2bo9bo$2o11b2o15b2o4bob2obob2o11b2ob3o3bobo2b2ob
12o7b12ob2o5bo2bo2bob2ob12o$bo11bo17bo11bo13bo12bo3bo2bo2bo2bo9bo2bo2b
o2bo3bo13bo3bo2bo2bo2bo$bo11bo17b13o13b14ob2o29b2ob15ob2o$15o15b2o2bo
2bo2bo2b2o11b2o2bo2bo2bo2bo2b2o29b2o2bo2bo2bo2bo2bo2b2o$bo2bo2bo2bo2bo
17bo11bo13bo15bo29bo19bo$bo11bo17bo11bo13bo15b2o27b2o19b2o$15o15b3o9b
3o11b3o13b2o29b2o17b2o$bo2bo2bo2bo2bo17bo11bo13bo15bo29bo19bo$73bo29bo
19bo$72b3o27b3o17b3o$73bo29bo19bo6$bo2bo2bo2bo2bo17bo2bo2bo2bo2bo$15o
15b15o$bo11bo17bo11bo$bo11bo17bo7bo3bo$2o11b2o15b2o3b3o3bob2o$bo11bo
17bo7bo3bo$bo11bo17bo11bo$15o15b15o$bo2bo2bo2bo2bo17bo2bo2bo2bo2bo12$b
o2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo$18o12b18o$bo14bo14bo14bo$bo14bo14b
o6bo7bo$2o14b2o12b2o4bo6b2ob2o$bo14bo14bo4bo6b2obo$bo14bo14bo6bo7bo$2o
14b2o12b2o14b2o$b16o14b16o$bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo$2o14b
2o12b2o14b2o$bo14bo14bo14bo$bo14bo14bo14bo$18o12b18o$bo2bo2bo2bo2bo2bo
14bo2bo2bo2bo2bo2bo!

This is one of a few B2 rules that allow those kind of boxes that are stable no matter what is inside them...I'm not sure if they have an accepted name but I've been calling them soup containers. Out of those B2/S23, B2/S34, B2/S45, B2/Sx56 for x = 1 to 3, and derivatives are kind of neat because you can also make ones with cut corners, like so:

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# p3, p4, p6, p16, p21, p28, p34 
x=57, y=28, rule=B2/S34
8bo15bo14bo10bo4bo$bo2bo2b3o7bo2bo3b2o6bo2bo3b2o6bo2bob5o$7obo7b8o7b8o8bob4o2bo$bo4bo10bo5bo8bo5bo7bobo4b2o$bo2bo2b3o
7bo2bo2bobo6bo5bobo5b2obo4bo$2obo3bob2o5b2obo3b2o6b2o2b2ob2o5bobo3bo2b2o$bo5bobo7bo5bo8bo5bo7b2o6bo$2bo4b2o8bo4bob2o
6bo4bob2o5bobo4b2o$2b5obo8b5obo8b5obo8bob4o2bo$bo3bo3bo5b2o3bobo7b2o3bobo9bo2bob5o$3o5b3o5bo2bo2bo8bo2bo2bo12bo4bo$bo
7bo4$27bo4bo6bo2bo2bo$9bo2bo4bo6bo2bob5o4b2o3bobo$8b6o2b3o5bob4o2bo7b7o2bo$7b2o5b2obo5bobo4b2o8bo5bobo$8bo3bo2bo7b2o
2bo3bo6bobo6b2o$8bo2bo3bo6bobo2b2o2bo7b2ob2o3bobo$7b2obo4b2o7bo6b2o7bo6bo2bo$8bo6bo7b2o6bo6b3o6b2o$8b2o4b2o6b2obo4b2o
8b2o5bo$7bo2b4o2bo7bob4o2bo9b5o$6b3obo2b5o5bo3bob5o7b2o2bo2bo$7bo2b3o3bo9bo2bo2bo7bo2bo$11bo32bo!

I imagine they'd be a good basis for a name, but I'd have to figure out more about how it's different from the other rules with similar containers. For small patterns there is also a 4-cell oscillator that works like a radar but slowed down by an extra step (a sonar?):

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# p6 with 4-8 cells
x=4, y=4, rule=B2/S34
bo$o$3bo$2bo!

[I6_I6]

(Doubleposting because the first post was sort of an intro post)
Reduction to actinophrys's p3:

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x = 11, y = 12, rule = B2/S34
bo2bo4bo$6o2b3o$bo4b2obo$bo2bo2bo$2obo3bo$bo5b2o$2bo4bo$2b5o$bo3b2o$3o
4bo$bo4b3o$7bo!

(Edit: Oops grammar)

[actinophrys]

Oops, thank you for that. Then in case they're of interest here a couple little p2 spaceships that work in this rule. The c/2 one is in gliders.db, the others are from stabilizing some fronts that often show up in explosions.

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x=70, y=12, rule=B2/S34
39b2o19b2o$39b2o19b2o$o9bo23b2o3b2o3b2o13bo2bo$o9bo6b2o2b2o2b2o6bo2bo6bo2bo13b2o$o4bo4bo5bo2bob2obo2bo11b2o15b2obo2bob2o
$o2bo3bo2bo42b2ob3o4b3ob2o$21b2o14bo4bo9b3o4b4o4b3o$2bob3obo11bo2bo32b2o6b2o$36bo6bo14bo4bo$3bo3bo46b2o10b2o$38bo2bo$55b
o10bo!