Ice8
Posted: June 6th, 2013, 8:07 am
I've come up with a shiny new 4-state CA for you guys ;D
Here's a quick explanation:
--State-2 cells are created from two state-1 neighbours
--State-3 cells are created from three state-1 neighbours
--State-1 cells are created from any of:
----One state-2 neighbour and one state-3 neighbour
----One state-2 neighbour and two state-3 neighbours
----Two state-2 neighbours and two state-3 neighbours
--All three ON states are subject to S3
It reminds me of both Brian's Brain and MilhinSA. Similarly to both of them, complicated codependent rake systems tend to form. Like any self-respecting CA, it has oscillators, spaceships, puffers, rakes, guns, breeders, replicators, and so on.
Notable objects include this tiny gun:
This is a simple replicator being stabilised by two oscillators:
Oscillators how up commonly at p4 and p6. It's fairly easy to constuct them at random other multiples of 4 using this replicator mechanism; I've only made a few, but I've managed p12, p16, p24, p28, and p124. p48 is constructible using the gun. Odd periods may or may not be possible: it's not /strictly/ an alternating rule, but it often behaves as one due to the rather weak suvival condition, resulting in "pseudoparities" where in some generations a pattern alternated between being dominated by either state 1 cells or states 2 and 3 cells, but occasionally enough cells will survive for an object to be created of a different "pseudoparity" than its parent, so I wouldn't give up hope just yet.
I'm fairly sure this is the smallest quadratic growth pattern, at 6 cells:
It has a similar but less explosive property to B2 lifelike rules; if the edge of a pattern in one of those rules consists of an uninterrupted line of cells of length 2, the pattern's edge will eternally move in that direction at c/1. In this rule, however, a line of length 4 is required.
The vast majority of spaceships are c/1, but this tiny c/2 spaceship is also very common:
Finally, here's an MSM breeder on width 1:
Code: Select all
n_states:4
neighborhood:Moore
symmetries:permute
var a={1,2,3}
var b={1,2,3}
var c={1,2,3}
var d={1,2,3}
var e={1,2,3}
var f={1,2,3}
var g={1,2,3}
var h={1,2,3}
var s={0,1,2,3}
var t={0,1,2,3}
var u={0,1,2,3}
var v={0,1,2,3}
var w={0,1,2,3}
var x={0,1,2,3}
var y={0,1,2,3}
var z={0,1,2,3}
0,1,1,0,0,0,0,0,0,2
0,1,1,1,0,0,0,0,0,3
0,2,3,0,0,0,0,0,0,1
0,2,3,3,0,0,0,0,0,1
0,2,2,3,3,0,0,0,0,1
1,a,b,c,0,0,0,0,0,1
2,a,b,c,0,0,0,0,0,1
3,a,b,c,0,0,0,0,0,1
1,s,t,u,v,w,x,y,z,0
2,s,t,u,v,w,x,y,z,0
3,s,t,u,v,w,x,y,z,0
--State-2 cells are created from two state-1 neighbours
--State-3 cells are created from three state-1 neighbours
--State-1 cells are created from any of:
----One state-2 neighbour and one state-3 neighbour
----One state-2 neighbour and two state-3 neighbours
----Two state-2 neighbours and two state-3 neighbours
--All three ON states are subject to S3
It reminds me of both Brian's Brain and MilhinSA. Similarly to both of them, complicated codependent rake systems tend to form. Like any self-respecting CA, it has oscillators, spaceships, puffers, rakes, guns, breeders, replicators, and so on.
Notable objects include this tiny gun:
Code: Select all
x = 4, y = 2, rule = ice8
4A$.A!
Code: Select all
x = 20, y = 9, rule = ice8
A18.A$A18.A$2.A14.A$2.A14.A2$3.2A$3.2A$3.2A$3.2A!
I'm fairly sure this is the smallest quadratic growth pattern, at 6 cells:
Code: Select all
x = 5, y = 3, rule = ice8
3.CB2$B2CB!
The vast majority of spaceships are c/1, but this tiny c/2 spaceship is also very common:
Code: Select all
x = 2, y = 3, rule = ice8
A$.A$A!
Code: Select all
x = 17, y = 1, rule = ice8
4A3.4A2.4A!