The rule which inspired this thread is known as Termitic Life without Death (TermiticLWOD). I had the idea for a CA based off of a rule with S0...8 but where decay caused by B8 puts a stop to chaotic infinite growth, and the resulting table has a body section consisting of just 6 lines.
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@RULE TermiticLWOD
rabbit, 2025-10-12
If a State 0 cell is surrounded by three State 1 cells and five State 0 cells, it becomes a State 1 cell.
If a State 0 cell is surrounded by eight State 1 cells, it becomes a State 2 termite.
A State 2 termite becomes State 3 no matter what.
A State 3 termite becomes State 4 no matter what.
A State 4 termite becomes State 0.
Any State 1 cell with at least one State 0 neighbour and one State 4 termite neighbour becomes a State 2 termite itself.
The resulting rule has quite interesting dynamics, and two very high period oscillators at p192 and p1876.
It also features common spaceships at many velocities, including 4c/12, 6c/14, c/3 diagonal, and (2, 1)c/6.
https://conwaylife.com/forums/viewtopic.php?f=11&t=7076#p219647
@TABLE
n_states:5
neighborhood:Moore
symmetries:permute
var a1 = {0, 1, 2, 3, 4}
var a2 = a1
var a3 = a1
var a4 = a1
var a5 = a1
var a6 = a1
var a7 = a1
var a8 = a1
0, 1, 1, 1, 0, 0, 0, 0, 0,1
0, 1, 1, 1, 1, 1, 1, 1, 1,2
1, 4,a1,a2,a3,a4,a5,a6, 0,2
2,a1,a2,a3,a4,a5,a6,a7,a8,3
3,a1,a2,a3,a4,a5,a6,a7,a8,4
4,a1,a2,a3,a4,a5,a6,a7,a8,0
@COLORS
1 255 255 255
2 255 255 0
3 160 160 0
4 96 96 0
@NAMES
1 Alive
2 TermiteS2
3 TermiteS3
4 TermiteS4
@ICONS
XPM
"7 28 2 1"
". c #000000"
"A c #FFFFFF"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AA.A.AA"
"AAAAAAA"
"A.AAA.A"
"AA...AA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AA.A.AA"
"AAAAAAA"
"A.....A"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AA.A.AA"
"AAAAAAA"
"AA...AA"
"A.AAA.A"
"AAAAAAA"Code: Select all
x = 84, y = 52, rule = TermiticLWOD
.B2A7.BA11.B21.A8.A20.D$B3A7.BA11.B2A9.D3A5.B3A5.B3A20.B$.BA8.B7.A4.B
2A5.BA.2D.3A5.3A6.3A4.B7.B7.B2A$5.BA4.B2A4.B2A3.B3A4.2A.2D4A4.B4A4.B
4A4.2A6.2A5.B2A$5.BA4.B2A4.B3A.2B3A4.BA2.D4A4.5A4.4A4.B2A5.B2A4.B5A$
6.A5.A6.BA2.2B.2A8.D2A6.2A7.2A6.B2A5.B2A3.C7A$5.B2A3.BA11.BA10.D2A6.B
A7.BA6.B7.B5.CAD4A$5.B2A3.BA23.D25.BA6.BA5.C2A.A$5.B56.B7.BA6.2A$5.BA
55.B2A5.B$5.BA55.B2A5.B2A$63.2A5.B2A$62.B8.2A$70.B7$C6.C$CA5.C$.2A$BA
5.C2A$3A5.3A$B2A4.C3A$.A5.C3A$7.C.A$7.CA$8.2A$7.BA$7.3A$7.B2A$8.A7$B
2C3.C.C3.3C5.CB3.BCB3.B9.CA$C3A3.ABA3.3A3.2C2A2.B3A3.A2B6.CA2.B$C3A2.
CB2A2.CB2A3.B2A3.B2A4.B3A5.C2A2.A2B$.2A4.2A4.2A5.A5.A5.B2A7.2A2.B3A$
33.A7.C.A2.B2A$41.CA4.A$41.C2A$38.C.C.A$39.ACA$39.C3A$39.C3A$40.2A!
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x = 320, y = 54, rule = TermiticLWOD
114.A119.A$112.5A115.5A$112.5A115.5A$112.5A115.5A$113.DAD117.DAD57.2A
$102.2A.2D115.2A.2D58.2A4.5A$102.3D117.3D58.4A3.B.BAB$104.D119.D57.4A
B$283.2BA4$50.A119.A59.A59.A25.A$49.3A.B115.3A.B55.3A.B55.3A.B8.A12.B
2A$49.3AB73.A.A.A.A36.3AB56.3AB13.A.A.A.A36.3AB7.2A2B11.B2A$48.5A71.
2A6C4A32.5A55.5A11.2A6C4A32.5A5.3A.B12.4A$48.4A2B70.3A5.C3A32.4A2B54.
4A2B10.3A5.C3A32.4A2B4.3AB14.B2A$49.2A.2B67.3AC2A5.C2A34.2A.2B55.2A.
2B7.3AC2A5.C2A34.2A.2B4.4A$51.AB68.3AC2.C3.3C2A35.AB14.2A42.AB8.3AC2.
C3.3C2A35.AB6.2A2B4.2A$121.3AC6.C2.CA50.5A50.3AC6.C2.CA42.2A3B3.5A$
122.2A10.C.A49.6A50.2A10.C.A27.B14.2AB4.6A5.B$133.2C2A48.A.4A62.2C2A
26.A2B2.2B9.2AB3.A.4A7.A$134.C3A47.3BAB64.C3A26.A.BA4B13.3BAB7.BA$
104.D2.2D.D23.C2A49.2B2.B33.D2.2D.D23.C2A27.5AB2A14.2B2.B6.3A$105.DAD
3.D113.DAD3.D16.A36.7A25.B2A$103.4AD.D113.4AD.D17.4A34.3A.A28.A$102.
7A113.7A18.4A$103.4A116.4A18.7A$103.4A116.4A17.D.D4A24.A28.A.3A$105.A
119.A16.D3.DAD25.2AB25.7A$163.B2.2B49.2AC23.D.2D2.D24.3A6.B2.2B14.2AB
5A$164.BA3B47.3AC55.AB7.BA3B13.4BAB.A$163.4A.A48.2A2C54.A7.4A.A3.B2A
9.2B2.2BA$162.6A49.A.C10.2A44.B5.6A4.B2A14.B$163.5A50.AC2.C6.C3A50.5A
3.3B2A$.BA58.BA58.BA42.2A14.BA35.2A3C3.C2.C3A8.BA42.2A4.2B2A6.BA$2B.
2A55.2B.2A55.2B.2A55.2B.2A34.2AC5.2AC3A7.2B.2A47.4A4.2B.2A$2B4A54.2B
4A54.2B4A54.2B4A32.3AC5.3A10.2B4A29.2AB14.B3A4.2B4A$.5A55.5A55.5A55.
5A32.4A6C2A11.5A29.4A12.B.3A5.5A$.B3A56.B3A56.B3A56.B3A36.A.A.A.A13.B
3A31.2AB11.2B2A7.B3A$B.3A55.B.3A55.B.3A55.B.3A55.B.3A31.2AB12.A8.B.3A
$3.A59.A59.A59.A59.A33.A25.A4$308.A2B$249.D57.B4A$249.3D47.BAB.B3.4A$
247.2D.2A46.5A4.2A$238.DAD58.2A$237.5A$237.5A$237.5A$239.A!
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x = 54, y = 30, rule = TermiticLWOD
48.2C2.C$47.3CAC$47.A.5A$2.A44.7A$.3A44.6A$6A42.3A$.3AB.B$2.BAB3.B$.B
2.2B.B15$22.DA.2A$23.5A$22.D5A$21.D6A$22.D2A$22.D2A$21.DA!
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x = 225, y = 46, rule = TermiticLWOD
3.2A130.B$.5A130.B2A$.4A130.BAB.2A$5AC129.2B.B3A$3A2BC132.4A$.A.B121.
B12.B2A24.3A$3.B121.D12.B2A21.2A.4A$124.D14.A19.10A$124.D34.4AD5A$
160.7A$159.6A3D54.B2A$158.3AD2.D57.B2A$159.2A60.2B2A$222.B$222.B$120.
B.BD78.A$121.B2A77.3A$121.2A3D2A72.4AC$121.A.5A73.4A$122.5A75.3A16.BA
$122.5A75.2A2C13.3BA$123.2A79.2A14.2A$220.B2A$220.B2A11$133.D$134.A$
133.DA.A$132.D5A$133.D4A$133.D3A60.3A$133.4A59.B3A$133.2A59.C5A$194.C
3A$193.5A$193.3A$193.3A!
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x = 32, y = 12, rule = TermiticLWOD
A.2A17.4A2.B$.5A.D12.6A2.A2B$6A2.A2D9.6A2.B3A$7A.D3A8.6A2.B2A$.6A.D3A
8.6A3.A$.6A2.3A9.4A$3.3A20.D$.D18.B6.A2D$2.A2D16.A2B3.D3A$2.D3A15.B3A
2.D3A$2.D3A15.B2A4.3A$3.3A16.A!
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x = 10, y = 10, rule = TermiticLWOD
2A$2.A$3.A$3.A$4.2A$5.A$6.A$7.2A$8.A$9.A!
There are also p4 oscillators with a termite rapidly being born and dying in the center:
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x = 7, y = 7, rule = TermiticLWOD
3.A$.5A$.5A$3A.3A$.5A$.5A$3.A!
I have devised a second simple ruletable in this theme as well, but I will have to do further research on it. I would be delighted if other users provide their own simple ruletables for exploration.