Hunting for oscillators in new rules

[Hdjensofjfnen]

I'd like to devote a thread to finding stuff in rules such as B2-a3i4aijk/S2a3-i4, B2-a3-in/S2-c3, B2-a3/S1c2a, and other testing rules, since the "Test" thread is getting overcrowded with tests.

NOTE: THIS THREAD IS FOR DISCOVERIES ONLY, NOT TESTING!

Here's an oscillator I found this afternoon in B2-a3i4aijk/S2a3-i4.

Code: Select all

x = 11, y = 5, rule = B2-a3i4aijk/S2a3-i4
3bo3bo$b4ob4o$2o3bo3b2o$b4ob4o$3bo3bo!

[Hdjensofjfnen]

Ok, new discovery. I'm calling it double sparked stairs.

Code: Select all

x = 9, y = 4, rule = B2-a3i4aijk/S2a3-i4
2bo3bo$b2o3b2o$2ob3ob2o$4bo!

[Hdjensofjfnen]

And a quadruple sparked stair (p3):

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo3bo$b2o3b2o$2obobob2o$2b2ob2o2$2b2ob2o$2obobob2o$b2o3b2o$2bo3bo!

[Hdjensofjfnen]

I shall call this the sparked bridge. It is period 4.

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo$b2o$2obo$2b2o2$5b2o$5bob2o$6b2o$6bo!

[Rhombic]

(link to discoveries so far here)
New eater:

Code: Select all

x = 13, y = 9, rule = B2-a3i4aijk/S2a3-i4
2b2o$2b2o$2o$2o2$8bo$7bobo$10bobo$8bo!

I shall call this the sparked bridge. It is period 4.

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo$b2o$2obo$2b2o2$5b2o$5bob2o$6b2o$6bo!

Do you think that it can be extended (and stabilised)?

xp3 that can be extended:

Code: Select all

x = 9, y = 10, rule = B2-a3i4aijk/S2a3-i4
3b2o$3b2o$2bo2b2o$2o3b2o$2o2bo2b2o$2b2o3b2o$2b2o2bo$4b2o$5b2o$6bo!

xp6

Code: Select all

x = 10, y = 7, rule = B2-a3i4aijk/S2a3-i4
2bo4bo$b2o4b2o$2obo2bob2o3$4b2o$4b2o!

Non-stair xp10!

Code: Select all

x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i4
b4o$o3bo$obobo$o3bo$4o!

[Rhombic]

Hdjensofjfnen, I have seen your nx1 polyominos that are oscillators (n=12,48,144,432,1296) and, after a quick search, I have found the next values for n=3888, 11664, 34992, 104976, 314928...
Unfortunately, even though it accurately predicts all values in the sequence, the generating function it gives does not match the sequence at all (or I am missing something).

[Bullet51]

Hdjensofjfnen, I have seen your nx1 polyominos that are oscillators (n=12,48,144,432,1296) and, after a quick search, I have found the next values for n=3888, 11664, 34992, 104976, 314928...
Unfortunately, even though it accurately predicts all values in the sequence, the generating function it gives does not match the sequence at all (or I am missing something).

It seems that the "correct" sequence should be 16,48,144,432,1296...

[Rhombic]

Side note

xp5 (spark on block)

Code: Select all

x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i4
2o$2o2bo$3bo$2bo$bo!

Absurdly unexpected synthesis

Code: Select all

x = 22, y = 9, rule = B2-a3i4aijk/S2a3-i4
b2o$b2o4$2o15bo$b2o13bobo$2bo16bobo$17bo!

[Hdjensofjfnen]

@Rhombic: Lol!

Not sure if this is known or not, might have been mentioned somewhere:

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
6bo$6b2o$7b2o$4bo$3bobo$4bo$2o$b2o$2bo!

EDIT: p2 (duoplets stablilized by blocks)

Code: Select all

x = 6, y = 6, rule = B2-a3i4aijk/S2a3-i4
2o$2o2bo$3bo$2bo$bo2b2o$4b2o!

[Hdjensofjfnen]

xp5 (spark on block)

Code: Select all

x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i4
2o$2o2bo$3bo$2bo$bo!

Riding your coattails. (non-trivial p5)

Code: Select all

x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i4
2o$2o2bo$3bo$2bo$bo2$6b2o$6b2o!

EDIT:
Oops...

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2o$2o2bo$3bo$2bo$bo5b2o$6b2o$5b2o$4b2o$4bo!

[Hdjensofjfnen]

Whoa, whoa, whoa! What's this?

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
4bo$2b2ob2o$b2o3b2o$bo5bo$o7bo$bo5bo$b2o3b2o$2b2ob2o$4bo!

EDIT: Synthesis for another still life:

Code: Select all

x = 9, y = 8, rule = B2-a3i4aijk/S2a3-i4
2o$2o2bo$3bo$2bo$bo$7b2o$6b2o$6bo!

EDIT 2: Sparked blocks (p2):

Code: Select all

x = 7, y = 7, rule = B2-a3i4aijk/S2a3-i4
2o$2o$2bo2$4bo$5b2o$5b2o!

EDIT 3: Another p2:

Code: Select all

x = 7, y = 7, rule = B2-a3i4aijk/S2a3-i4
2o3b2o$2o3b2o$2bobo$b2ob2o$2bobo$2o3b2o$2o3b2o!

[Rhombic]

Possible synthesis of p2:

Code: Select all

x = 19, y = 7, rule = B2-a3i4aijk/S2a3-i4
2o2b2o$2o2b2o2$14bo$4bo8bobo$4b2o10bobo$5b2o7bo!

4G synthesis of loaf p38:

Code: Select all

x = 58, y = 19, rule = B2-a3i4aijk/S2a3-i4
55b3o$55bo$13b3o38bo2bo$4bo8bo$4bo7bo2bo38bobo$2b2ob2o$2ob2o7bobo$4bo
43bo$2bo47bo$49bo2$53bo2$11bo41bo$10bo2bo$11bo$12bo2$12bo!

xp8:

Code: Select all

x = 7, y = 8, rule = B2-a3i4aijk/S2a3-i4
3b2o$3b2o2$2bo$2o$b2o$2bo2b2o$5b2o!

Two xp6:

Code: Select all

x = 7, y = 8, rule = B2-a3i4aijk/S2a3-i4
2b2o$2b2o2$2bo$2o$b2o$2bo2b2o$5b2o!

Code: Select all

x = 8, y = 7, rule = B2-a3i4aijk/S2a3-i4
5bo$5b2o$6b2o$4bo$2o$b2o$2bo!

xp7!!!

Code: Select all

x = 7, y = 8, rule = B2-a3i4aijk/S2a3-i4
b2o$b2o2$4bo$2o$b2o$2bo2b2o$5b2o!

xp11!!!

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo$b2o3b2o$2obo2b2o2$3bo$4bobo$7b2o$6b2o$6bo!

[Rhombic]

Potential partial:

Code: Select all

x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo3b2o$b2o3bobo$2obo3b2o2$3bo$4bobo$7b2o$6b2o$6bo!

[Rhombic]

I'm currently apgsearching this rule. Funnily enough, this xp4 has not appeared yet:

Code: Select all

x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i4
6b2o$6b2o2$3bo$4bo$2bo$2o$2o!

[Hdjensofjfnen]

xp2's:

Code: Select all

x = 4, y = 4, rule = B2-a3i4aijk/S2a3-i4
2o$2o$2b2o$ob2o!

Code: Select all

x = 4, y = 6, rule = B2-a3i4aijk/S2a3-i4
2b2o$2b2o$bo2$2o$2o!

[Hdjensofjfnen]

One xp4:

Code: Select all

x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i4
2o$2o2$4bo$3bo!

[Rhombic]

Please check this page to know which oscillators are already known (check the four symmetries that I have already apgsearched).

[Hdjensofjfnen]

One xp2 (trivial?):

Code: Select all

x = 6, y = 1, rule = B2-a3i4aijk/S2a3-i4
ob2obo!

[Hdjensofjfnen]

A synthesis:

Code: Select all

x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i4
2o$2o3$6bo$5bobo$4bo2bo$5b2o!

[Rhombic]

Hdjensofjfnen, I have seen your nx1 polyominos that are oscillators (n=12,48,144,432,1296) and, after a quick search, I have found the next values for n=3888, 11664, 34992, 104976, 314928...
Unfortunately, even though it accurately predicts all values in the sequence, the generating function it gives does not match the sequence at all (or I am missing something).

The periods of the first four are 14, 2046, 1022, 65534. This seems to be some sort of 2^f(n) - 2 where f is some function. f(n) for n=1,2,3,4 gives 4, 11, 10, 16.

This is weird.