Trichromatic Life A

[strake]

This rule has 3 live states, each which alone is Conway's Life, but which can interact. The rule is fully symmetric in permutation of colors.

• A cell with 3 live neighbors of the same color is born with or converted to that color.
• A cell with 2 live neighbors of nonsame colors is born with or converted to the remaining color.
• A live cell with 3 live neighbors, 1 of each color, survives.
• A live cell with 2 live neighbors of its own color survives.
• Any other cell dies.

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@RULE TriLifeA

@TABLE
n_states:4
neighborhood:Moore
symmetries:permute
var a={1,2,3}
var b={1,2,3}
var c={1,2,3}
var r={0,1,2,3}
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}
w,a,a,a,0,0,0,0,0,a
a,1,2,3,0,0,0,0,0,a
a,a,a,0,0,0,0,0,0,a
w,2,3,0,0,0,0,0,0,1
w,3,1,0,0,0,0,0,0,2
w,1,2,0,0,0,0,0,0,3
r,s,t,u,v,w,x,y,z,0

@COLORS
0  48  48  48
1 255   0   0
2   0 255   0
3   0   0 255

It has speed 2/3 spaceships! Some I found:

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x = 7, y = 15, rule = TriLifeA
3.2A$.A3.A$6.A$3B2.B$6.C$.C3.C$3.2C2$3.2C$.C3.C$B5.C$.2B2.B$B5.A$.A3.
A$3.2A!

I call these hoop-ships.

Some oscillators I found:

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x = 27, y = 4, rule = TriLifeA
A7.C3.2B4.B5.B$.B4.A4.A4.2AB3.B3.A$C6.B5.B3.A2B2.B3.A$17.A6.A!

Alas, the colors seem to interact mostly destructively. I created this rule with these constraints in mind:
• Symmetry in permutation of colors
• That each color alone be Conway's Life
I found no such rule in which colors interact more constructively.

[praosylen]

All of the collisions between a glider and a differently-colored block:

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x = 66, y = 49, rule = TriLifeA
42.2A2.2B$42.2A.2B$47.B5$26.2B$25.2B$22.2A3.B$22.2A10$4.2B$3.2B$5.B
36.2A$2A40.2A2.2B$2A43.2B$47.B8$60.2A$60.2A$26.2B$22.2A.2B36.3B$22.2A
3.B35.B$64.B6$43.2A$43.2A$47.2B$46.2B$48.B!

[strake]

2 puffers I found:

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x = 31, y = 45, rule = TriLifeA
13.B11.5B$11.B3.B9.B4.B$10.B14.B$10.B4.B10.B3.B$10.5B13.B2$.A2.A$A$A
3.A$4A$6.3A$6.2A.2A$6.3A$4A$A3.A$A$.A2.A2$10.5B13.B$10.B4.B10.B3.B$
10.B14.B$11.B3.B9.B4.B$13.B11.5B3$6.5B$6.B4.B$6.B$7.B3.B$9.B3$6A$A5.
2A$A5.A.2A$.A3.A$3.A$2.2A$.4A$2A.2A$.2A$13.2B$12.2B.3B$13.5B$14.3B!