Multicolor Life variants

[fluffykitty]

People have made quite a few multicolor life variants, including Immigration and QuadLife. With the restrictions that live cells cannot change color and colors must be treated completely symmetrically, those and ordinary B3/S23 are the only possible variants. However, other variants should be possible if smaller symmetry groups are allowed. Which permutation groups can be realized with multicolor Life variants, and what interesting patterns exist in these?

[MathAndCode]

With the restrictions that live cells cannot change color and colors must be treated completely symmetrically, those and ordinary B3/S23 are the only possible variants.

I can think of at least one other such variant: There are two colors, and each newly-born cell takes the color that an odd number of live neighbors have. One interesting question concerning this rule is whether patterns in this rule would tend to eventually all become one color,

[bubblegum]

I can think of at least one other such variant: There are two colors, and each newly-born cell takes the color that an odd number of live neighbors have. One interesting question concerning this rule is whether patterns in this rule would tend to eventually all become one color,

I think (don't quote me on this) that the last possible variants for two-colour Life are "Even" and "Minority".

[MathAndCode]

Here are the four distinct gliders in Minority besides color inversions.

Code: Select all

x = 13, y = 13, rule = Minority
.A9.A$2A8.2A$A.A7.A.B8$.A9.A$AB8.AB$A.A7.A.B!

The two gliders in the top row each have period four, and the two gliders in the bottom row each have period 28. All four gliders are glide-reflective, and none are their own color inversions.

[Hunting]

FYI, I'm the creator of Minority, because I had this idea a few days ago. It was originally created as a more aggressive variant of Immigration (to prefer attacks), but the ash turned out to be stripy.

Two LWSSes I know of so far:

Code: Select all

x = 5, y = 11, rule = Minority
A2BA$A3.B$B$.A2.B4$2ABA$A3.A$A$.A2.A!

They have impressive periods.

I also created Infect to get rid of the "living cells must not change color" restriction.

[MathAndCode]

Two LWSSes I know of so far:

Code: Select all

x = 5, y = 11, rule = Minority
A2BA$A3.B$B$.A2.B4$2ABA$A3.A$A$.A2.A!

In Minority, any two colorations of the same repeating pattern in ConwayLife can have their colorations XORed in all phases.

Code: Select all

x = 12, y = 10, rule = Minority
A2BA$A3.B$B$.A2.B2.AB2A$7.A3.B$7.B$2ABA4.A2.B$A3.A$A$.A2.A!

[Moosey]

You can also have variants in which, say, cells of a different color are born from three of the same color

[bubblegum]

You can also have variants in which, say, cells of a different color are born from three of the same color

Those being what I originally meant when I said Even and Minority, though I can't complain about the interpretation.

[Hunting]

Two LWSSes I know of so far:

Code: Select all

x = 5, y = 11, rule = Minority
A2BA$A3.B$B$.A2.B4$2ABA$A3.A$A$.A2.A!

In Minority, any two colorations of the same repeating pattern in ConwayLife can have their colorations XORed in all phases.

Code: Select all

x = 12, y = 10, rule = Minority
A2BA$A3.B$B$.A2.B2.AB2A$7.A3.B$7.B$2ABA4.A2.B$A3.A$A$.A2.A!

Code: Select all

x = 14, y = 14, rule = Minority
2A$A$.A.A2$3.A.A2$5.A.B2$7.A.A2$9.A.A2$11.A.A$12.2A!

[MathAndCode]

Code: Select all

x = 14, y = 14, rule = Minority
2A$A$.A.A2$3.A.A2$5.A.B2$7.A.A2$9.A.A2$11.A.A$12.2A!

Code: Select all

x = 25, y = 29, rule = Minority
2A9.2A$A10.A$.A.A8.A.B2$3.A.A8.A.A2$5.A.B8.A.B2$7.A.A8.A.A2$9.A.A8.A.
B2$11.A.A8.A.A$12.2A9.2A2$5.2A$5.A$6.A.B2$8.A.A2$10.A.A2$12.A.A2$14.A
.B2$16.A.A$17.2A!

[creeperman7002]

Code: Select all

x = 14, y = 14, rule = Minority
2A$A$.A.A2$3.A.A2$5.A.B2$7.A.A2$9.A.A2$11.A.A$12.2A!

Code: Select all

x = 25, y = 29, rule = Minority
2A9.2A$A10.A$.A.A8.A.B2$3.A.A8.A.A2$5.A.B8.A.B2$7.A.A8.A.A2$9.A.A8.A.
B2$11.A.A8.A.A$12.2A9.2A2$5.2A$5.A$6.A.B2$8.A.A2$10.A.A2$12.A.A2$14.A
.B2$16.A.A$17.2A!

It appears that is an emulation of Rule 150.

[smjg]

It just so happens I've just been studying these. Specifically, I've been looking at the possibilities for colourified CAs subject to these constraints:

• The underlying CA (colours flattened) is Life-like in the strictest sense - 2D square grid, two states, outer-totalistic, Moore neighbourhood.
• Surviving cells don't change colour.
• Colour-totalistic - colour of a born cell depends only on the bag of neighbour colours, not how they are arranged.
• Colour-symmetric - if the colours are permuted the CA behaves the same.

With Conway's Life as the underlying CA, I have concluded that there are six possibilities:

• Two live state colours: majority (Immigration), odd, even, minority
• Four live state colours: remaining colour for 3 different colours in neighbourhood (necessary for colour-symmetry); majority (QuadLife) or odd for 1 or 2 different colours in neighbourhood.

For other base rules, the possibilities are different. Specifically, they depend on the B part of the rule string. Under B2, the only possibility is a three-colour analogue of QuadLife. Any base rule containing B6, such as HighLife, can't be colourified within these constraints at all, since:

• There would need to be a unique third state for 3+3 to give birth to.
• Thus there are at least three states, thus must be a unique fourth state for 2+2+2 to give birth to.
• However, this fourth state means the aforementioned third state can't be unique.

I haven't yet studied possibilities for multiple dead cell colours. I can see that if dead cell colours are separate from live cell colours then this would work only in universes containing S8. But having the same set of colours for dead and live cells would open up possibilities.

[Entity Valkyrie 2]

By the way, my rule EV2QuadColor is a marked version of QuadLife.

[smjg]

By the way, my rule EV2QuadColor is a marked version of QuadLife.

Is this something you've published somewhere? I can't seem to find it.

BTW, I recently made a QuadLife rule file for Golly (as yet unpublished), intended for study purposes, with Unknown and Influence states. Unknown means a live cell whose colour is unknown. Influence is the same with the added rule that, when a cell is born, if Unknown and Influence are both in the neighbourhood that gave birth to it then the born cell is Influence; as such, it's good for seeing what future cells might possibly be influenced by the colour of a specific cell.

[KazukiMutoh]

I would like to introduce the ruleset I named "FrontLine Life," which I continue to refine.

In addition to standard B/S (Birth/Survival) rules, this system determines the state of the next generation based on majority or minority voting—as well as various other conditions—specifically in "frontline" areas where multiple colors coexist in close proximity.

It incorporates numerous parameters to control these frontline dynamics, including:

・Number of colors
・Majority/Minority voting
・Reversal switch
・Limit switch
・Frontline-specific Birth/Survive/Change switches
・Resistance switch

...and others, totaling 13 types in all.

You can try Frontline Life here.
https://codepen.io/ichimonzi/pen/PwqeXrL

Here are some distinctive rules I’ve discovered in Frontline Life so far.

Tiger Pattern
The spaceships collide with one another, eventually forming a colorful leopard-print pattern.
https://codepen.io/ichimonzi/full/PwqeXrL?r=tiger

Intracloud lightning
It features a chaosic rule that looks like lightning streaking through the clouds.
https://codepen.io/ichimonzi/full/PwqeXrL?r=lightning

TriColShips
The rules under which a three-color mixed spaceship can spontaneously emerge.
https://codepen.io/ichimonzi/full/PwqeX ... hip&p=oss2

Night Walkers
The rules combine majority rule and minority rule.
https://codepen.io/ichimonzi/full/PwqeXrL?r=nwalker

Bicolor Stripes
The rule that allows for the creation of a spaceship using a mix of three or more colors.
https://codepen.io/ichimonzi/full/PwqeX ... ipe&p=oss8

Other distinctive rules are also registered in the presets.
The rule string used here is local and cannot be used elsewhere.

[MDA]

I developed a multicolor Life variant called “Domination”.

Rules:

Cells can be dead, dominant, or recessive.

A dead cell becomes recessive if it has five dead neighbors and three recessive neighbors.

A dead cell becomes dominant if it has five dead neighbors and at least one of its other neighbors is dominant.

A dominant cell stays dominant if it has exactly two or three living neighbors.

A recessive cell stays recessive if it has 2 or 3 living neighbors and all dominant cells around it will survive in the next generation.

A recessive cell can also stay recessive if it has 2 or 3 living neighbors and none of them are dominant.

A recessive cell becomes dominant if any of its neighbors is dominant and will not survive to the next generation.

Ruletable:

Code: Select all

@RULE Domination

@TABLE

n_states:7
neighborhood:Moore
symmetries:permute

var a={3,4,5,6}
var b=a

var c={4,5}

var d={0,1,2}
var e=d
var f=d
var g=d
var h=d
var i=d
var j=d
var k=d

var l={3,6}
var m=l
var n=l

var o={1,2}
var p=o
var q=p

var r={0,3,4,5,6}
var s=r
var t=r
var u=r
var v=r
var w=r
var x=r
var y=r

0,l,m,n,0,0,0,0,0,1
0,a,b,c,0,0,0,0,0,2

1,o,p,0,0,0,0,0,0,3
1,o,p,q,0,0,0,0,0,3

1,d,e,f,g,h,i,j,k,6

2,o,p,0,0,0,0,0,0,4
2,o,p,q,0,0,0,0,0,4

2,d,e,f,g,h,i,j,k,5

3,5,s,t,u,v,w,x,y,2
3,r,s,t,u,v,w,x,y,1

4,r,s,t,u,v,w,x,y,2

5,r,s,t,u,v,w,x,y,0

6,r,s,t,u,v,w,x,y,0


@COLORS

0 000 000 000
1 000 000 255
2 255 000 000
3 128 000 255
4 255 128 000
5 255 192 000
6 192 128 255

Note that this rule runs at half the speed of regular Life, because it requires knowing whether dominant cells survive or die in the next generation.

This rule is useful for determining necessary cells for catalysis. By reflecting dominant gliders using recessive Snarks, you can observe what parts of the Snark are essential to catalyze certain reactions:

Code: Select all

x = 65, y = 65, rule = Domination
25.2A3.2A$25.2A2.A.3A$29.A4.A$25.4A.2A2.A$25.A2.A.A.A.2A$28.A.A.A.A$
29.2A.A.A$33.A2$19.2A$20.A7.2A$20.A.A5.2A$21.2A7$31.2A8.B13.A$31.A10.
B10.3A$32.3A5.3B9.A$20.2B12.A17.2A$19.B.B$21.B$60.2A.2A$61.A.2A$61.A$
53.2A4.3A$4.A48.2A3.A3.2A$2.5A14.2A35.4A2.A$.A5.A13.A22.2A15.A.2A$.A
2.3A12.A.A21.A.A12.3A2.A$2A.A15.2A22.A13.A5.A$A2.4A35.2A14.5A$.2A3.A
3.2A48.A$3.3A4.2A$3.A$2A.A$2A.2A$43.B$43.B.B$11.2A17.A12.2B$12.A9.3B
5.3A$9.3A10.B10.A$9.A13.B8.2A7$42.2A$35.2A5.A.A$35.2A7.A$44.2A2$31.A$
30.A.A.2A$30.A.A.A.A$29.2A.A.A.A2.A$30.A2.2A.4A$30.A4.A$31.3A.A2.2A$
33.2A3.2A!
[[ STEP 2 ]]

@RULE Domination

@TABLE

n_states:7
neighborhood:Moore
symmetries:permute

var a={3,4,5,6}
var b=a

var c={4,5}

var d={0,1,2}
var e=d
var f=d
var g=d
var h=d
var i=d
var j=d
var k=d

var l={3,6}
var m=l
var n=l

var o={1,2}
var p=o
var q=p

var r={0,3,4,5,6}
var s=r
var t=r
var u=r
var v=r
var w=r
var x=r
var y=r

0,l,m,n,0,0,0,0,0,1
0,a,b,c,0,0,0,0,0,2

1,o,p,0,0,0,0,0,0,3
1,o,p,q,0,0,0,0,0,3

1,d,e,f,g,h,i,j,k,6

2,o,p,0,0,0,0,0,0,4
2,o,p,q,0,0,0,0,0,4

2,d,e,f,g,h,i,j,k,5

3,5,s,t,u,v,w,x,y,2
3,r,s,t,u,v,w,x,y,1

4,r,s,t,u,v,w,x,y,2

5,r,s,t,u,v,w,x,y,0

6,r,s,t,u,v,w,x,y,0


@COLORS

0 000 000 000
1 000 000 255
2 255 000 000
3 128 000 255
4 255 128 000
5 255 192 000
6 192 128 255