Ice8

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

Ice8

Post by Pteriforever » June 6th, 2013, 8:07 am

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: 920
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Re: Ice8

Post by bprentice » June 6th, 2013, 1:07 pm

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

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Tropylium
Posts: 421
Joined: May 31st, 2011, 7:12 pm
Location: Finland

Re: Ice8

Post by Tropylium » June 6th, 2013, 3:33 pm

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: 920
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Re: Ice8

Post by bprentice » June 6th, 2013, 5:28 pm

Here is another gun:

Code: Select all

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

Post by Pteriforever » June 9th, 2013, 10:32 pm

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:

Code: Select all

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

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

Re: Ice8

Post by michaeljee » June 12th, 2013, 3:19 am

Nice surprise about this shorter form. Can you tell us what it is you are talking/writing about?
Has any info. about this shorter form been posted before (and i just missed it)?

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

Re: Ice8

Post by Pteriforever » June 24th, 2013, 1:37 am

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.

User avatar
Resu
Posts: 774
Joined: May 23rd, 2025, 10:47 am
Location: In an age of macro-spaceships
Contact:

Re: Ice8

Post by Resu » August 19th, 2025, 4:12 pm

Rake making a weird eating/sparking reaction:

Code: Select all

x = 94, y = 84, rule = ice8
4.A$3.2A$5.A$2.A2$2.A3$89.A$89.2A$88.A$91.A2$91.A5$10.3A$3.A4.A2.3A$6.
A.A7.A2.A.A$3.A2.A6.A7.A$12.A8.A$8.A7.A2.A.A$9.A2$81.3A$80.3A2.A4.A$6.
A3.A61.A.A2.A7.A.A$9.2A61.A7.A6.A2.A$9.A62.A8.A$72.A.A2.A7.A$5.2A2.C3.
A70.A$9.B2.A$10.C$7.A5.A$11.A.A69.A3.A$7.A2.A.A70.2A$84.A2$80.A3.C2.2A
$81.A2.B$83.C$80.A5.A$80.A.A$81.A.A2.A3$5.A$3.A3.A$7.5A$3.A$2.A4$88.A
$86.A3.A$7.2A73.5A$7.A82.A$5.2A84.A2$8.A$8.A$2.A$A6.A$8.A76.2A$A4.A3.
2A75.A$4.A.2A79.2A$2.A.3A.A$85.A$4.A80.A$3.A87.A$4.6A76.A6.A$85.A$5.4A
74.2A3.A4.A$86.2A.A$85.A.3A.A2$89.A$90.A$84.6A2$85.4A!

Code: Select all

x = 31, y = 13, rule = C
8.2X2.3X.3X.X.X$8.X.X.X3.X3.X.X$8.X.X.3X.3X.X.X$8.2X2.X5.X.X.X$8.X.X.
3X.3X.3X$M2.M$4.M$M3.M$.4M$27.2M$27.M.M$29.M$29.2M! [[ AUTOSTART GPS 10 ]]

User avatar
ThePlayzr
Posts: 698
Joined: April 19th, 2025, 1:33 am
Location: Australia
Contact:

Re: Ice8

Post by ThePlayzr » August 20th, 2025, 8:04 am

Resu wrote:
August 19th, 2025, 4:12 pm
Rake making a weird eating/sparking reaction:

Code: Select all

x = 94, y = 84, rule = ice8
4.A$3.2A$5.A$2.A2$2.A3$89.A$89.2A$88.A$91.A2$91.A5$10.3A$3.A4.A2.3A$6.
A.A7.A2.A.A$3.A2.A6.A7.A$12.A8.A$8.A7.A2.A.A$9.A2$81.3A$80.3A2.A4.A$6.
A3.A61.A.A2.A7.A.A$9.2A61.A7.A6.A2.A$9.A62.A8.A$72.A.A2.A7.A$5.2A2.C3.
A70.A$9.B2.A$10.C$7.A5.A$11.A.A69.A3.A$7.A2.A.A70.2A$84.A2$80.A3.C2.2A
$81.A2.B$83.C$80.A5.A$80.A.A$81.A.A2.A3$5.A$3.A3.A$7.5A$3.A$2.A4$88.A
$86.A3.A$7.2A73.5A$7.A82.A$5.2A84.A2$8.A$8.A$2.A$A6.A$8.A76.2A$A4.A3.
2A75.A$4.A.2A79.2A$2.A.3A.A$85.A$4.A80.A$3.A87.A$4.6A76.A6.A$85.A$5.4A
74.2A3.A4.A$86.2A.A$85.A.3A.A2$89.A$90.A$84.6A2$85.4A!
Umm, I'm pretty sure posting that breaks rule 3b: do not post in a thread that has been inactive for over a year unless for a good reason.
This has been inactive for over a decade, so I think it really does.
Please help me prove b3s23-a5 omniperiodic!
Please visit my ruleset and contribute!
User:ThePlayzr
Finally got LLS! Time to do way too much searching!

User avatar
Resu
Posts: 774
Joined: May 23rd, 2025, 10:47 am
Location: In an age of macro-spaceships
Contact:

Re: Ice8

Post by Resu » August 20th, 2025, 8:20 am

ThePlayzr wrote:
August 20th, 2025, 8:04 am
Umm, I'm pretty sure posting that breaks rule 3b: do not post in a thread that has been inactive for over a year unless for a good reason.
This has been inactive for over a decade, so I think it really does.
It says “for a good reason”, and I think this reaction is quite novel. I’ve never seen a reaction like this before.
I think that’s a good reason.

Code: Select all

x = 31, y = 13, rule = C
8.2X2.3X.3X.X.X$8.X.X.X3.X3.X.X$8.X.X.3X.3X.X.X$8.2X2.X5.X.X.X$8.X.X.
3X.3X.3X$M2.M$4.M$M3.M$.4M$27.2M$27.M.M$29.M$29.2M! [[ AUTOSTART GPS 10 ]]

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