Trichromatic Life A

For discussion of other cellular automata.
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strake
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Trichromatic Life A

Post by 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.
Last edited by strake on October 8th, 2014, 9:06 pm, edited 1 time in total.
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praosylen
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Re: Trichromatic Life A

Post by 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!
former username: A for Awesome
praosylen#5847 (Discord)

The only decision I made was made
of flowers, to jump universes to one of springtime in
a land of former winter, where no invisible walls stood,
or could stand for more than a few hours at most...
strake
Posts: 26
Joined: October 8th, 2014, 7:47 am
Location: Mountain View, California
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Re: Trichromatic Life A

Post by 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!
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tommyaweosme
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Joined: January 15th, 2024, 9:37 am

Re: Trichromatic Life A

Post by tommyaweosme »

3-glider synthesis of certain color block

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x = 10, y = 10, rule = TriLifeA
7.C$.A5.C.C$2.A4.2C$3A4$5.3B$5.B$6.B!
im sure this will be useful someday
here's the gosper glider gun

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#R life
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o!
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hotcrystal0
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Re: Trichromatic Life A

Post by hotcrystal0 »

TriLifeA has been explored in the Hybrid CAs thread. Take this, for example:
FWKnightship wrote: April 18th, 2023, 3:40 am EDIT: P16 in TriLifeA:

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x = 9, y = 9, rule = TriLifeA
A$C.C$B4.B$4.B.B$5.B2$7.C2$6.BCA!
2c/4 spaceship:

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x = 4, y = 5, rule = TriLifeA
.2B$.B.B$A2.B$2.2B$.B!
24c/36 glider backrake:

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x = 31, y = 74, rule = TriLifeA
15.CAB$14.A3.A$13.C5.B$13.C5.B$15.3A3$15.2A$15.A.A$14.A2.A$14.A2.2A$
14.A2.A$15.2A$15.2A2$15.2A9$14.A$13.3A$15.A$10.A2.A$3.A6.A$2.B.C6.A3.
A11.A$.C.A.B6.A3.A9.C.B$2CB.C2B10.A7.B.A.C$12.2A10.2BC.B2C$12.2A.2A$
3.A10.A$27.A$3.2A$3.2A21.2A$2.A2.A5.A14.2A$2.A2.A5.A.A11.A2.A$3.2A6.
2A12.A2.A$26.2A12$6.A$7.A.A$7.3A16$2.A$2.A.A$2.2A!
P24, P62:

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x = 78, y = 37, rule = TriLifeA
50.A17.A$49.A.A15.A.A$48.A3.A13.A3.A$49.A.A15.A.A3$8.2B5.2B35.B13.B$
8.2B5.2B26.A7.2B13.2B7.A$42.A.A29.A.A$41.A35.A$42.A.A3.B21.B3.A.A$8.
3A3.3A26.A3.2B21.2B3.A2$9.A5.A$2B3.A13.A3.2B$2B3.A.A9.A.A3.2B$5.A13.A
4$5.A13.A$2B3.A.A9.A.A3.2B$2B3.A13.A3.2B$9.A5.A2$8.3A3.3A26.A3.2B21.
2B3.A$42.A.A3.B21.B3.A.A$41.A35.A$42.A.A29.A.A$8.2B5.2B26.A7.2B13.2B
7.A$8.2B5.2B35.B13.B3$49.A.A15.A.A$48.A3.A13.A3.A$49.A.A15.A.A$50.A
17.A!
EDIT2: 2c/12 spaceship!

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x = 10, y = 7, rule = TriLifeA
.A6.A$A.A.2A.A.A$2A2.2A2.2A$4.2A2$4.2B$4.2B!

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x = 69, y = 24, rule = TriLifeA
.A6.A$A.A.2A.A.A10.3A$2A2.2A2.2A13.A.3A$4.2A13.A3.A$19.A3.A$2.2A2.2A$
2.2A2.2A15.A20.3A14.3A$3.4A14.2A16.3A.A20.A.3A$3.A2.A14.A21.A3.A12.A
3.A$2.A4.A14.3A18.A4.A10.A4.A$2.A4.A13.A.A.A23.A8.A$2.A.2A.A14.A.3A
18.A7.2A7.A$3.A2.A17.A.A19.2A.2A.4A.2A.2A$3.A2.A17.2A24.A.A2.A.A$23.A
.A3$.A6.A11.A6.A22.A6.A$A.A.2A.A.A9.A.A.2A.A.A20.A.A.2A.A.A$2A2.2A2.
2A9.2A2.2A2.2A20.2A2.2A2.2A$4.2A17.2A28.2A2$4.2B17.2B28.2B$4.2B17.2B
28.2B!
EDIT3: And 4c/10!

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x = 13, y = 5, rule = TriLifeA
.3C5.3C$.C.C2.C2.C.C$C2.C5.C2.C$3.B5.A$6.C!
112 days until New York's age verification law goes into effect.

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x = 192, y = 53, rule = B3/S23
33$42b4o$41b6o$40b2ob4o$41b2o3$41b2o$39bo6bo$38bo8bo$38bo8bo$38b9o3$42b
4o$41b6o$40b2ob4o$41b2o!
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