Oscillators in one-dimensional rules

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dingxutong
Posts: 7
Joined: April 4th, 2023, 1:54 am

Oscillators in one-dimensional rules

Post by dingxutong »

Hi there!

I'm recently interested in oscillators in n-range one-dimensional rules, especially with two states, 0 and 1. Only those with finite bounding box are considered.

One can prove that, when n=1, there only exist 1- and 2-period oscillators, where the latter only exist in Rule W108, for example:

Code: Select all

x = 15, y = 1, rule = W108
3ob3ob3ob3o!
What if n get larger, for example, 2, or 3? There must exist oscillators with long period, but what can their periods be?

P.S. I'm not very familiar with the terms here, especially in English. I apologize if I made any mistake.
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pipsqueek
Posts: 304
Joined: September 10th, 2022, 4:42 pm
Location: Abstract mathematical space

Re: Oscillators in one-dimensional rules

Post by pipsqueek »

here is a p3

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x = 14, y = 1, rule = R2,C0,S0-5,B2,4-5,N@0003E0
ob4ob3o3bo!
this rule actually has some interesting things, and I think it might be self complementary

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x = 101, y = 1, rule = R2,C0,S0-5,B2,4-5,N@0003E0
o3b4obo21bob4ob2o19bo2b4ob2o10bo2b16ob2o!
there is also a p5 agar

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x = 59, y = 1, rule = R2,C0,S0-5,B2,4-5,N@0003E0:T60,100
2b3ob2ob2ob3o3bo3b3ob2ob2ob3o3bo3b3ob2ob2ob3o3bo!
EDIT: another rule with an impressive p23

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x = 26, y = 1, rule = R2,C0,S0-5,B2,4,N@0003E0
4o3b4o4b4o3b4o!
a real p5

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x = 20, y = 1, rule = R3,C0,S0-7,B2,5-6,N@0000001FC000
o2bo4bo2bo4bo2bo!
p4

Code: Select all

x = 3, y = 1, rule = R3,C0,S0-7,B3-4,N@0000001FC000
3o!

Code: Select all

x=17,y=16,rule=B3/S23
3bo3bobo2bob2o$bobo4bo4b4o$bobo5bobo2b3o$b2obob2o3b2o$3o4b2ob2o2b2o$4b
o4bo$4b2obobob2ob3o$3ob3o2b2o$b3o2bobobo5bo$o3b2o3bobo2b2o$4bo3bob2o3b
o$2obo2bobobo2b2o$3b3o5bo2b2o$2obo4bo2bob2o$o3bob2obo3b2o$2bo8bobobo![[ STOP 3 GPS 4 ]]
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dingxutong
Posts: 7
Joined: April 4th, 2023, 1:54 am

Re: Oscillators in one-dimensional rules

Post by dingxutong »

Btw, why are 1D CAs not popular in this forum? It seems that almost all of the threads are about 2D ones.
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bibunsekibun
Posts: 345
Joined: April 17th, 2021, 7:58 pm
Location: Japan

Re: Oscillators in one-dimensional rules

Post by bibunsekibun »

P4

Code: Select all

x = 16, y = 1, rule = R3,C0,S2,4-5,B3,N@000007E00000
5obo2bob5o!
P14

Code: Select all

x = 13, y = 1, rule = R3,C0,S1,4,B2,N@000007E00000
2ob3ob2ob3o!
P34

Code: Select all

x = 26, y = 1, rule = R3,C0,S1,4,B2,N@000007E00000
2o6bo3b2o3bo6b2o!
P6

Code: Select all

x = 11, y = 1, rule = R3,C0,S1,B2,4,6,N@000007E00000
o5bobobo!
P3

Code: Select all

x = 17, y = 1, rule = R3,C0,S1-2,5-6,B2,N@000007E00000
o2b2o3bo3b2o2bo!
P9

Code: Select all

x = 12, y = 1, rule = R3,C0,S1,4,B2,6,N@000007E00000
2o8b2o!
Another P3

Code: Select all

x = 13, y = 1, rule = R3,C0,S1,4,B2,5-6,N@000007E00000
o3bo3bo3bo!
P2,3,6

Code: Select all

x = 20, y = 19, rule = R3,C0,S1,4,B2,4-6,N@000007E00000
o4bob3o9$o4b2o5b2o4bo9$o3b2o8b2o3bo!
P7

Code: Select all

x = 10, y = 1, rule = R3,C0,S1,5,B2,4-6,N@000007E00000
obo4bobo!
P428

Code: Select all

x = 16, y = 1, rule = R3,C0,S1,5-6,B2,4-6,N@000007E00000
obo4bobo5bo!
sorry I can only speak Japanese, English is made by machine translation
I'm a fan of methuselahs
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