## Ice8

For discussion of other cellular automata.
Pteriforever
Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Ice8

I've come up with a shiny new 4-state CA for you guys ;D

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
``````
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:

Code: Select all

``````x = 4, y = 2, rule = ice8
4A\$.A!
``````
This is a simple replicator being stabilised by two oscillators:

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!
``````
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:

Code: Select all

``````x = 5, y = 3, rule = ice8
3.CB2\$B2CB!
``````
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:

Code: Select all

``````x = 2, y = 3, rule = ice8
A\$.A\$A!
``````
Finally, here's an MSM breeder on width 1:

Code: Select all

``````x = 17, y = 1, rule = ice8
4A3.4A2.4A!
``````

bprentice
Posts: 674
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Ice8

Pteriforever,

What do you mean by "All three ON states are subject to S3"? It seems that a cell in state 1, 2, or 3 turns to state 1 if it has 3 neighbors in states 1, 2 or 3.

A very nice rule though!

Brian Prentice

Tropylium
Posts: 406
Joined: May 31st, 2011, 7:12 pm
Location: Finland

### Re: Ice8

Well, that tiny gun is awesome.

Most objects seem to be simply phoenixes that alternate between state 1 vs. state 2+3 though, so it's fairly firmly in the Brian's Brain-esque category, even though the width-4 engines have a definite MilhinSA resemblance. Similarly it's also noticable how the two p4s and the p6 are just about the only natural stationary objects…

Also I feel this needs an icier color set:

Code: Select all

``````color=0 127 159 255
color=1 0 0 63
color=2 31 95 255
color=3 0 31 159``````

bprentice
Posts: 674
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Ice8

Here is another gun:

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``````x = 49, y = 163, rule = ice8
42.2A2\$40.2A7\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$35.
2A6.2A\$35.2A6.2A\$35.2A6.2A\$35.2A6.2A2\$26.A\$26.A18.4A\$24.A20.4A\$24.A
2\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A7\$40.2A2\$42.2A8\$42.2A2\$40.2A
15\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$
45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$19.2A6.2A6.2A6.2A\$19.2A6.2A6.
2A6.2A\$19.2A6.2A6.2A6.2A\$19.2A6.2A6.2A6.2A2\$2.A\$2.A42.4A\$A44.4A\$A2\$
45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.4A\$45.4A3\$45.
4A\$45.4A3\$45.4A\$45.4A15\$40.2A2\$42.2A!
``````

Brian Prentice

Pteriforever
Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Ice8

Code: Select all

``````x = 4, y = 4, rule = ice8
A\$2.2A2\$3.A!
``````
Here's a 4-cell predecessor of that tiny gun, making this the new smallest-by-population infinite growth pattern. I'm totally certain that a bounding box of 2x4 is unbeatable though, although I haven't looked at all possibilities for 3x3 yet. The smallest width-1 infinite growth pattern is a tie between these two, both at 1x12 and 8 cells:

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``````x = 12, y = 29, rule = ice8
A.2A.2A2.3A28\$4A4.4A!
``````

michaeljee
Posts: 1
Joined: June 12th, 2013, 3:14 am

### Re: Ice8

Pteriforever
Posts: 37
Joined: April 10th, 2013, 9:43 pm

### Re: Ice8

Code: Select all

``````x = 59, y = 36, rule = ice8
49.2A2\$47.2A6\$8.2A2\$10.2A\$46.A\$45.2A\$46.A\$46.A2\$56.A\$56.A\$58.A\$12.A
45.A\$12.2A\$12.A\$12.A2\$2.A\$2.A\$A\$A2\$41.2A2\$39.2A2\$16.2A2\$18.2A!
``````
I made a gun for the little c/2 spaceship.