B0156/S2

[Extrementhusiast]

This rule is quite interesting, in my opinion. As with all B0 rules, odd periods are impossible. Here is a collection of various things:

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x = 339, y = 177, rule = B0156/S2
180b2o2$180b2o$180b2o$180b2o$180b2o$180b2o$113b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o29b2o$180b2o$113b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o29b2o$113b38o29b2o$113b38o29b2o$113b38o29b2o$113b38o29b2o$113b38o29b
2o$180b2o$180bo2$180bo$180bo2$180bo$180bo$179b3o$179b3o$179b3o$179b3o
28bobo$179b3o29b2o$179b3o31bo$179b3o$179b3o$179b3o$179b3o$179b3o$179b
3o$179b3o$179b3o$179b3o$179b3o10$80b2o2$80b2o$80b2o$80b2o$81bo$134bo$
81bo54bo$81bo51b3obo$ob7o72bo49bo5bo$ob7o124b3obo$6b3o127bo$3bo3b2o
125bo189b6o$6b3o315b3ob4ob2obo$ob7o320bo6bo$ob7o12$254b2o$253b4o$253b
4o$255bo2$254bo2bo$39b2o3b2o3b2o31bobo$255bo$39b2o3b2o3b2o202b4o$39b
12o202b4o$39b12o30bobo170b2o$44b2o34b5o124b2o$40b2obo2bob2o31b4o120bo
3b2o$43bo2bo33bob3o121bo$41bo6bo34b2o120b2o$83bo121bo$84bo$80b3obo122b
3o$79b2o126b3o$79bobobobo$80bobobo$318bo7bobo$321b2o$321b2o2bo2b2o2bo
3bo$320b2o10bo3bobo$318b3o17bo$318b3o17bo$320b2o10bo3bobo$321b2o2bo2b
2o2bo3bo$321b2o$318bo7bobo11$158b2o$158b2o$158b2o37b3o64b3o$154b6o37b
3o64b3o$154b2o2b2o37b2o$154b2o2b2o37bo52b3o12bo$154b2o3bo90b3o$154b3o
2bo37bo63b9o$156bob2o36b3o62b9o16b2obo$158b2o36b3o87b2obo$158b2o90b3o$
250b3o2$270b2o$270b3o$271b2o$272bo2$272bo$271b2o$270b3o$270b2o5$251b3o
$251b3o42b2o6bo$296b4ob2obo$296b2o2$250b5o$250b5o2$197b2o$197b2o$200bo
b2o$202b2o3$187b2o6b2o$187b2o2bo3b2o$191bo5$177b2o$177b2o$181bo$181bo$
185b2o$185b2o2$302bo$294b4ob2o2bo$293b6o3bo$294b3o3bo2bo$293b3o4bobo$
294bobo3b2obo$301b2o!

Note the 41-cell breeder.

[p46beth]

The r-pentomino results in quadratic growth. I have not found any 4 cell pattern with quadratic growth, though some quite possibly exist.

EDIT:

Code: Select all

x = 4, y = 4, rule = B0156/S2
obo3$2b2o!

Also:

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x = 2, y = 3, rule = B0156/S2
o$o$2o!

And another one:

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x = 4, y = 3, rule = B0156/S2
obo$3bo$o!

And yet another 4 cell quadratic growth pattern:

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x = 5, y = 4, rule = B0156/S2
bo2bo$bo2$o!

Another one:

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x = 4, y = 2, rule = B0156/S2
2bo$2obo!

There seem to be a lot of these:

Code: Select all

x = 4, y = 4, rule = B0156/S2
2o$2bo2$3bo!

Now, could there be any 3-cell patterns with near-quadratic growth? Less likely, but possible.
So far, the fastest growth rate for a 3 cell pattern I have found is

Code: Select all

x = 4, y = 3, rule = B0156/S2
o2$2b2o!

But this is still linear.

EDIT:
Wow!

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x = 1, y = 4, rule = B0156/S2
o2$o$o!

Not only is this 3-cell quadratic growth, but it is symmetrical AND fits in a 1 by 4 box!

Finally, it is pretty clear that no 2-cell pattern could ever have quadratic growth in this rule.

[Extrementhusiast]

Actually, the rightmost cell in your fourth pattern is unnecessary. To whit:

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.O
.O
..
O.

This five-cell pattern seems to grow quadratically, but then settles down to a linear rate:

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..O.
....
O..O
..OO

[Awesomeness]

Are all B0 rules like day and night or something?

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x = 66, y = 33, rule = B0156/S2
66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$o6bob57o$o
6bob57o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$66o$
66o!

[alex79]

Actually Day and Night is not like any b0 rules. In Day and Night the inverse of a pattern is stable if the background is filled with cells stabilized in a certain way, but the background never oscillates. in b0 rules the background oscillates, and it may or may not be self-complementary.

[Rhombic]

Code: Select all

x = 5, y = 3, rule = B0156/S2
3o$obobo$3o!