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Hunting for oscillators in new rules
Posted: August 21st, 2016, 6:17 pm
by 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$3bo3bo!
Re: Hunting for oscillators in new rules
Posted: August 21st, 2016, 6:31 pm
by Hdjensofjfnen
Ok, new discovery. I'm calling it double sparked stairs.
Code: Select all
x = 9, y = 4, rule = B2-a3i4aijk/S2a3-i4
2bo3bo$b2o3b2o$2ob3ob2o$4bo!
Re: Hunting for oscillators in new rules
Posted: August 21st, 2016, 6:40 pm
by Hdjensofjfnen
And a quadruple sparked stair (p3):
Code: Select all
x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo3bo$b2o3b2o$2obobob2o$2b2ob2o2$2b2ob2o$2obobob2o$b2o3b2o$2bo3bo!
Re: Hunting for oscillators in new rules
Posted: August 22nd, 2016, 9:19 pm
by Hdjensofjfnen
I shall call this the sparked bridge. It is period 4.
Code: Select all
x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo$b2o$2obo$2b2o2$5b2o$5bob2o$6b2o$6bo!
Re: Hunting for oscillators in new rules
Posted: August 26th, 2016, 7:04 am
by 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$8bo!
Hdjensofjfnen wrote:I shall call this the sparked bridge. It is period 4.
Code: Select all
x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo$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!
Re: Hunting for oscillators in new rules
Posted: August 26th, 2016, 7:52 am
by 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).
Re: Hunting for oscillators in new rules
Posted: August 26th, 2016, 8:22 am
by Bullet51
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...
Re: Hunting for oscillators in new rules
Posted: August 26th, 2016, 9:17 am
by 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!
Re: Hunting for oscillators in new rules
Posted: August 28th, 2016, 4:47 pm
by 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!
Re: Hunting for oscillators in new rules
Posted: August 28th, 2016, 4:51 pm
by Hdjensofjfnen
Rhombic wrote:
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!
Re: Hunting for oscillators in new rules
Posted: August 28th, 2016, 5:03 pm
by 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!
Re: Hunting for oscillators in new rules
Posted: August 29th, 2016, 7:46 am
by 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$6bo!
Re: Hunting for oscillators in new rules
Posted: August 29th, 2016, 9:55 am
by Rhombic
Potential partial:
Code: Select all
x = 9, y = 9, rule = B2-a3i4aijk/S2a3-i4
2bo3b2o$b2o3bobo$2obo3b2o2$3bo$4bobo$7b2o$6b2o$6bo!
Re: Hunting for oscillators in new rules
Posted: September 1st, 2016, 6:23 am
by 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!
Re: Hunting for oscillators in new rules
Posted: September 2nd, 2016, 8:54 pm
by 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!
Re: Hunting for oscillators in new rules
Posted: September 2nd, 2016, 8:56 pm
by Hdjensofjfnen
One xp4:
Code: Select all
x = 5, y = 5, rule = B2-a3i4aijk/S2a3-i4
2o$2o2$4bo$3bo!
Re: Hunting for oscillators in new rules
Posted: September 3rd, 2016, 8:23 am
by Rhombic
Please check
this page to know which oscillators are already known (check the four symmetries that I have already apgsearched).
Re: Hunting for oscillators in new rules
Posted: September 3rd, 2016, 11:57 am
by Hdjensofjfnen
One xp2 (trivial?):
Code: Select all
x = 6, y = 1, rule = B2-a3i4aijk/S2a3-i4
ob2obo!
Re: Hunting for oscillators in new rules
Posted: September 3rd, 2016, 12:25 pm
by Hdjensofjfnen
A synthesis:
Code: Select all
x = 8, y = 8, rule = B2-a3i4aijk/S2a3-i4
2o$2o3$6bo$5bobo$4bo2bo$5b2o!
Re: Hunting for oscillators in new rules
Posted: September 4th, 2016, 6:46 am
by Rhombic
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.