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Plasmath

...

With things like this I also do wonder what happens if you start with soups that have other densities. Some explosive rules have a tendency to form stable patterns when the density is low, which presumably changes their temperature.

I tried this out with 5% soup density, and unfortunately ...

Plasmath

On the graph, I would plot the locations of some example rules (Seeds, Life, Gems, etc.) to make it easier to understand which rules with certain conditions go where.

Here's a graph with some named (and a few unnamed) rules on it:

plot.png

I can try making one of the axes the rule integer ...

Plasmath

Wolfram's classification for cellular automata kind of sucks (at least, when it comes to analyzing 2D rules). In principle, I think that the idea of classifying cellular automata into one of a few categories is a great idea, but I've got some problems with his system:

It was meant for 1D rules ...

Plasmath

A c/314d spaceship:

Code: Select all

x = 23, y = 10, rule = B3aceik4aq5aejr6aen7e/S2aen3-acy4iqt5aekn6kn7c8
2b3o$4b2o$5bo$2b2o$o$2o$b3o$20bobo$20bo$20b3o!

Plasmath

Anyone know what 1D rule this is simulating? I don't recognize it.
x = 3, y = 3, rule = B3ai4ekqty5cry6cn7e8/S2-c3-acey4inr5eqy
2o$obo$3o!

x = 227, y = 196, rule = B3ai4ekqty5cry6cn7e8/S2-c3-acey4inr5eqy
2o$obo$3o4b2o$7bobo$7b3o4b2o$14bobo$14b3o4b2o$2b3o6b3o7bobo$2bobo6bobo
7b3o4b2o ...

Plasmath

This replicator appears to have a bounding box which grows upward at a logarithmic pace:

Code: Select all

x = 5, y = 5, rule = B3airy4ewz/S2-i3-ac4i5aHistory
.2A$2A.2A$.A2.A$4.A$2.2A!

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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