Every other Langton's Ants
Posted: July 23rd, 2020, 5:29 am
This thread is dedicated for Langton's Ant rules other than the standard one.
In LLU there's a common two-cell-thick orthogonal highway, and can produce very very very very very behaviour:
Code: Select all
x = 2, y = 80, rule = LangtonsAnt_LLU
C79$.C!
Code: Select all
x = 1, y = 31, rule = LangtonsAnt_LLU
A15$C15$A!
Code: Select all
x = 24, y = 3, rule = LangtonsAnt_LLN
NC22B$2B$.A22B!
LRU probably qualifies as an interesting rule.
Now I wonder about the behaviour of the counter.Hunting wrote: April 27th, 2020, 9:32 am LangtonsAnt_LRU tends to produce super-high-period oscillator, or possibly, patterns that explodes, but with a hilariously slow speed.
Those oscillators have a single engine containing ants and purple ashes it throws off. They looks like they are restricted to a certain bounding box, I don't know why.
For example, a single ant is a p276 oscillator:If you add one green cell to it, it becomes a p25212 oscillator:Code: Select all
x = 1, y = 1, rule = LangtonsAnt_LRU C!I don't even know if these two patterns stabilizes:Code: Select all
x = 2, y = 1, rule = LangtonsAnt_LRU AC!Two-ant patterns tends to produce methuselahs with temporary oscillator engines. Here's a ~49800M:Code: Select all
x = 31, y = 2, rule = LangtonsAnt_LRU 30.A$CA28.C!I don't know what exactly is the lifespan since it ends with emitting a p30 c/15 wickstrecher:Code: Select all
x = 2, y = 1, rule = LangtonsAnt_LRU 2C!
I challenge people to come up with either a spaceship or a proof that spaceship cannot exist. (With arbitrary number of ants of course.)Code: Select all
x = 3, y = 11, rule = LangtonsAnt_LRU 3B$3B$3B$3B$3B$3B$3B$3B$3B$BC$BE!
Two ants can also form a spacefiller, similar to the Langton's Ant space non-filler. It can decay, but not as reversible as Langton's Ant:The above pattern demonstrates that, unlike usual LangtonsAnt rules, there are fuses. That particular one travels at p64 c/16:Code: Select all
x = 38, y = 39, rule = LangtonsAnt_LRU 37.A37$C$C!To end this post, here is a p132 oscillator, currently the lowest period known (which is rather unusual again). I challenge everyone to come up with an oscillator with period less than 100.Code: Select all
x = 11, y = 31, rule = LangtonsAnt_LRU 2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$ 2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$2.B$BLD6.CB$.2B6.EB$8.3B$8.3B$8.3B!EDIT: Oh I forgot to mention this bizarre counter(?):Code: Select all
x = 2, y = 2, rule = LangtonsAnt_LRU .C$A!Code: Select all
x = 1, y = 4, rule = LangtonsAnt_LRU C3$E!
Only in xxN rules the highways are real "highways" because once they are built other ants can travel on the highways at lightspeed. The width of the highway is also adjustable (!) I think this might be the first adjustable speed highway in any Langton's Ant rule
Code: Select all
x = 1, y = 40, rule = LangtonsAnt_LRN
C39$C!
Code: Select all
x = 2, y = 20, rule = LangtonsAnt_LUL
.A10$.C4$AB$BA$2B$2A2$.A!
In LUU patterns cannot escape its bounding box+1.
In LUN there's a bi-colored highway and a higher-period wickstrecher based off it:
Code: Select all
x = 22, y = 84, rule = LangtonsAnt_LUN
10.A$9.B.B2$9.2A2B$7.3BA.2A$5.A.B3.3A$5.BA.B.2AB2.B$6.2A2.BA.B.A$11.A
.A.B$9.2BAB.2A$10.2A2.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$
10.A$10.A$10.A$10.A$9.B.B2$9.2A2B$7.3BA.2A$5.A.B3.3A$5.BA.B.2AB2.B$6.
2A2.BA.B.A$11.A.A.B$9.2BAB.2A$10.2A2.A$10.A$10.A$10.A$10.A$10.A$10.A$
10.A$10.A$10.A$10.A$10.A$10.A$10.A$9.B.B2$9.2A2B$7.3BA.2A$5.A.B3.3A$
5.BA.B.2AB2.B$6.2A2.BA.B.A$11.A.A.B$9.2BAB.2A$10.2A2.A$10.A$10.A$10.A
$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.A$10.
A$10.A$10.2AK$10.2A2BH$11.AB.A$10.BA$11.2A!