Project OmniOsci

[muzik]

This is an attempt to aggregate the smallest known oscillators of each period for each possible kinetic symmetry type, from the lowest periods upwards. The 5s restrictions apply - all oscillators must be in range-1 Moore isotropic rules.

All currently documented oscillators, currently up to period 16 can be found at the overview page. Blue is used to mark optimal minimum populations. I'd recommend checking through each of the objects marked green to check whether their population is the lowest possible for that period-symmetry combination.

This thread can be used to propose oscillators for inclusion within the project that are not already in the above tables, as well as any improvements to the documented oscillators such as a lower minimum population. For example, many of the listed oscillators have 8 cells, and I'm doubtful as to whether this is optimal for certain cases such as +k and +k*k.

[pipsqueek]

asymmetric p5

Code: Select all

x = 3, y = 4, rule = B2ek3jn4rw/S01e2ak3ij5i
2bo2$2bo$o!

asymmetric p6

Code: Select all

x = 4, y = 2, rule = B2i3aiqr/S01c2-ce3ae4an
o$bobo!

asymmetric p7

Code: Select all

x = 3, y = 4, rule = B2eik3ry4n/S01e2ac4ar
2bo2$o$2bo!

[muzik]

All periods up to 4 now have an oscillator documented for each symmetry type. There are, of course, improvements to be made - everything marked in blue is "almost certainly optimal" whereas those marked in green are "possibly optimal - someone who knows more than I do should check whether this is the case".

There's probably far too many of these marked as green, though. For the time-asymmetric oscillators, would it be fair to make the following assumptions?:
- D2_+2-symmetric oscillators must have at least 4 cells
- D8-symmetric oscillators (excluding the p1 dot) must have at least 4 cells
- D4_+4-symmetric oscillators must have at least 8 cells, as any arrangements in this symmetry with a lower amount of cells would either be the D8_4-symmetric block, or interaction between the two parts would require B2a or B1, resulting in runaway growth

These all seem to make sense to me, but I'd prefer more formal input from someone who knows more about rulespace restrictions like these. If there's any other minimum population arguments that can be made for other symmetry combinations, please discuss these in the thread so we can more rigorously prove more oscillators to be optimal.

[yujh]

another solution for asymmetric p7:

Code: Select all

x = 5, y = 3, rule = B2ekn3aej4ceirtz5ijq6n/S02ce3aey4aekrt5r6c7c8
obo2$4bo!

n8, 3:

Code: Select all

x = 4, y = 3, rule = B2ein3-ci4acjkt5i6-ik7c8/S01c2-an3akr4acjnrt5acjn6-e78
o2bo2$2bo!

n9, 3:

Code: Select all

x = 4, y = 3, rule = B2cek3-acjy4inr5cinqy6-in/S02ain3-ajqy4ijkrtw5cejr6ak
bobo2$o!

n10, 3:

Code: Select all

x = 4, y = 5, rule = B2ekn3ajnqr4aijknt5ikq6akn/S01c2ein3cer4ikqw5ikqy6aek7c
3bo2$2bo2$o!

n11, 3:

Code: Select all

x = 3, y = 5, rule = B2-ak3anq4-cijr5-cjkr6cn7e/S12-ek3-aij4cikrtwz5acjqy6ck7c
2bo2$2bo2$o!

n12, 3:

Code: Select all

x = 3, y = 6, rule = B2ein3air4ijrtwy5jkqry6-kn7c/S012c3-eijr4ceiknz5-einq6aei7e
o2$o3$2bo!

-f13, 3:

Code: Select all

x = 5, y = 3, rule = B2in3eiry4eiknq5-eiqr6ce78/S01c2acn3jkqy4-ceiqr5ekqr6kn7c
o3bo2$2bo!

/13, 3:

Code: Select all

x = 3, y = 3, rule = B2cin3-ekq4-jnqy5aijnq6-a7e8/S2-a3r4aceikry5-acnq6-cn7c
o2$obo!

n13, 3:

Code: Select all

x = 5, y = 4, rule = B2kn3aenqr4-inrtz5cikqr6c8/S01c2-a3-acnq4ejqrz5eij6-n8
2bo$o2$4bo!

+e should have 4 as the mininum if its period is 2 and above.
FOr now, i should try and complete the n column.
n14, 3:

Code: Select all

x = 4, y = 3, rule = B2in3-ijkq4eijknwy5acqy6cek7c8/S01c2-en3-i4acekn5-ejkq6-e7e
2bo$3bo$o!

/15, 3:

Code: Select all

x = 3, y = 3, rule = B2ckn3aeiqr4-aejnr5en6-an7c/S01c2-k3-acek4ceijqrw5cjqy6akn7c
2bo2$obo!

non-bd-escaping -f15, 3:

Code: Select all

x = 3, y = 4, rule = B2c3cqr4-ainqr5-jy6-i7/S02-ei3-qr4-ceiky5iknqy6-ek
obo3$bo!

n15, 3:

Code: Select all

x = 6, y = 4, rule = B2en3eiqy4cejktwz5ijnqy6cen7c8/S01c2-k3acekr4-jkry5-cery6i78
o$5bo2$3bo!

[C_R_116]

Asymmetric P32 mod 8 with pipsqueek's p5 rule

Code: Select all

x=0, y=0,rule=B2ek3jn4rw/S01e2ak3ij5i
o$2b2o$$2obo

[yujh]

Since there is already a new post, I shall double post.
I like how there is just a ton of dot hasslers.
n16, 3:

Code: Select all

x = 6, y = 4, rule = B2-ak3c4antwyz5ejnry6aci7c/S03-anr4aceinqz5ciry6aei7e
5bo$o2$2bo!

[muzik]

Here's some info from the existing Smallest Oscillators thread, reinterpreted to fit the goal of this project:

The wickstretcher approach for 3-cell oscillators of any sufficiently high period gets us 3-cell -c symmetric oscillators for all of said periods, which are optimal for this symmetry in terms of cell count (although bounding boxes can still - and should - be optimised).

Fully asymmetric oscillators can be realized with 4 cells for all odd periods 11 and up:

Code: Select all

x = 6, y = 4, rule = B2ei3ir4r/S012ce3j
5bo$2bo$o$2bo!

Code: Select all

x = 7, y = 4, rule = B2ein3aciq4jkny5any6ck/S012ce3ejnr4jknrwy5-aiky6ci7e
6bo$2bo$o$2bo!

-c+c is possible in 4 cells for all even periods 12 and up:

Code: Select all

x = 13, y = 24, rule = B2ei3i/S012ce3j
2bo$o5bo$2bo5$2bo$o7bo$2bo5$2bo$o9bo$2bo5$2bo$o11bo$2bo!

Code: Select all

x = 13, y = 24, rule = B2ei3i/S012ce3j4t
2bo$o5bo$2bo5$2bo$o7bo$2bo5$2bo$o9bo$2bo5$2bo$o11bo$2bo!

-c+e is possible in 4 cells for all even periods 8 and up:

Code: Select all

x = 12, y = 24, rule = B2ei3i/S012ce3j
2bo$o4bo$2bo5$2bo$o6bo$2bo5$2bo$o8bo$2bo5$2bo$o10bo$2bo!

Code: Select all

x = 12, y = 24, rule = B2ei3i/S012ce3j4t
2bo$o4bo$2bo5$2bo$o6bo$2bo5$2bo$o8bo$2bo5$2bo$o10bo$2bo!

Many examples of n-c, n.c, n-e and n.e are also possible with a minimum of 5 cells:

Code: Select all

x = 7, y = 4, rule = B2ein3aciq4jkny5any6ck/S012ce3ejnr4jknrwy5-aiky6ci7e
o5bo$3bo$2bo$3bo!

Code: Select all

x = 7, y = 5, rule = B2ein3aciq4jkny5any6ck/S012ce3ejnr4jknrwy5-aiky6ci7e
o$3bo$2bo$3bo$6bo!

Code: Select all

x = 6, y = 4, rule = B2ei3ir4r/S012ce3j
o4bo$2bo$3bo$2bo!

Code: Select all

x = 6, y = 5, rule = B2ei3ir4r/S012ce3j
o$2bo$3bo$2bo$5bo!

[yujh]

I have thrown some of my finds here: https://docs.google.com/spreadsheets/d/ ... sp=sharing
since I'm slightly too lazy to post all of them. A few there are better than the ones on Lifewiki.
I also would assume that all oscillators this project collect are non-adjustable just like sssss and sossp.
Edit: I just absolutely like this one:

Code: Select all

x = 3, y = 5, rule = B2ace3ekr4ijr5cek6acn7e8/S01e2ac3-cijy4ceijk5q6i
o2$2bo2$2bo!

I also just added a bunch of n.e irreducibles to that document.

[LaundryPizza03]

A few of the results can be improved from my EPE compilation of small low-period oscillators and spaceships.

p3 +f can be reduced to 3 cells:

Code: Select all

x = 3, y = 1, rule = B2ai/S1e2ci3e
3o!

p4 +f can be reduced to 2 cells:

Code: Select all

x = 3, y = 1, rule = B2ai5i/S01e2i3e4c
obo!

4-cell -e solutions with periods 6 and 7:

Code: Select all

x = 4, y = 2, rule = B2k3aij4w/S012ek3j5q
b2o$o2bo!

Code: Select all

x = 4, y = 2, rule = B2k3aij4a/S1c2k3ajn4r
b2o$o2bo!

4-cell .v solutions with 4 cells, up to period 7:

Code: Select all

x = 4, y = 2, rule = B2e3aej4r/S1e2ac4r
2o$2b2o!

Code: Select all

x = 4, y = 2, rule = B2ce3jn5q/S1e2ac3iy4k6c
2o$2b2o!

Code: Select all

x = 4, y = 2, rule = B2ce3jn5q/S1e2ac3iy4kr6ac
2o$2b2o!

Code: Select all

x = 4, y = 2, rule = B2ce3ajn5c/S1e2ac3eny4krz5eij7c
2o$2b2o!

3-cell xf solutions with periods 5 and 6:

Code: Select all

x = 5, y = 5, rule = B2en6n/S03c4ek
o2$2bo2$4bo!

Code: Select all

x = 5, y = 5, rule = B2en6n/S03c4aekw6n
o2$2bo2$4bo!

Additionally, many of the low periods can probably be solved using LLS. For example, 4-cell p9 oscillator with symmetry *f.

Code: Select all

x = 3, y = 3, rule = B2ikn3acei4-cinw5-cin6-en8/S12cn3enr4-ckqrw5ainq68
obo2$obo!

[LaundryPizza03]

4 cells is optimal for mod1 nrf. Some 3-cell LLS results for period/mod = 4 are presented below.

mod5 nrf:

Code: Select all

x = 2, y = 5, rule = B2-a3cikry4cejktyz5cekqy6-ak8/S12-in3-eij4-kqtwz5eijky6aei8
o2$o2$bo!

mod5 nrv:

Code: Select all

x = 4, y = 3, rule = B2-ai3iky4-ikqrw567c8/S01c2-ac3-jknr4-aijry5-a6-kn78
2bo2$o2bo!

mod6 nrf:

Code: Select all

x = 3, y = 4, rule = B2-i3qy4qrt5r6in8/S02-a3cekn4aerw5aejr6-i7
obo3$2bo!

mod6 nrv:

Code: Select all

x = 2, y = 5, rule = B2-a3-aen4jkqryz5ejkqy6-ei7e8/S12ack3jkq4jqwyz5eijkn6ei7c
o2$bo2$bo!

mod7 nrf:

Code: Select all

x = 2, y = 5, rule = B2ckn3-cnr4-aijkqy5-qr6-in/S013acqy4-acjry5-jn6ack
o2$bo2$bo!

mod7 nrv:

Code: Select all

x = 2, y = 4, rule = B2ce3ceiry4aceikw5cer6-kn/S01c2ac3aij4qz5-cekn6aei7e8
bo$o2$bo!

mod8 nrf:

Code: Select all

x = 2, y = 3, rule = B2cen3acekr4-iqwyz5ijkqy6-n/S012ai3ceiqy4-ijnr5-iqry6aen7c
2o2$bo!

mod8 nrv:

Code: Select all

x = 3, y = 4, rule = B2ikn3-cqr4-acejrz5cijry6cei/S01e2ace3cejq4-cjqrtw5ackr6k7e
obo3$2bo!

mod9 nrf:

Code: Select all

x = 4, y = 2, rule = B2ekn3acei4kt5inq6ak/S1e2ae3eijnr4iw5ckn6a
o2bo$2bo!

mod9 nrv:

Code: Select all

x = 3, y = 4, rule = B2ce3ceiqy4eq5-ceqy6a/S01c2-e3ac4ry5-ceir6-en7c8
o$bo2$2bo!

mod10 nrf:

Code: Select all

x = 2, y = 4, rule = B2en3aiqry4-ajkqr5-cijk6ik/S012-a3aekqy4knyz5acny6an7c8
bo$o2$bo!

mod10 nrv:

Code: Select all

x = 2, y = 4, rule = B2-ai3-ijkr4-ijnqz5ejqr6en7e/S01e2aei3iy4cejwyz5ey6ae7
o2$bo$bo!

I noticed that this project effectively supersedes SOSSP, since it is a minimal-example database which is finer than SOSSP. Any results from SOSSP will also be useful for OmniOsci.

[yujh]

Completed all the n. on my document, please check for mistakes.
I'm done for today, feel free to edit my document as well. (I do not know how google works though)
Some interesting oscillators:

Code: Select all

x = 3, y = 6, rule = B2aik3aej4ck5i/S02ae3acr4en5cin7e
o2$o3$2bo!

Code: Select all

x = 4, y = 4, rule = B2-e3ak4a5ry6a8/S01c2e3eijnr4iqy5ciny
o$3bo2$3bo!

[muzik]

Completed all the n. on my document, please check for mistakes.

"D2_+2 FD4_+2"p6 appears to be in the wrong place, since it's D2_+1-symmetric.

Also, so that I can copy things over easier, would it be possible for oscillators under period-16 which are on the sheet but not in the wiki overview page to be marked in red so I can see which ones are new?

[yujh]

Update on progress:
Filled D8_1 with b1e oscillators.
need help on C4_4 for p3, p4, p5.
P15 for C4_1.
n-f p6, p8.
need verification that 5 is the absolute lowest for any C4_1 patterns.
I'm leaving my EPE open for P15 for C4_1 and will check back tomorrow.

[muzik]

Here's some results from the SOSSP thread that have been superseded by 2-cell examples, but are still useful here due to being minimal examples for their specific symmetry. This list should be relatively complete, since aside from in large summary lists I doubt I've missed anything.

Fair warning, I haven't checked if these are in their minimal rules.

-c73

Code: Select all

x = 2, y = 3, rule = B2ce3cry4cejkwy6e7c8/S123acnq4kqr5inqy
o$bo$o!

-c284

Code: Select all

x = 3, y = 2, rule = B2-an3aq4c5iy6i/S01c2n3nqy4cejkwy5aeik6aik8
obo$bo!

-c316

Code: Select all

x = 4, y = 1, rule = B2-ak3acek4aetyz5cekr6k/S1e2ak3jn4ckn6ai
2obo!

/65

Code: Select all

x = 3, y = 3, rule = B2ikn3acijy4aceikt5ackr6ak/S012n3ciny4ekqrty5-acnr6ce
obo2$o!

*c49

Code: Select all

x = 3, y = 3, rule = B2-a3ar4eiqz5-aiy6eik7e8/S02-c3eijn4tw5ein6a8
bo$obo$bo!

n.c122

Code: Select all

x = 4, y = 2, rule = B2-ae3acnr4nqr5-ceky6ckn7/S1c2aei3q4ajkqr5-qry6-a
o2bo$bo!

-c+c60

Code: Select all

x = 2, y = 3, rule = B2cei3inq4jt5i6ci/S012ein3qry4q5an6i
o$bo$o!

-c+c68

Code: Select all

x = 2, y = 3, rule = B2ce3nqry4aer5eijy6c7e/S12k3eqr4iqyz5aiy6i7e
o$bo$o!

-c+c94

Code: Select all

x = 2, y = 3, rule = B2cek3iy4iq5aci/S01c4a5k6c
o$bo$o!

-c+c102

Code: Select all

x = 2, y = 3, rule = B2cen3-cikn4acijr5cinr6ck/S1e3ai5i
o$bo$o!

-c+c108

Code: Select all

x = 2, y = 3, rule = B2-a/S12-i3i
bo$o$bo!

-c+c190

Code: Select all

x = 2, y = 3, rule = B2cei3ciq4ajnqz5ejk6ck7e/S01c2-ek3q4rwy5aek6c
o$bo$o!

-c+c228

Code: Select all

x = 3, y = 2, rule = B2-a3ajy4aejkwy5qr6n7/S01c2ce3eik4e5jn6k
obo$bo!

-c+c244

Code: Select all

x = 3, y = 2, rule = B2-ak3aq4ajw5ary6aik8/S13enqy4-irtw5aijr6ci7e
obo$bo!

-c+c246

Code: Select all

x = 3, y = 2, rule = B2-a3jr4acjrz5aejq6ai7/S12in3qy4acenry5knqr6ci7c8
obo$bo!

-c+c248

Code: Select all

x = 2, y = 3, rule = B2cen3kn4aceqry5acjky6en78/S01c2cei3jkry4ceqyz5-ciqr6c7e
o$bo$o!

-c+c270

Code: Select all

x = 3, y = 2, rule = B2-an3ikn4cei5ejnr6aei/S1c2cei3aejnr4ey5cr6a7
obo$bo!

-c+c310

Code: Select all

x = 3, y = 2, rule = B2-a3aeqry4acjkt5ein6ei7e/S1c2a3ejny4ceijrty5jy6ci7c
obo$bo!

-c+c364

Code: Select all

x = 3, y = 2, rule = B2-a3y4-ciknt5eqry6cn/S01c2akn3-akr4-aknq5-einr6-ik
obo$bo!

-c+c434

Code: Select all

x = 3, y = 2, rule = B2-ai3cqry4-acerz5ckny6aek7c8/S12n3ejny4ceijtyz5ciny6c
obo$bo!

-c+c550

Code: Select all

x = 3, y = 2, rule = B2cei3ajny4eijnqwy5cr6ac7e8/S1c2-kn3ek4jnw5-ejry6cek8
obo$bo!

-c+c698

Code: Select all

x = 3, y = 2, rule = B2-ac3aeiq4krtwz5r6i7e8/S1c2ae3eijy4airt5k6-k7e
obo$bo!

-c+e82

Code: Select all

x = 4, y = 1, rule = B2cek3ckny4eiqt5-ikry8/S02en3iqry4inr5cy6c
2obo!

-c+e106

Code: Select all

x = 3, y = 3, rule = B2-ae3-knqy4ijky5aejnq/S02ei3aein4cijqrw5ai
o$2bo$o!

-c+e112

Code: Select all

x = 2, y = 3, rule = B2-ak3jqy4wy5acer6i/S01c2en3-cq4jqrtwy5ky
o$bo$o!

-c+e136

Code: Select all

x = 2, y = 3, rule = B2-ak3ac4ejkr5airy6ce7c/S12ain3knq4nqr5cijr6i7e
o$bo$o!

-c+e148

Code: Select all

x = 2, y = 3, rule = B2-ak3inqy4acjqrtz5aekry6k7c/S01c3kq5y7e
o$bo$o!

-c+e158

Code: Select all

x = 2, y = 3, rule = B2-ak3-ckqr4eiknqt5cny6ce7e/S1c2i3e4ej5y6a
o$bo$o!

-c+e162

Code: Select all

x = 2, y = 3, rule = B2-ai3nr4jkt5jry/S12ace3cknr4qz5eijry6i
o$bo$o!

-c+e188

Code: Select all

x = 2, y = 3, rule = B2cei3ir4cekwy5aeq6a/S12k3ij4ejy5ciry6ei
o$bo$o!

-c+e320

Code: Select all

x = 2, y = 3, rule = B2ein3-jn4kn5aijkq6-i78/S01c2-cn3ijqy4eikw5cey6ci7e
o$bo$o!

-c+e342

Code: Select all

x = 3, y = 2, rule = B2-a3i4eknw5-jn6in7/S02e3cei5aeqr6-an
obo$bo!

-c+e356

Code: Select all

x = 4, y = 1, rule = B2ce3-ackn4kntz5j6ae/S12i3ij4ijnqz5j6ei7c
2obo!

-c+e384

Code: Select all

x = 3, y = 2, rule = B2-ak3aq4etz5cejy6a7c/S12aen3cj4ajqtyz5-ciky6ci7c
obo$bo!

-c+e398

Code: Select all

x = 3, y = 3, rule = B2cen3eijkq4acejtw5ej6cin/S01c3kny4aikqryz5iq6ci7
obo2$bo!

-c+e448

Code: Select all

x = 3, y = 2, rule = B2-a3iq4jnryz5ceiky6-en7c8/S1c2e3aenr4qtw5en6k7c8
obo$bo!

-c+e460

Code: Select all

x = 3, y = 3, rule = B2cik3aekn4ntw5cjqry6ae7c/S12ek3iqy4cijrw5aj6acn7c8
obo2$bo!

-c+e484

Code: Select all

x = 3, y = 2, rule = B2-ak3ijk4cijkq5eijy6aen7c8/S01c3aijy4cqr5ijqr6ck8
obo$bo!

-c+e512

Code: Select all

x = 3, y = 2, rule = B2-ac3-jnry4eityz5aknqy6n7c8/S2-k3inqr4cqrz5-ikny6in7c
obo$bo!

-c+e1222

Code: Select all

x = 3, y = 4, rule = B2cin3-knry4anrz5k6ein7e/S02cin3ejknr4-akty5ceir6c7c8
obo3$bo!

/xc98

Code: Select all

x = 3, y = 3, rule = B2-ac3acik4cenqt5ijnqy6e7c8/S02ack3ceky4-iknyz5aejq6c7e
obo2$o!

/xc142

Code: Select all

x = 3, y = 3, rule = B2cen3aqr4arw5ijknr6cn7c/S01c2ae3-aeiy4cejnqz5ckry6acn
obo2$o!

/xc222

Code: Select all

x = 3, y = 3, rule = B2-a3aek4cenrtyz5-cenq6ak7/S02-ce4jkq5cikn6in7c
obo2$o!

/xc292

Code: Select all

x = 3, y = 3, rule = B2-ae3aeikn4-jwy5cekr6k7/S02n3acikr4-anryz5ckr6e7e8
obo2$o!

/xc396

Code: Select all

x = 3, y = 3, rule = B2eik3-eknq4ainqwyz5i6-in7c/S02k3acjqy4aj
obo2$o!

/xk66

Code: Select all

x = 3, y = 3, rule = B2en3ceijr4kqrwy5ikq6n7c/S012i3ij4ci5ery6n
obo2$o!

/xk116

Code: Select all

x = 3, y = 3, rule = B2-ae3aejy4knqrz5cek6aik8/S01c2cn3jq4qwy5kn6c
obo2$o!

/xk118

Code: Select all

x = 3, y = 3, rule = B2ein3cijkr4jknrtyz5-ceir6-ai7c8/S01c2acn3cejy4-cijny5ay6-ce7
obo2$o!

/xk156

Code: Select all

x = 3, y = 3, rule = B2-ae3aejqy4cjwz5-akn6akn7/S02ai3cekry4acjktwy5ceiq6aek78
obo2$o!

/xk168

Code: Select all

x = 3, y = 3, rule = B2-ai3enqy4aiqt5iknr6cek7/S02-cn3enqr4iqz5cqr7
obo2$o!

/xk312

Code: Select all

x = 3, y = 3, rule = B2-ak3akn4ciwy5aceny6k7e/S12acn3-aijn4aiknz5jknqy6ci
obo2$o!

/xk390

Code: Select all

x = 3, y = 3, rule = B2cei3ajry4rz5acikn6ae/S01c2-c3iqy4eiz5-eknr6-i78
obo2$o!

nrc72

Code: Select all

x = 4, y = 3, rule = B2cen3ajn4aeijknt5ay6a7c/S023ry4it5aiy6a7e
o2bo2$bo!

nrc96

Code: Select all

x = 4, y = 2, rule = B2-ac3aeijn4n5a/S03ijk4qwz
o2bo$bo!

nrc100

Code: Select all

x = 3, y = 4, rule = B2c3ajq4ejnr5cjr6n/S01c2ci3cijny4aeknrtz5aijr6ace
obo3$o!

nrc120

Code: Select all

x = 5, y = 2, rule = B2cin3-jknq4ekrtwy5ainr6ik7e8/S02cen3-aknq4acrw5iqry6e
obo$4bo!

nrc128

Code: Select all

x = 4, y = 2, rule = B2eik3ijqr4knqrtz5ijkn6-ci7e/S02aei3cijqy4aknq5c6e
o2bo$bo!

nrc368

Code: Select all

x = 2, y = 3, rule = B2ce3iny4aeinqw5acr6-ci7c/S12e3knr4acjrt5ai6e
2o2$bo!

nrc392

Code: Select all

x = 2, y = 3, rule = B2cek3cq4ny5-cnr6c7c/S01e2kn3-aeij4atz5knqr6cin7e
2o2$bo!

nrk80

Code: Select all

x = 4, y = 2, rule = B2-an4eit6k/S1e2aek3ry
o2bo$bo!

nrk84

Code: Select all

x = 2, y = 3, rule = B2-ae3aejr5jq7c/S01e2-ck3cei4artw5cein6k7c
2o2$bo!

nrk144

Code: Select all

x = 4, y = 2, rule = B2-an3ajky4ainqt5-aeny6ck/S02ck3ekry4aijkrz5inr6ak7e
o2bo$bo!

nrk172

Code: Select all

x = 2, y = 3, rule = B2ce3en4acntwyz5ei6ei/S12ek3jn4enr5jr6e
2o2$bo!

nrk180

Code: Select all

x = 5, y = 2, rule = B2cek3ciky4anqr5cknr7c/S01c2ckn3eiry4ajryz5ekry6ae
obo$4bo!

nrk224

Code: Select all

x = 5, y = 2, rule = B2-ae3aejr4ajkntyz5kq6a7e8/S01c2i3jqr4acijrwz5ceikn6ik7c
obo$4bo!

nrk304

Code: Select all

x = 2, y = 3, rule = B2cek3ekny4aejnwz5-cjqr6k7c8/S12-ac3iqy4z5ein6ce7e
2o2$bo!

nrk412

Code: Select all

x = 3, y = 2, rule = B2-ai3jk4eiqt5aciq6aek8/S12cen3-einr4ny5ary6aek8
2o$2bo!

[yujh]

There are some examples that can be manually reduced, like this xf7, 3:

Code: Select all

x = 5, y = 5, rule = B2en4cq5c6n/S03c4ak6n
o2$2bo2$4bo!

[muzik]

I've finished scouring the RRO thread for some higher-period nrc and nrk examples. Only about three of these ended up being 3-cell oscillators - the rest have a higher population and I anticipate that many will end up being replaced at some point in the future. Oscillators with a minimum population of 4, 5 and 6 are currently marked in green, and those with a minimum population of 7 to 207 are yellow. The lowest period we currently don't have an example for is period-104 mod-26.

In other news, we're only four examples away of having one example of each period-kinetic symmetry combination for oscillators of any period 8 and below.

[LaundryPizza03]

I've finished scouring the RRO thread for some higher-period nrf and nrv examples. Only about three of these ended up being 3-cell oscillators - the rest have a higher population and I anticipate that many will end up being replaced at some point in the future. Oscillators with a minimum population of 4, 5 and 6 are currently marked in green, and those with a minimum population of 7 to 207 are yellow. The lowest period we currently don't have an example for is period-104 mod-26.

In other news, we're only four examples away of having one example of each period-kinetic symmetry combination for oscillators of any period 8 and below.

I filled in all of the remaining gaps up to period 8 using LLS.

Please add links to the Catagolue pages for all of the new entries.

[muzik]

According to the current collection, we're only four oscillators away for having an example for every oscillator up to and including period 9; we just need examples for .c, .e, .k and xc. The same four symmetries are needed to have a complete set of period-11 oscillators. For period-13, we need .c, .e, .k and -e.

In other news, I've since made improvements to several p/m=4 oscillators and also added 2-cell +c*c examples up to and including period 100. The two lowest periods we don't have +c*c examples for are 20 and 22.

[muzik]

For time-asymmetric patterns up to period 16, I now have an example for every single period. However, many of these are incredibly un optimised, going up to a minimum population of 126: https://conwaylife.com/wiki/LifeWiki:Pr ... ew#p/m_=_1

Optimisations of any size are more than welcome.

[Period1GliderGun]

It might be interesting to try to prove the symmetrical case using a rule such as this one:

Code: Select all

x = 9, y = 3, rule = B2ci3-inqy4ej5i6k7c8/S01c2cin3jkny4cekrtw5ijy6c7e
o$8bo$o!

In general, this is the idea:
1. Have a 2-cell seed for a quad-wickstretcher or whitespace.
2. Have a dot at one end to either suppress one wickstretcher or cause the whitespace to decay.
3. If Whitespace: Have the whitespace decay into the 2-cell seed at the same place. If wickstretcher: Have the wickstretchers decay into spaceships that travel backward and synthesize the 2-cell seed.
I got the idea from toroidalet's 3-cell sawtooth.

[muzik]

It might be interesting to try to prove the symmetrical case using a rule such as this one:

By "the symmetrical case" you mean "time-symmetric", right? We already have examples for time-asymmetric D2_+1 oscillators up to infinity using this principle, as I said here in my first reply to the thread:

The wickstretcher approach for 3-cell oscillators of any sufficiently high period gets us 3-cell -f symmetric oscillators for all of said periods, which are optimal for this symmetry in terms of cell count (although bounding boxes can still - and should - be optimised).

It seems entirely possible that the same could be done with a dot that isn't centered on the two cell seed so we can have time-asymmetric space-asymmetric 3-cell oscillators for any desired period. As for other symmetries, including time symmetries, there are definitely other potential approaches, but I'm not sure which. An off-center dot whose position flips every time the wickstretchers hit it would probably be just as easy to find as an off-center dot that doesn't, netting us arbitrary-period "n-c" oscillators.

[muzik]

We're currently only 14 examples away from having one oscillator per kinetic symmetry for every period 16 and below. Currently, only the following are missing:

- .cxc10
- .crc10
- rc*c10
- -e+e12
- .crc12
- .crc14
- .krk14
- rk*k14
- -e+e16
- -e+k16
- .c+c16
- .cxc16
- .krk16
- rk*k16

There are, of course, also many periods whose currently known smallest examples are far from being the minimal possible example. The two lowest periods with clearly reducible examples are p6 (n-c) and p8 (.c and .k).

There's also some kinetic symmetries for which a minimum population is yet to be proven; I've commented these on the google sheet for anyone interesting in proving these. Reducing the minimum population of kinetic symmetry periods with known oscillators as well as proving the minimum population for specific cases is just as useful as filling in gaps.

[muzik]

Just for fun, here's some oscillators which are smaller than the examples we have for each period-symmetry combination in the collection, but can't be included since they come from different rulespaces:

3-cell nrk4 (current record is 5, provably optimal)

Code: Select all

x = 2, y = 3, rule = MAPAkUggAEAgIAAEAAAAAAACAAAoAAAAAAA4EACAAAAAAACAAAAggAAQAAAAACAAAAAAAAQAAgAAAAAgAAAgAAAAA
bo$o$o!

2-cell .kxk2 (current record is 4, provably optimal)

Code: Select all

x = 2, y = 4, rule = R2,C0,S,B2,NX
o3$bo!

4-cell +k*k2 (current record is 8, almost certainly optimal)

Code: Select all

x = 2, y = 4, rule = R2,C0,S,B2,NX
2o3$2o!

2-cell .e+e2 (current record is 4, provably optimal)

Code: Select all

x = 2, y = 3, rule = R2,C0,S,B2,N+
o2$bo!

[muzik]

It's been a while, but all periods up to 16 now have an example. However, two of these are pseudo-objects, and the rest have likely suboptimal minimum populations, so help with reducing these (or proving them minimal) would be appreciated.

https://conwaylife.com/wiki/LifeWiki:Pr ... ew#p/m_=_2

In other news, OmniOsci is now accepting orthogonal and diagonal spaceships, as they can have different types of kinetic symmetry as well. (Oblique spaceships necessarily must be asymmetric, and to include them would be to duplicate the 5s project, so we're leaving the responsibility of documenting them to there.) Currently, the lowest-period things we're missing are an asymmetric 2c/3 and an odd-symmetric 3c/3.

Any and all assistance appreciated!

[hibiscus]

2c/3o asymmetric

Code: Select all

x = 4, y = 5, rule = B2ace3ace4nt/S1e3cery4r6c
3bo$2bo$bobo$2bo$obo!

3c/3o odd-symmetric

Code: Select all

x = 2, y = 3, rule = B2ac3ai/S3e
bo$2o$bo!

2c/4o asymmetric

Code: Select all

x = 6, y = 7, rule = B3aijnq4ant6ak7/S2-ik3-aciy4airz5j6ac
o$2bo$o$2o3bo$2b4o$obo2bo$4b2o!

c/4o asymmetric

Code: Select all

x = 4, y = 4, rule = B2i3aij4w5jq/S2aei3ejnr4z5n
2b2o$3bo$bobo$3o!