Colorised Life

[PkmnQ]

So is it possible to create a reflector in Immigration which always inverts the color from red to blue and blue to red?

How about a reflector which turned one color into its anti-state in NiemecLife?

[Moosey]

So is it possible to create a reflector in Immigration which always inverts the color from red to blue and blue to red?

How about a reflector which turned one color into its anti-state in NiemecLife?

Probably, but I haven’t seen any. You’d just need to find a conduit which changes the color of something without any parts of the conduit. Sadly, a lot of conduits don’t work like that.

Code: Select all

x = 17, y = 23, rule = Immigration
6.2A3.2A$6.2A2.A.3A$10.A4.A$6.4A.2A2.A$6.A2.A.A.A.2A$9.A.A.A.A$10.2A.
A.A$14.A2$2A$.A7.2A$.A.A5.2A$2.2A7$12.2A$3.2B7.A$2.B.B8.3A$4.B10.A!

Code: Select all

x = 6, y = 13, rule = Immigration
.2A$2.A$.A$.2A6$B3.2A$2B2.2A$.2B$2B!

Code: Select all

x = 41, y = 36, rule = Immigration
2.B$B.B$.2B10$25.A$23.3A$22.A$22.2A$7.2A$8.A$8.A.2A$9.A2.A23.A$10.2A
24.A$25.2A9.3A$25.2A11.A4$34.A3.2A$33.A.A3.A$32.A.A3.A$28.2A.A.A3.A$
28.2A.A2.4A.A$32.A.A3.A.A$28.2A.2A2.A2.A.A$29.A.A2.2A3.A$17.2A10.A.A$
17.2A11.A!

However...

Code: Select all

x = 17, y = 19, rule = Immigration
16.B$14.2B$15.2B10$4.2A$3.A2.A$3.A.A$.2A.A$A2.A$A.A$.A!

You could hook the HB reaction up to a huge matching that rebuilds the HB where it was, using a splitter to extract a signal AND reflect the now-red/green G.

Also,

Code: Select all

x = 84, y = 87, rule = Immigration
16.B$14.2B$15.2B10$4.2A$3.A2.A$3.A.A$.2A.A$A2.A$A.A$.A3$17.A$16.A$16.
A4.A$16.5A38$78.A$76.2A$77.2A10$66.2A$65.A2.A$65.A.A$63.2A.A$62.A2.A$
62.A.A$63.A3$79.A$78.A$78.A4.A$78.5A!

The color info isn’t lost immediately.

EDIT:
A poly color SL synth

Code: Select all

x = 36, y = 19, rule = Immigration
23.A$22.A$18.B3.3A$.A14.2B$2.A14.2B$3A5$16.3A$16.A16.2B$17.A15.B.B$
33.B$2.2B$3.2B$2.B9.3B$12.B$13.B!

[PkmnQ]

For the HB, I found out that the bottom loaf dictates the glider color, and the top loaf dictates the reconstructed HB's loaves.

[Moosey]

For the HB, I found out that the bottom loaf dictates the glider color, and the top loaf dictates the reconstructed HB's loaves.

Actually, that’s only true when the bottom loaf is the color of the Glider; otherwise the top has the last say:

Code: Select all

x = 49, y = 20, rule = Immigration
48.A$16.B29.2A$14.2B31.2A$15.2B9$36.2B$4.2B29.B2.B$3.B2.B28.B.B$3.B.B
27.2A.B$.2A.B27.A2.A$A2.A28.A.A$A.A30.A$.A!

All non-congruent reactions

Code: Select all

x = 49, y = 55, rule = Immigration
48.A$16.B29.2A$14.2B31.2A$15.2B9$36.2B$4.2B29.B2.B$3.B2.B28.B.B$3.B.B
27.2A.B$.2A.B27.A2.A$A2.A28.A.A$A.A30.A$.A16$48.A$16.B29.2A$14.2B31.
2A$15.2B9$36.2A$4.2A29.A2.A$3.A2.A28.A.A$3.A.A27.2A.A$.2A.A27.A2.A$A
2.A28.A.A$A.A30.A$.A!

Suddenly I think we have a use for matrices in immigration
Blue = 1
Green = 0
First binary digit = color of top loaf
2nd Binary digit = color of bottom loaf

[ 10 10 ]
[ 00 00 ]
+
[ 1 0 ]
[ 1 0 ]
->
[ 11 11 ]
[ 00 00 ]
+
[ 1 0 ]
[ 0 0 ]

Let’s call these BAKEtrices

Technically, we need an additional 2 values for gliders.

Code: Select all

x = 116, y = 55, rule = Immigration
48.A66.A$16.B29.2A35.B29.2A$14.2B31.2A32.2B31.2B$15.2B65.2A9$36.2B65.
2B$4.2B29.B2.B32.2B29.B2.B$3.B2.B28.B.B32.B2.B28.B.B$3.B.B27.2A.B33.B
.B27.2A.B$.2A.B27.A2.A32.2A.B27.A2.A$A2.A28.A.A32.A2.A28.A.A$A.A30.A
33.A.A30.A$.A66.A16$48.A66.A$16.B29.2A35.B29.2A$14.2B31.2A32.2B31.2B$
15.2B65.2A9$36.2A65.2A$4.2A29.A2.A32.2A29.A2.A$3.A2.A28.A.A32.A2.A28.
A.A$3.A.A27.2A.A33.A.A27.2A.A$.2A.A27.A2.A32.2A.A27.A2.A$A2.A28.A.A
32.A2.A28.A.A$A.A30.A33.A.A30.A$.A66.A!

[Macbi]

I believe that in Immigration changing the colour of a cell in one generation can only change cells in later generations in the same direction. So a colour changing reflector is impossible.

[fluffykitty]

What about in QuadLife? Monotonicity doesn't hold there.

Code: Select all

x = 8, y = 5, rule = QuadLife
ABC2.ABD3$.D4.C$D.D2.C.C!

[Macbi]

What about in QuadLife? Monotonicity doesn't hold there.

Code: Select all

x = 8, y = 5, rule = QuadLife
ABC2.ABD3$.D4.C$D.D2.C.C!

That's a good question. The other thing I'd like to see is an oscillator in QuadLife where for each of the colours there's a phase where that colour is completely missing.

[Entity Valkyrie 2]

I believe that in Immigration changing the colour of a cell in one generation can only change cells in later generations in the same direction. So a colour changing reflector is impossible.

Is there a mathematical proof for this statement?

Also, unlike the Snark, when a glider hits a Snark64, the color of the beehive determines the output glider's color:

Code: Select all

x = 31, y = 27, rule = Immigration
7.2A$3.2A3.A$3.A2.A4.2A$4.4A3.2A3.2A12.A$16.A.A.2A.A4.2A$6.2A10.A.A.
2A5.2A$5.A.A10.2A$5.2A6$13.2B$12.B2.B$13.2B3$2.2A$.A.A7.A6.2A$.A8.A.A
5.2A$2A4.2A.A.A$5.A.A.A.A.A$5.A4.A.2A$6.3A.A$8.A.A$9.A!

[g0t0]

I believe that in Immigration changing the colour of a cell in one generation can only change cells in later generations in the same direction. So a colour changing reflector is impossible.

Is there a mathematical proof for this statement?

Also, unlike the Snark, when a glider hits a Snark64, the color of the beehive determines the output glider's color:

Code: Select all

x = 31, y = 27, rule = Immigration
7.2A$3.2A3.A$3.A2.A4.2A$4.4A3.2A3.2A12.A$16.A.A.2A.A4.2A$6.2A10.A.A.
2A5.2A$5.A.A10.2A$5.2A6$13.2B$12.B2.B$13.2B3$2.2A$.A.A7.A6.2A$.A8.A.A
5.2A$2A4.2A.A.A$5.A.A.A.A.A$5.A4.A.2A$6.3A.A$8.A.A$9.A!

Prove:

The color of a cell can be calculated from the init state (red->0,blue->1) by using some AND/OR gate.

AND / OR is both monotonicity so Immigration is monotonicity .

[otismo]

the most adorable pattern ever by Chente Rodri

Code: Select all

x = 148, y = 118, rule = LifeSuper
63.2pA$63.2pA$3.2G.2G2.2pA4.2pA2.Q2.2Q.Q4.W6.2W2.2G.G2.2G.G2.E2.2E.E
6.2S.2S.S12.2G.2G2.2pA4.2pA2.2A4.2A12.2Q.2Q2.2E4.2E2.2A4.2A$2.G.G.2G
2.pA6.pA2.4Q.2Q3.W.W5.W3.G.2G2.G.2G2.4E.2E5.S.S.S.2S11.G.G.2G2.pA6.pA
2.A5.A12.Q.Q.2Q2.E6.E2.A5.A$.G.G7.pA4.pA13.W2.W5.W6.2G17.S.S16.G.G7.pA
4.pA4.A5.A10.Q.Q7.E4.E4.A5.A$.G8.2pA4.2pA2.2Q7.2W3.W3.2W6.G7.2E9.S18.
G8.2pA4.2pA2.2A4.2A10.Q8.2E4.2E2.2A4.2A$2G8.pA6.pA2.Q12.2W3.W8.G6.E
11.S16.2G8.pA6.pA2.A5.A10.2Q8.E6.E2.A5.A$G11.pA.3pA5.Q.2Q3.2W2.W5.W6.
2G8.E.2E7.S.2S12.G11.pA.3pA4.A5.A9.Q11.E.3E4.A5.A$.G9.3pA.pA5.3Q.Q3.W
5.W2.2W6.G8.3E.E8.2S.S12.G9.3pA.pA4.2A4.2A10.Q9.3E.E4.2A4.2A$2G8.pA6.
pA2.Q9.W3.2W11.G6.E17.S10.2G8.pA6.pA2.A5.A10.2Q8.E6.E2.A5.A$G9.2pA4.
2pA2.2Q7.2W3.W3.2W6.2G6.2E17.S9.G9.2pA4.2pA3.A5.A9.Q9.2E4.2E3.A5.A$.G
9.pA4.pA12.W5.W2.W7.G24.S.S10.G9.pA4.pA3.2A4.2A10.Q9.E4.E3.2A4.2A$2.G
.2G.G2.pA6.pA2.4Q.2Q3.W5.W.W8.G6.4E.2E4.2S.S.S.S12.G.2G.G2.pA6.pA4.2A
.A13.Q.2Q.Q2.E6.E4.2A.A$3.2G.2G2.2pA4.2pA2.Q2.2Q.Q2.2W6.W8.2G6.E2.2E.
E4.S.2S.2S14.2G.2G2.2pA4.2pA4.A.2A14.2Q.2Q2.2E4.2E4.A.2A58$73.2J$72.
2J2I$59.2I10.2IJ2IJ$58.JIJI8.I7J$57.J2I3J7.4J2I2J$56.6JIJ5.6JI3J$56.
4J3IJ5.2I3JI2JIJ$55.5JIJI2J3.J5I3JI2J$44.3J.3J4.JI3JI2JIJ4.8JIJ$43.J
2IJ.J2IJ2.JIJIJ5I2J5.J4.J$43.JIJI.IJIJ3.JI3J2IJIJ34.2E.2Q.2Q.2E$44.IJ
I.IJI6.J4.J35.E.E.2Q.2Q.E.E$43.3JI.I3J45.E13.E$43.2J2I.2I2J44.E15.E$
44.J2I.2IJ44.E10.K4.2E$95.2E8.K2LK$105.K2LK2.2D$35.D10.Q.Q46.2D10.K4.
D$34.D.D7.3Q.3Q44.2D14.D$35.D7.A7.E4.O5.O4.O4.O4.O4.O3.O20.K3.2D$42.O
.E5.E.E2.O2.O.O2.O.O2.O.O2.O.O2.O.O2.O2.O2.2K4.2G8.3K$35.G4.3O.E4.E2.
E2.O2.O.O2.O.O2.O.O2.O.O2.O.O2.O2.O3.K3.G2.G6.E6.2pA$34.G.G2.pA4.2E3.
E.E5.O3.O4.O4.O4.O4.O8.K.2EG2.G2S3.E.Q5.pA$34.G.G2.pA.2W3.B3.E40.E3.
2G3.pA.E2.Q6.pA$33.2G.2G.pA.W.2O3A3.3B38.2AB2.ABApA.S.2Q.2E2.2pA$34.I
.A2.pAMB.B.B2A.4B2A.2A3B2A3B2A3B2A3B2A3B2A3B2A4B.BAB2A2.B.S2.B.E.BA$
34.E.2AB.A.4AB2A2B2AB2A3B2A3B2A3B2A3B2A3B2A3B2A3B2A2B3.ABAB2A.ABA.BAB
3A$35.E2.B2AB.A.ABAB2AB.B.A3B2A3B2A3B2A3B2A3B2A3B2A3B2AB2AEC.BABAB2A.
2A2B.B2.A$31.2pA3.EI3.pA.E2.E3.2B2pA2.2A3B2A3B2A3B2A3B2A3B2A3B2A3BA2B
.CA6.2B2A2B3.2A$29.2B.pA5.2I.pA.2E.E.2O2.pA39.B2.E8.4B$29.BAB6.I.2pA.
E2.E.2O4.pA37.2pA.E.E14.2pA$28.ABA3.2pA8.2E7.2pA16.pA8.2pA11.pA2.2E
14.pA$27.3B3.A.pA19.2E2.2E9.pA.pA6.pA2.pA8.pA.pA19.pA$26.ABA3.B.B20.E
.BA.E5.BA3.pA3.BA3.2pA3.BA4.2pA6.BA7.AB4.pA$25.3B3.A.A4.BA3.BA3.BA6.A
2.B5.ABAB5.ABAB6.ABAB.2E7.ABAB5.BABA4.pA$24.ABA3.B.B4.ABAB.ABAB.ABAB
4.B4.A3.B4.A3.B4.A4.B4.A.E6.B4.A3.A4.B4.pA$22.4B3.A.A4.G4.E4.O4.A2.2A
4.2B.2A4.2B.2A4.2B2.2A5.B6.2A4.2B.2B4.2A2.2pA$22.B2A3.B.B4.G.3EG.G2EO
.O3EB2.2B4.2A.2B4.2A.2B4.2A2.2B5.A6.2B4.2A.2A4.2B$21.G.B3.G.A6.G4.G4.
E4.A3.A4.B3.A4.B3.A4.B4.A4.B.G.GE3.A4.B3.B4.A3.2G$21.2G4.2G8.ABAB.ABA
B.ABAB5.BABA5.BABA5.BABA6.BABA.GE.EG4.BABA5.ABAB4.2G$38.BA3.BA3.BA7.A
B7.AB7.AB8.AB12.AB7.BA2$9.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D
2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D
2.D2.D2.D2.D2.D2.D2.D$7.135B$6.D$7.135B$9.D2.D2.D2.D2.D2.D2.D2.D2.D2.
D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.
D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D2.D!

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