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## Hunting for oscillators in new rules

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.

### 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.

`x = 11, y = 5, rule = B2-a3i4aijk/S2a3-i43bo3bo\$b4ob4o\$2o3bo3b2o\$b4ob4o\$3bo3bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
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.

`x = 9, y = 4, rule = B2-a3i4aijk/S2a3-i42bo3bo\$b2o3b2o\$2ob3ob2o\$4bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

And a quadruple sparked stair (p3):

`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i42bo3bo\$b2o3b2o\$2obobob2o\$2b2ob2o2\$2b2ob2o\$2obobob2o\$b2o3b2o\$2bo3bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
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.

`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i42bo\$b2o\$2obo\$2b2o2\$5b2o\$5bob2o\$6b2o\$6bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

(link to discoveries so far here)
New eater:
`x = 13, y = 9, rule = B2-a3i4aijk/S2a3-i42b2o\$2b2o\$2o\$2o2\$8bo\$7bobo\$10bobo\$8bo!`

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

`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i42bo\$b2o\$2obo\$2b2o2\$5b2o\$5bob2o\$6b2o\$6bo!`

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

xp3 that can be extended:
`x = 9, y = 10, rule = B2-a3i4aijk/S2a3-i43b2o\$3b2o\$2bo2b2o\$2o3b2o\$2o2bo2b2o\$2b2o3b2o\$2b2o2bo\$4b2o\$5b2o\$6bo!`

xp6
`x = 10, y = 7, rule = B2-a3i4aijk/S2a3-i42bo4bo\$b2o4b2o\$2obo2bob2o3\$4b2o\$4b2o!`

Non-stair xp10!
`x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i4b4o\$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”?

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).

It seems that the "correct" sequence should be 16,48,144,432,1296...
Still drifting.
Bullet51

Posts: 523
Joined: July 21st, 2014, 4:35 am

### Re: Hunting for oscillators in new rules

Side note

xp5 (spark on block)
`x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i42o\$2o2bo\$3bo\$2bo\$bo!`

Absurdly unexpected synthesis
`x = 22, y = 9, rule = B2-a3i4aijk/S2a3-i4b2o\$b2o4\$2o15bo\$b2o13bobo\$2bo16bobo\$17bo!`
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

@Rhombic: Lol!

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

`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i46bo\$6b2o\$7b2o\$4bo\$3bobo\$4bo\$2o\$b2o\$2bo!`

EDIT: p2 (duoplets stablilized by blocks)

`x = 6, y = 6, rule = B2-a3i4aijk/S2a3-i42o\$2o2bo\$3bo\$2bo\$bo2b2o\$4b2o!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

Rhombic wrote:xp5 (spark on block)
`x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i42o\$2o2bo\$3bo\$2bo\$bo!`

Riding your coattails. (non-trivial p5)

`x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i42o\$2o2bo\$3bo\$2bo\$bo2\$6b2o\$6b2o!`

EDIT:
Oops...

`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i42o\$2o2bo\$3bo\$2bo\$bo5b2o\$6b2o\$5b2o\$4b2o\$4bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

Whoa, whoa, whoa! What's this?

`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i44bo\$2b2ob2o\$b2o3b2o\$bo5bo\$o7bo\$bo5bo\$b2o3b2o\$2b2ob2o\$4bo!`

EDIT: Synthesis for another still life:

`x = 9, y = 8, rule = B2-a3i4aijk/S2a3-i42o\$2o2bo\$3bo\$2bo\$bo\$7b2o\$6b2o\$6bo!`

EDIT 2: Sparked blocks (p2):

`x = 7, y = 7, rule = B2-a3i4aijk/S2a3-i42o\$2o\$2bo2\$4bo\$5b2o\$5b2o!`

EDIT 3: Another p2:

`x = 7, y = 7, rule = B2-a3i4aijk/S2a3-i42o3b2o\$2o3b2o\$2bobo\$b2ob2o\$2bobo\$2o3b2o\$2o3b2o!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

Possible synthesis of p2:
`x = 19, y = 7, rule = B2-a3i4aijk/S2a3-i42o2b2o\$2o2b2o2\$14bo\$4bo8bobo\$4b2o10bobo\$5b2o7bo!`

4G synthesis of loaf p38:
`x = 58, y = 19, rule = B2-a3i4aijk/S2a3-i455b3o\$55bo\$13b3o38bo2bo\$4bo8bo\$4bo7bo2bo38bobo\$2b2ob2o\$2ob2o7bobo\$4bo43bo\$2bo47bo\$49bo2\$53bo2\$11bo41bo\$10bo2bo\$11bo\$12bo2\$12bo!`

xp8:
`x = 7, y = 8, rule = B2-a3i4aijk/S2a3-i43b2o\$3b2o2\$2bo\$2o\$b2o\$2bo2b2o\$5b2o!`

Two xp6:
`x = 7, y = 8, rule = B2-a3i4aijk/S2a3-i42b2o\$2b2o2\$2bo\$2o\$b2o\$2bo2b2o\$5b2o!`

`x = 8, y = 7, rule = B2-a3i4aijk/S2a3-i45bo\$5b2o\$6b2o\$4bo\$2o\$b2o\$2bo!`

xp7!!!
`x = 7, y = 8, rule = B2-a3i4aijk/S2a3-i4b2o\$b2o2\$4bo\$2o\$b2o\$2bo2b2o\$5b2o!`

xp11!!!
`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i42bo\$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:
`x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i42bo3b2o\$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:
`x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i46b2o\$6b2o2\$3bo\$4bo\$2bo\$2o\$2o!`
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

xp2's:

`x = 4, y = 4, rule = B2-a3i4aijk/S2a3-i42o\$2o\$2b2o\$ob2o!`

`x = 4, y = 6, rule = B2-a3i4aijk/S2a3-i42b2o\$2b2o\$bo2\$2o\$2o!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

One xp4:

`x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i42o\$2o2\$4bo\$3bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

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

One xp2 (trivial?):

`x = 6, y = 1, rule = B2-a3i4aijk/S2a3-i4ob2obo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Hunting for oscillators in new rules

A synthesis:

`x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i42o\$2o3\$6bo\$5bobo\$4bo2bo\$5b2o!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### 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”?

Rhombic

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