HighAndLowLife - A variant on the "3-state life" concept

[azulavoir]

Code: Select all

x = 4, y = 3, rule = HighAndLowLife
A$.2B$A2.B$3.B$2.A.A!

@RULE HighAndLowLife

@COLORS
0 0 0 0
1 0 128 128
2 0 255 255

@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a1 = {0, 1, 2}
var a2 = {0, 1, 2}
var a3 = {0, 1, 2}
var a4 = {0, 1, 2}
var a5 = {0, 1, 2}
var a6 = {0, 1, 2}
var a7 = {0, 1, 2}
var a8 = {0, 1, 2}
var b = {0, 1}
var c = {0, 2}
var d = {1, 2}

1, 1, 1, 0, 0, 0, 0, 0, 0, 1
1, 2, 0, 0, 0, 0, 0, 0, 0, 1

b, 1, 1, 1, 0, 0, 0, 0, 0, 1
b, 1, 2, 0, 0, 0, 0, 0, 0, 1

2, 1, 1, 1, 1, 0, 0, 0, 0, 2
2, 1, 1, 2, 0, 0, 0, 0, 0, 2
2, 2, 2, 0, 0, 0, 0, 0, 0, 2

2, 1, 1, 1, 1, 1, 0, 0, 0, 2
2, 1, 1, 1, 2, 0, 0, 0, 0, 2
2, 2, 2, 1, 0, 0, 0, 0, 0, 2

c, 1, 1, 1, 1, 1, 1, 0, 0, 2
c, 1, 1, 1, 1, 2, 0, 0, 0, 2
c, 1, 1, 2, 2, 0, 0, 0, 0, 2
c, 2, 2, 2, 0, 0, 0, 0, 0, 2

2, 1, 1, 1, 1, 1, 1, 1, 0, 2
2, 1, 1, 1, 1, 1, 2, 0, 0, 2
2, 1, 1, 1, 2, 2, 0, 0, 0, 2
2, 1, 2, 2, 2, 0, 0, 0, 0, 2

d, a1, a2, a3, a4, a5, a6, a7, a8, 0

In this rule I thought up, the darker cells run B3/S23, and the lighter cells run B6/S4567 - BUT! The lighter cells count as two cells apiece! This means a single light cell can support a single dark cell by S2, which can lead to wacky little still lives like the one depicted above.

I also found this cute little p3:

Code: Select all

x = 5, y = 5, rule = HighAndLowLife
2.2A$2.A.A$2A.2A$A.A$.2A!

Since the lighter cells require "more neighbors" to stay alive, they tend to die out more readily than the darker cells in soups.

Edit: Here's a p4, too!

Code: Select all

x = 4, y = 5, rule = HighAndLowLife
2.A$.B.A$2.B$.B.A$2.A!

Edit2: removed the ruletable from all but the first RLE codeblock, since someone (Confocaloid, I think) put the ruletable on the wiki for me.

[confocaloid]

Two light gliders hit two dark loaves which are moved and rotated while remaining dark and creating sparks which collide to form a light block:

Code: Select all

x = 23, y = 27, rule = HighAndLowLife
14.A$13.A.A$12.A2.A$13.2A7$21.2B$20.2B$22.B$.B$2.B$3B8$9.2A$8.A2.A$8.
A.A$9.A!

Edit:
The resulting spark evolves for some time before hitting a loaf

Code: Select all

x = 17, y = 26, rule = HighAndLowLife
7.A$6.A.A$5.A2.A$6.2A7$14.2B$14.B.B$.B12.B$2.B$3B8$9.2A$8.A2.A$8.A.A$9.A!

The sparks collide to form a dark glider which hits a loaf

Code: Select all

x = 23, y = 26, rule = HighAndLowLife
14.A$13.A.A$12.A2.A$13.2A7$21.2B$20.2B$.B20.B$2.B$3B8$9.2A$8.A2.A$8.A.A$9.A!
#C [[ T 73 PAUSE 1 ]]

This creates a sideways dark glider but one of two loaves is recreated in a different way

Code: Select all

x = 18, y = 25, rule = HighAndLowLife
9.A$8.A.A$7.A2.A$8.2A6$16.B$15.2B$.B13.B.B$2.B$3B8$9.2A$8.A2.A$8.A.A$9.A!

Edit 2: eight light gliders to two dark gliders

Code: Select all

x = 216, y = 208, rule = HighAndLowLife
B.B$.2B$.B9$51.B$52.B$50.3B8$43.B$44.B$42.3B24$89.A$88.A.A$87.A2.A$
88.2A6$96.B$95.2B$81.B13.B.B$82.B$80.3B8$89.2A$88.A2.A$88.A.A$89.A17$
88.2A$87.A2.A$87.A.A$88.A67$175.3B$175.B$176.B35$213.3B$213.B$214.B8$
205.3B$205.B$206.B!
#C [[ ZOOM 6 X -20 Y -35 ]]

Edit 3: five light gliders to one dark glider

Code: Select all

x = 80, y = 74, rule = HighAndLowLife
B.B$.2B$.B10$43.2A$29.B13.2A$27.B.B$28.2B5$17.B$18.B18.2A$16.3B17.A2.
A$36.A.A$37.A6$26.2A$25.A2.A$25.A.A$26.A4$16.2A$16.2A17$77.2B$77.B.B$
77.B14$59.3B$59.B$60.B!

[azulavoir]

Oh would you look at that, clock is actually relatively common in this rule!

The top 10 most common p2 oscillators according to Catagolue (C1) are:
1. Low blinker
2. High blinker
3. Low toad
4. Low beacon
5. High toad
6. Our first alien oscillator, xp2_hxh_04h4:

Code: Select all

x = 5, y = 5, rule = HighAndLowLife
A.B.A2$.B.B2$A.B.A!

7. High beacon
8. xp2_295_04:

Code: Select all

x = 3, y = 4, rule = HighAndLowLife
.2A$A$.BA$.A!

9: Low bipole
10: Low clock! Which has a 4-cell predecessor:

Code: Select all

x = 4, y = 2, rule = HighAndLowLife
B.A$.A.B!

Interesting that bipole and clock swapped from their vanilla Life orders.

[galoomba]

when the ship is very long

Code: Select all

x = 5, y = 5, rule = HighAndLowLife
4.A$.B$3.B$AB2.A$3.A!

[azulavoir]

Code: Select all

x = 6, y = 6, rule = HighAndLowLife
2A2.2A$A4.A$2.2B$2.2B$A4.A$2A2.2A!

This still life reminds me of the companion cube.

[confocaloid]

p460 alien 3c/11o spaceship factory

Code: Select all

x = 197, y = 194, rule = HighAndLowLife
52.2B10.2B36.2B$51.B2.B8.B2.B17.2B16.B.B$51.3B10.3B17.2B17.B$54.10B9.
B$53.B2.6B2.B8.3B17.2B$53.2B2.4B2.2B11.B6.2B7.B2.2B8.2B$75.2B6.2B6.6B
8.2B$93.4B2$58.2B26.B$49.2B7.2B7.2B6.B5.B2.2B.B$50.B16.B7.B5.5B.B5.4B
$50.B.B12.B.B7.B5.3B2.B4.6B8.2B$51.2B12.2B17.2B6.B2.2B8.2B$71.B5.3B4.
2B7.2B$71.3B$74.B28.B$73.2B27.B.B$102.2B34.2B36.2B10.2B$17.B119.B.B
16.2B17.B2.B2.4B2.B2.B$17.3B43.3B72.B17.2B17.3B2.6B2.3B$8.2B10.B42.B
9.B11.2B65.B2.B12.B9.10B$7.B.B9.2B43.B7.B.B8.B2.B60.B3.B3.3B8.3B8.B
10.B$7.B.B.2B44.B15.2B8.2B2.2B46.2B9.B7.3B.B6.B11.2B8.2B$8.B.B.B43.B.
B26.2B2.B45.2B9.B2.2B4.B.2B6.2B$10.B45.B.B24.2B3.2B57.2B5.2B$10.2B9.
2B8.2B24.B24.B.B63.3B3.2B$10.3B7.B2.B6.B2.B27.2B20.B$10.3B3.2B2.B2.B
7.2B28.B.B.2B81.3B3.2B4.B5.B6.2B16.2B$10.3B3.2B3.2B40.B.B2.B78.2B5.B.
B3.B5.B7.B6.2B8.B$10.3B50.B2.3B9.2B55.2B9.B2.2B5.B3.B5.B7.B.B4.2B6.B.
B$10.2B22.2B26.2B7.B6.B56.2B9.B8.2B18.2B12.2B$10.B23.B3.B29.4B7.3B65.
B3.B10.3B5.B$8.B.B.B22.4B29.B12.B70.B15.3B$7.B.B.2B56.B68.B28.B$7.B.B
9.2B14.2B31.2B67.B.B27.2B$8.2B10.B9.2B3.B.B44.2B36.2B10.2B4.2B$17.3B
10.B.B4.B43.B.B16.2B17.B2.B2.4B2.B2.B$17.B12.B5.2B.2B.B39.B17.2B17.3B
2.6B2.3B$39.B.2B39.2B28.B9.10B23.2B7.B$39.B40.6B3.B20.3B8.B10.B22.B2.
B4.B2.4B$21.2B15.2B39.B2.4B2.B.B10.2B6.B11.2B8.2B20.2B2.2B5.3B17.B$
22.B6.B49.2B4.2B3.B10.2B6.2B41.B2.2B8.B17.B.B$10.2B10.B.B3.B.B55.B2.B
62.2B3.2B24.B.B$11.B11.2B4.2B30.B24.3B68.B.B24.B$11.B.B3.3B39.B.B44.
3B17.2B30.B20.2B$12.2B46.2B24.3B17.3B8.2B6.B2.B6.2B38.2B.B.B$15.B5.B
64.B2.B16.B2.B8.B7.2B7.B37.B2.B.B$15.B5.B15.2B40.2B4.2B3.B17.B9.B.B
12.B.B26.2B9.3B2.B$15.B5.B15.B.B39.B2.4B2.B.B28.2B12.2B28.B6.B7.2B$
39.B40.6B3.B24.B45.3B7.4B$17.3B19.2B41.2B18.B9.3B10.2B33.B12.B$33.B
48.B20.2B6.B12.B.B45.B$12.2B15.2B.B.B46.B.B18.2B7.2B13.B45.2B$8.2B2.
2B16.B.2B48.2B$8.2B18.B2.B$28.2B.B$30.B68.2B11.B$30.B.B66.B2.B8.B.B$
12.3B3.3B10.2B64.2B2.2B8.2B15.B$12.B2.B.B2.B75.B2.2B26.B.B$11.B3.B.B
3.B74.2B3.2B24.B.B$11.4B3.4B79.B.B24.B$12.B7.B81.B20.2B$119.2B.B.B$
117.B2.B.B$106.2B9.3B2.B$107.B6.B7.2B$104.3B7.4B$104.B12.B$116.B$116.
2B$7.2B15.2B$7.B.B13.B.B99.B$8.B15.B100.B.B$12.2B5.2B104.2B$12.2B5.2B
4$23.2B5.2B$23.2B5.2B$19.B15.B$18.B.B13.B.B$18.2B4.B5.B4.2B$23.3B3.3B
$22.2B2.B.B2.2B$22.B3.B.B3.B$22.B.2B3.2B.B$22.2B7.2B4$100.2A$99.A.A$
100.A$188.A$42.2B144.A$41.B.B146.A3.2A$41.B150.A3.A$39.2B.B141.2A5.A
4.A$19.2B11.B6.B2.B81.B67.A3.A$19.2B2.2B8.2B6.B.2B80.B64.A3.2A$23.2B
7.2B6.2B.B.B77.3B62.A$44.B143.A$50.2B$50.B71.2A$29.3B16.B.B71.A.A58.
2B5.2B$29.B18.2B73.A59.2B5.2B$29.B.B147.B15.B$23.2B6.B146.B.B13.B.B$
22.B.B5.B147.2B15.2B$22.B11.2B4.2B$21.2B10.B.B3.B.B141.3B3.3B$33.B6.B
141.B2.B3.B2.B$32.2B15.2B131.2B.B3.B.2B$50.B$50.B.2B$28.B18.2B.2B.B$
28.3B17.B$19.2B10.B14.B.B$18.B.B9.2B14.2B$18.B.B.2B$19.B.B.B22.4B$21.
B13.B9.B3.B121.2B$21.2B12.B.B7.2B124.B.B$21.3B5.2B4.2B56.2B78.B$21.3B
5.2B63.2B76.B.2B6.B$21.3B18.2B49.B78.B2.B5.B12.2B$21.3B17.B2.B70.2B
53.2B.B7.3B6.2B2.2B$21.2B19.2B71.B53.B.B.2B15.2B$21.B81.B12.B53.B$19.
B.B.B79.3B7.4B46.2B$18.B.B.2B82.B6.B7.2B41.B$18.B.B9.2B73.2B9.3B2.B
42.B.B15.3B$19.2B10.B84.B2.B.B43.2B16.2B$5.2B5.2B14.3B78.B3.2B3.2B.B.
B58.B$5.2B5.2B14.B72.B7.B3.B.B6.2B61.B4.2B$.B15.B82.B.B5.B6.B11.B57.B
4.B.B$B.B13.B.B76.2B3.2B12.2B10.B.B44.2B4.2B4.B6.B$2B15.2B76.B2.2B26.
B.B44.B.B3.B.B10.2B$5.3B3.3B82.2B2.2B8.2B15.B46.B6.B$5.B2.B.B2.B84.B
2.B8.B.B51.2B15.2B$4.B3.B.B3.B83.2B11.B52.B$4.4B3.4B90.B55.2B.B$5.B7.
B91.B55.B.2B.2B18.B$81.2B83.B17.3B$80.B.B20.B6.2B54.B.B14.B10.2B$81.B
28.B56.2B14.2B9.B.B$111.3B77.2B.B.B$87.3B23.B51.4B8.B13.B.B.B$78.2B5.
B4.B15.B11.2B12.2B31.B3.B8.2B13.B$78.2B5.B5.B14.B10.B.B12.B.B33.2B7.
2B12.B2.B$24.2B64.B14.3B9.B16.B51.B7.B$23.B.B62.2B26.2B7.2B7.2B49.B.B
2.B3.B$23.B101.2B33.2B9.2B12.B.B2.B3.B$21.2B.B63.2B69.2B9.B2.B12.B7.B
$.2B12.B5.B2.B65.B70.B9.2B18.B2.B$.2B2.2B6.B.B7.B.2B51.2B5.B5.B8.2B6.
2B83.B$5.2B7.2B6.2B.B.B50.2B5.B4.B9.2B6.B11.2B8.2B59.B.B.B$23.B2.B60.
3B19.3B8.B10.B59.2B.B.B$23.B2.B5.2B77.B9.10B52.2B9.B.B$13.B8.B9.B48.B
17.2B17.3B2.6B2.3B49.B10.2B$12.B9.B3.B2.2B.B47.B.B16.2B17.B2.B2.4B2.B
2.B50.3B$11.2B7.2B5.B3.B49.2B36.2B10.2B53.B$12.2B5.B4.B$5.2B6.B5.B3.B
.B$4.B.B4.B7.B4.B4.B$4.B6.B4.2B2.2B5.2B$3.2B10.B.B4.B3.B$15.B6.B3.B$
14.2B7.3B5.2B$32.B$32.B.2B$10.B18.2B.2B.B$10.3B17.B$.2B10.B14.B.B$B.B
9.2B14.2B$B.B.2B$.B.B.B22.4B$3.B23.B3.B$2.B2.B21.2B$2.B$2.B3.B2.2B$2.
B3.B2.2B13.2B$2.B20.B2.B$2.B2.B18.2B$3.B$.B.B.B$B.B.2B$B.B9.2B$.2B10.
B$10.3B$10.B!
#C [[ MAXGRIDSIZE 9 ]]

Edit: the gliders interact:

Code: Select all

#C https://catagolue.hatsya.com/object/xq4_235_y1ocg/x10x7x4xhighandlowlife
x = 8, y = 5, rule = HighAndLowLife
.2A$2A$2.A3.B$5.2B$5.B.B!

Code: Select all

x = 40, y = 24, rule = HighAndLowLife
7.2B$8.B$8.B.B$9.2B2$37.2A$37.A.A$30.2B5.A$30.2B2$9.B$9.B.B$9.3B$11.B
5$2.2B$3.B$3B$B$20.2B$20.2B!

[qqd]

I tried making a hybrid catalyst, but this is the only working one I found, and not much useful:

Code: Select all

x = 9, y = 14, rule = HighAndLowLife
B$3B$3.B3.2A$2.2B3.2A7$B$B.B$3B$2.B!

I also found this one, but this almost always fails in practice:

Code: Select all

x = 8, y = 7, rule = HighAndLowLife
6.2B$6.2B$5.A$2B$2.B$.B2.2A$4.2A!

[azulavoir]

p460 alien 3c/11o spaceship factory

Code: Select all

rle snipped

I believe I proposed calling this the Eurekaship, so here we have a Eurekagun!

Edit: Here's a silly cis-loaf-with-tail 5-predecessor.

Code: Select all

x = 5, y = 8, rule = HighAndLowLife
$.A$2A2$3.2A$2.B$2.B$2.A!

[confocaloid]

A soup-based dark synthesis for a 20-bit still life

Code: Select all

x = 69, y = 69, rule = HighAndLowLife
7.A$8.A$6.3A$67.A$66.A$66.3A3$51.A$50.A$50.3A$.A$2.A$3A8$61.A$61.A.A$
61.2A9$58.2A$58.A.A$58.A21$52.3A$52.A$53.A$14.3A$16.A$15.A6$8.3A$10.A
$9.A!

Soup:

Code: Select all

#C https://catagolue.hatsya.com/hashsoup/C1/k_tHeDzcuk5LyH1368746/x10x7x4xhighandlowlife
#C Soup k_tHeDzcuk5LyH1368746 was found on 2023-10-24 at 06:58:03 UTC and is owned by JMM
x = 16, y = 16, rule = HighAndLowLife
obbbbooobboboooo$
bboobboobbbbobbb$
boooboobobobbobb$
obobbooobbbboobo$
booboobbbobbbobo$
booobbooobbboobo$
bbbbobooooobbobo$
bobooboboooooboo$
bbbobbooobbbbbbo$
oobobboooooobbbb$
obooobboobbboooo$
bboooooooobooooo$
oobooobooooooobo$
oooboobbbooooobo$
bobbboobobbboboo$
ooboobbooobbbbob!

[azulavoir]

Now I wonder if it's possible to make a pi-ship in this rule?

It kind of looks like it moves down slowly while it becomes the familiar three of low blinker/high blinker/low blinker.

[qqd]

You just need three cells to make a low glider:

Code: Select all

x = 2, y = 3, rule = HighAndLowLife
A$B$.A!

Probably the 3-cell pattern which has the highest population when it settles:

Code: Select all

x = 2, y = 4, rule = HighAndLowLife
A2$.B$.A!

And probably the 4-cell highest population when settled:

Code: Select all

x = 3, y = 3, rule = HighAndLowLife
B.A$B$.A!