## Hunting for oscillators in new rules

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Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Hunting for oscillators in new rules

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!
``````
"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!
``````

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

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!
``````
"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!
``````

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

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!
``````
"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!
``````

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

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!``````
"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!
``````

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

(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!
``````
Hdjensofjfnen wrote: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!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

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).
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Bullet51
Posts: 536
Joined: July 21st, 2014, 4:35 am

### Re: Hunting for oscillators in new rules

Rhombic wrote: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...
Still drifting.

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

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!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

@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!``````
"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!
``````

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

Rhombic wrote: xp5 (spark on block)

Code: Select all

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

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!``````
"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!
``````

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

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!``````
"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!
``````

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

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!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

Potential partial:

Code: Select all

``````x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo3b2o\$b2o3bobo\$2obo3b2o2\$3bo\$4bobo\$7b2o\$6b2o\$6bo!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

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!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

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!
``````
"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!
``````

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

One xp4:

Code: Select all

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

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

One xp2 (trivial?):

Code: Select all

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

Hdjensofjfnen
Posts: 1338
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

A synthesis:

Code: Select all

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

Rhombic
Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Hunting for oscillators in new rules

Rhombic wrote: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.
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?