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Plasmath

From making a few manual soups I don't think this rule is explosive (even in symmetric soups!), but it does have this very common methuselah, with a maximum population of 13521 and a minimum population of 5:

Code: Select all

x = 3, y = 3, rule = B2-an3-i46n/S1c25k78
obo$bo$obo!

It stabilizes after 9774 generations.

Plasmath

I have no idea what rule this replicator follows. x = 4, y = 4, rule = B2n3acijr4ceikqt5k6k/S2-ci3ijnqr4cik5jr b2o$ob2o$2obo$b2o! I lined them up to get a better look at what 1D rule it simulates, pretty interesting: x = 469, y = 469, rule = B2n3acijr4ceikqt5k6k/S2-ci3ijnqr4cik5jr 316b2o$315bob2o$31...

Plasmath

An "almost symmetric" p200 oscillator: x = 23, y = 11, rule = B2n3acijr4ceikqt5ky6ikn8/S2-ci3ijnqr4ceik5ijr6ain8 5bo$4b3o10bo$3bo2b2o8b3o$3b2o2bo7b2o2bo$6b2o7bo2b2o$b2o2b2o8b2o$2o2b2o 10b2o2b2o$bo2b2o11b2o2b2o$2b3o12b2o2bo$3bo14b3o$19bo! Surprisingly, the symmetric version of it does not work. x = 2...

Plasmath

get_Snacked wrote: ↑
November 15th, 2023, 9:31 am

Plasmath wrote: ↑
November 15th, 2023, 12:15 am
2442c/98 orthogonal
that doesn't seem possible. do you mean 98c/2442?

You're right. I fixed it

Plasmath

[/code] Here is the 6c/67d for an example x = 11, y = 11, rule = B3-cjy4atwz5-ajy6ak7e/S2-i3cikry4ainqz5ejn6e 2o$bo$2o7$8b3o$8bobo! Interesting rake in a closely related rule, it's 98c/2442 orthogonal and emits 14 T-ships per period: x = 7, y = 6, rule = B3-cjy4atwz5-ajy6ak7e/S2-i3cikry4ainqz8 2bo$...

Plasmath

Found this replicator in a similar rulespace to the above post:

Code: Select all

x = 4, y = 4, rule = B2n3acijr4cijt5r6i8/S2aek3ijnqr4ei5-ckqy6e
b3o$o2bo$o2bo$3o!

What (1D) rule does it follow?

EDIT:
Another cool replicator

Code: Select all

x = 4, y = 3, rule = B2n3acijr4ijqt5ry6i7e8/S2aek3ijnqr4cei5eijnr6-ac7e
3o$o2bo$ob2o!

Plasmath

Massive p10944 RRO that's 1,2,3,4-able: x = 573, y = 445, rule = B2n3acijr4cijqt5y6i7e8/S2aek3ijnqr4ci5-ckqy6ac7c 436bo$435b4o$435bo3bo$436bo2bo$436b3o5$419b3o$419bobo$422bo$419bo3bo$ 419bo3bo$423bo$421b2o6$425b2o$419b3o2bob2o$419bobo3b2o$419bo3bobo$423b o$422bo9$569bo$568bo$219bo346bobo3bo$218bo346...

Plasmath

104c/3844 orthogonal spaceship x = 6, y = 14, rule = B2n3acijr4ijqt5y6i7e/S2aek3ijnqr4ci5aceij6-en8 3b2o$b5o$o4bo$o3b2o$2o2bo$2b2o3$b2o$bob2o$bo3bo$b2o2bo$2b3o$3bo! 22c/2346 diagonal spaceship x = 42, y = 17, rule = B2n3acijr4ijqt5y6i7e8/S2aek3ijnqr4ci5-kqry6cei7c 4bobo20bo12b2o$26b2o11bobo$25b2o11b...

Plasmath

1,2,4,8-loopable p232 RRO x = 78, y = 77, rule = B2k3aeiry4ct5ckq6c8/S2-in3ijkqr4cinq5acikr6cin8 2o45b2o$bo46bo$o46bo$obo44bobo$3o44b3o20$75b3o$75bobo$77bo$76bo$76b2o 18$25b3obo28b3o11b3obo$2o23bo2b2o17b2o8b2o2b2obo7bo2b2o$bo23b2o21bo9b o3bo2bo6b2o$o46bo11bo4bo$obo44bobo15bo$3o44b3o16bo$65b4o$65bobo...

Plasmath

hotcrystal0 wrote: ↑
October 17th, 2023, 3:42 pm
What is the limit for 3x4?

I believe that the current upper limit is 3392, based on the bounds found in this post. The current lower limit is this p248 oscillator found by b3s23love:

Code: Select all

x = 3, y = 4, rule = B2ek3acjy4cjkrz5-ceky6-ae8/S012acn3aiq4-cknqy5eky6-en
o$2bo2$2bo!

Plasmath

x = 9, y = 43, rule = B2-a3-ai4inrtwyz5-jky6-cn78/S3k4-jqt5-aer6-ac7 4bo$ob2ob2obo$obo3bobo$4ob4o$b2o3b2o$3o3b3o$o3bo3bo$3obob3o$3bobo$3o3b 3o$2o5b2o$2o2bo2b2o$ob5obo$obobobobo$2bo3bo$ob2ob2obo2$4bo$2ob3ob2o$4o b4o$3obob3o$o3bo3bo$4ob4o$obobobobo$3o3b3o$ob5obo$obo3bobo$9o$ob5obo$b 2obob2o$2o5b2o$ob...

Plasmath

haaaaaands wrote: ↑
October 12th, 2023, 5:52 am
banned because tldr

banned because tser (Too Short, Easy Read)

Plasmath

When does this pattern become periodic? It hasn't stabilized for 770,000,000 generations: x = 16, y = 16, rule = B2-a3-ai4inrtwyz5-jky6-cn78/S3k4-jqt5-aer6-ac7 bobo5bob2ob2o$ob2o4bo4b2o$obobobo2bob5o$4bob2o3b5o$2b2o2b5o2b3o$4bobo bo4b2o$o5bo2bobobo$3o4b2obo4bo$bobo5bobo3bo$3b2ob3obo3b2o$2o2b6o2bo$o ...

Plasmath

Here's an 8x8 p27334 found through manual search, which I think is a new lower bound (still not a great one considering the size of the oscillator):

Code: Select all

x = 8, y = 8, rule = B2-ac3-i45ai78/S01234-ir5aci6-c7e8
o2b5o$b3ob2o$2ob4o$b6o$o5bo$o2b3obo$ob2obobo$o2b5o!

Plasmath

Here's a lower bound for a k-state 1xN oscillator, using a base-(k-3) counter: (This is a base-3 example, but it should make sense how to generalize it to any base) x = 10, y = 19, rule = osc1xn E2$2E2$3E2$4E2$5E2$6E2$7E2$8E2$9E2$10E! @RULE osc1xn @TABLE n_states:6 neighborhood:vonNeumann symmetries...

Plasmath

The 2-state 1xN cases are pretty simple but haven't had a rigorous proof yet, so I'll show that their maximum period is 2 (other than 1x2 and 1x1, their periods are 1): Because we are currently disregarding B0 rules and any B1e-like birth transition will result in an explosive rule, we are left with...

Plasmath

This replicator creates decaying chains of itself with blocks: x = 2, y = 3, rule = B2e3eiq4artz5jy7e/S1c2aci3ajy4iz o$bo$o! Its population graph also looks interesting too. This one starts off acting like a normal replicator, but then it starts creating a doubled stack of replicators within it: x =...

Plasmath

Moved to rules with interesting replicators.

Plasmath

This rule looks like it should be explosive, but it seems to always stabilize into lots of solid linear growth patterns: x = 51, y = 50, rule = B2c3ai4cekqyz5i/S01c2-c3-e4ainr5-cjkn6-ek78 b3ob3o2bo4bob3obo5b3o2bo2b2o2b2obobob2o$5ob2ob3o6bo3b3ob2obobo3b5o3b2o b3obo$o3bobob3ob2o2bobobobo2b2obo2bo3b4o2...

Plasmath

9 oscillators:

Code: Select all

x = 34, y = 18, rule = B2cik3aejry4aw/S2ci3aeijk4i6i
bo$obo3b2o$bo4b2o3$25bo$12bobo4bo7bo5bo$3o3b2o11b2o3bo6b2o$bo5b2o3bobo
3bo7bo6bo8$obobobo!

2 p1s, 6 p2s, 1 p4

Plasmath

And as for the weird replicator, it's just a Lorentz-shifted rule 90. Compare: rle rle Interesting! I've never seen a Lorentz-shifted replicator before. (I've also never seen a moving replicator gun before. Very cool.) I've also created a (messy, incomplete) oscillator stamp collection of the natur...

Plasmath

hotdogPi wrote: ↑
September 7th, 2023, 1:19 pm
∜(1538/45) ≈ 2.41788675 (+3.427e-7)

25/8 - 1/√(2) ≈ 2.4178932188134525 (+6.468e-6)

Plasmath

unname4798 wrote: ↑
September 3rd, 2023, 5:36 am

Plasmath wrote: ↑
August 8th, 2023, 10:42 am

hotcrystal0 wrote: ↑
August 8th, 2023, 10:19 am
log(261.3) ≈ 2.4171394 (+ 0.000039)
2+e^(-1/ln(π)) ≈ 2.4174591737782 (+0.000319764)
40291*0.00006 = 2.41746 (+0.00000082622)

4tan(e/5) ≈ 2.417642874 (+0.000182874)

Plasmath

Ships from various sources: # 5S collection updated - 270 new and 328 improved speeds out of 600 ships. # Orthogonal speeds updated: # [(92, 0, 940), (56, 0, 1562), (52, 0, 1584), (98, 0, 1750), (30, 0, 1864), (52, 0, 2138), (90, 0, 2226), (48, 0, 2236), (4, 0, 2528), (34, 0, 2626), (68, 0, 2798), (...

Plasmath

This soup was marked as zz_LINEAR when it's just an oscillator: x = 32, y = 32, rule = B3ai4ekqty5cy6cn/S2-c3-ace4ainr5enqry6an78 b6ob2ob10ob2ob6o$2o2bob2o3b3o4b3o3b2obo2b2o$o2bob3ob2o2bo4bo2b2ob3obo 2bo$obo5bo2bo8bo2bo5bobo$2o3b2o2bo2bo2b2o2bo2bo2b2o3b2o$obobo2bob2ob2o 4b2ob2obo2bobobo$3obob2o2b3o...

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Re: Rules with interesting replicators

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