muzik wrote:Dies there exist a (totalistic or non-totalistic) rule where all oscillators must have a prime period?
muzik wrote:Does there exist a (totalistic or non-totalistic) rule where all oscillators must have a prime period?
...
I was more meaning rules where every prime number is possible as a period.
toroidalet wrote:muzik wrote:Are these oscillators or spaceships in any rules?
The first one's trivial:Code: Select allx = 4, y = 5, rule = B7e/S0123456-i78
bo$4o$bo$4o$bo!
x = 4, y = 5, rule = B3ak5i/S1c2ac3i6i
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B3j4ij5ceiy8/S12ae3-ckqr4aijq5qr6i
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B2ek3aiy4akry5eiy/S12ce3jkqr4j5iy
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B2ce3er4aei6ik7e/S12ak3ci4nt6i
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B2cen3y/S2an3i
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B2e3ij4a5iy/S2ak3j4j
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B2c3aejr4aeirtw5i/S2a3e4ey6i
bo$4o$2bo$4o$bo!
x = 4, y = 5, rule = B2cek3-cik4ejkqrty5acjk6aei78/S02ac3ejnry4ekrw5-einr6ck7e8
bo$4o$2bo$4o$bo!
x = 4, y = 9, rule = B45678SHistory
3.D$2.D$.D$B$D$D$D$D$D!
x = 4, y = 9, rule = B45678SHistory
3.D$2.D$.D$AF$.F$2A$D$D$D!
x = 4, y = 9, rule = B45678SHistory
3.D$2.D$.E$BC$EC$D$D$D$D!
x = 4, y = 9, rule = B45678SHistory
3.D$2.D$.D$AF$.F$2A$D$D$D!
x = 5, y = 2, rule = B3/S23
2o2bo$4bo!
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
x = 3, y = 10, rule = B2c3aj4nrt5i6c78/S01c23enr4aet5-iq67
obo$bo$bo$bo$bo$bo$bo$bo$bo$3o!
x = 1, y = 2, rule = B2a4i/S
o$o!
x = 1, y = 1, rule = W50
o!
x = 60, y = 60, rule = B3-ky4iw5cy/S2-n3-eky4t
30b2o$29b4o$28b2o2bo$29b2o2bo$30b4o22$3bo$o2bo$b3o3$56b3o$56bo2bo$56bo
23$26b3o$28bo$28bo$27bo!
drc wrote:Does this stabilize? 6M+ and it's still going:Code: Select allx = 60, y = 60, rule = B3-ky4iw5cy/S2-n3-eky4t
30b2o$29b4o$28b2o2bo$29b2o2bo$30b4o22$3bo$o2bo$b3o3$56b3o$56bo2bo$56bo
23$26b3o$28bo$28bo$27bo!
#C [[ AUTOFIT ]]
x = 7, y = 9, rule = B34tw/S23
2o$2o$4b2o$6bo$3bo2bo$6bo$4b2o$2o$2o!
muzik wrote:Are there any known 1D replicators where the central replicator stays alive after every replication cycle, resembling a one-dimensional version of the Fredkin rule and simulating Wolfram rule 150?
x = 2, y = 1, rule = B1e/S1e2i
2o!
x = 1, y = 1, rule = W254
o!
x = 1, y = 1, rule = W150
o!
x = 5, y = 22, rule = bs012345678History
.2E$.2E6$2.C$.3C$C.C.C$2.C$2.C$2.C3$2.A$.3A4$.2E$.2E!
x = 5, y = 22, rule = bs012345678History
2.2E$2.2E3$.3A$2.A3$2.C$2.C$2.C$C.C.C$.3C$2.C7$.2E$.2E!
x = 5, y = 22, rule = bs012345678History
.2E$.2E6$2.C$.3C$C.C.C$2.C$2.C$2.C3$2.A$.3A4$.2E$.2E!
muzik wrote:Here's a potential approach to adjustable-speed spaceship rules I've had on mind for quite a while now:
<snip>
wildmyron wrote:Searching for this by presuming what the small ship and the SL are from the start is probably a needle in a haystack kind of search. I suspect you'd have more luck restricting the search to a rule (or set of rules) with an extremely common small ship, several extremely common small SL and which is productive but settles down fairly quickly - i.e. dynamics akin to JustFriends but with an orthogonal small ship.
x = 13, y = 5, rule = B3-y4q5a/S23-e
5bo4b2o$5bobobo2bo$b2o2b2o3b2o$o2bo$b2o!
wildmyron wrote:muzik wrote:Here's a potential approach to adjustable-speed spaceship rules I've had on mind for quite a while now:
<snip>
- Searching for this by presuming what the small ship and the SL are from the start is probably a needle in a haystack kind of search. <snip>
A for awesome wrote:About the last bit: If you use a diagonal ship instead and search for diagonal offsets for the SL, you can use JustFriends almost as-is with the actual diagonal glider that already exists. This has the advantage that the SL (probably a domino) may be translated a single diagonal while still keeping the ship glide-reflective, potentially allowing perfect speeds, whereas an orthogonal variation would require semiperfect speeds or other pseudo-period speeds.
All in all, it seems very likely that there is a rule in which a particular collision between a JustFriends glider (or c/4 equivalent without S2k) and a domino translates the domino laterally by (1,1) and reflects the glider 180 degrees onto a lane 1hd from its input in the same direction as the domino's translation. The non-totalistic rulespace is huge.
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
muzik wrote:Any pattern can be a spaceship in some non-isotropic rules, which are non-totalistic.
x = 93, y = 81, rule = B/S01234678
76bo$76bo55$o24$91b2o!
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
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