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Three-state outer-totalistic von Neumann rules

https://conwaylife.com/forums/viewtopic.php?t=7086

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Three-state outer-totalistic von Neumann rules

Posted: October 24th, 2025, 4:04 pm
by hibiscus
I've been investigating the rules in this space for a little bit now (and I would certainly like a better place for centralized discussion than my personal thread in the Sandbox).

Some of the objects I've found in this space (which has 3^45 rules, by the way):
5c/29o:

Code: Select all

x = 5, y = 7, rule = OTVN3-021010000000112-010000000000000-010001000100000
5A2$2.A2$2.A$A3.A$2.A!
@RULE OTVN3-021010000000112-010000000000000-010001000100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a = 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,2,0,1
0,2,2,2,2,2
0,1,2,2,2,1
0,1,1,1,1,1
1,1,0,0,0,1
2,1,0,0,0,1
2,2,2,0,0,1
2,2,0,0,0,1
a,b,c,d,e,0
p79:

Code: Select all

x = 15, y = 13, rule = OTVN3-021000020000122-010000020000000-010001020100000
2A11.2A12$2A11.2A!
@RULE OTVN3-021000020000122-010000020000000-010001020100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a = 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,2,0,1
0,2,2,2,2,2
0,1,2,2,2,2
0,1,1,2,0,2
1,1,0,0,0,1
1,1,1,2,0,2
2,1,0,0,0,1
2,2,2,0,0,1
2,2,0,0,0,1
2,1,1,2,0,2
a,b,c,d,e,0
3c/10d in Roommates (OTVN3-001001000000000-002002000000000-002002000000000):

Code: Select all

x = 9, y = 9, rule = Roommates
.ABA3$A3.A$2B3.A$8.A$8.B$4.B3.A$4.BA!
Some objects found by other users include this c/6o in "vNtest" (OTVN3-001201020020200-002120012012121-220222022022222):
pifricted wrote: July 27th, 2024, 6:21 am

Code: Select all

#c/6o
x = 7, y = 3, rule = vNtest
3.B$A5BA$2.3B!
@RULE vNtest
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a={0,1,2}
var s=a
var d=a
var f=a
var q={1,2}
var w=q
var e=q
var r=q
0,2,0,0,0,1
0,1,1,0,0,1
1,1,1,0,0,2
a,q,w,e,a,2
q,w,e,0,0,0
1,a,0,0,0,0
The notation I've been using to describe these rules isn't that great - it's just a list of the 45 unique transitions, packed into 15 conditions for all 3 states and separated by hyphens. Each set of 15 is the set of transition rules for a particular state.

Edit (2025/12/16 16:19): underscores changed to hyphens to allow rules to be uploaded to LifeWiki.

Re: Three-state outer-totalistic von Neumann rules

Posted: October 24th, 2025, 10:46 pm
by Citation needed
Here is a template for this graded rule space.

Code: Select all

x = 0, y = 0, rule = OTVN3GBT-template
!
@RULE OTVN3GBT-template

Hibiscus's OTVN3 Rulespace Graded By Transition

(Compare [[Rule:LGBT|Life Graded By Transition]], which doesn't grade dead cells)

@TABLE

n_states:49
neighborhood:vonNeumann
symmetries:permute

#C Distribute the numbers 1 through 45 between these three sets
var offq={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
var oneq={16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}
var twoq={31,32,33,34,35,36,37,38,39,40,41,42,43,44,45}

var offp={48,offq}
var off={0,offp}
var one={46,oneq}
var two={47,twoq}

var off1=off
var off2=off
var off3=off
var off4=off

var one1=one
var one2=one
var one3=one
var one4=one

var two1=two
var two2=two
var two3=two
var two4=two

offp,off1,off2,off3,off4,1
off,off1,off2,off3,one4,2
off,off1,off2,off3,two4,3
off,off1,off2,one3,one4,4
off,off1,off2,one3,two4,5
off,off1,off2,two3,two4,6
off,off1,one2,one3,one4,7
off,off1,one2,one3,two4,8
off,off1,one2,two3,two4,9
off,off1,two2,two3,two4,10
off,one1,one2,one3,one4,11
off,one1,one2,one3,two4,12
off,one1,one2,two3,two4,13
off,one1,two2,two3,two4,14
off,two1,two2,two3,two4,15

one,off1,off2,off3,off4,16
one,off1,off2,off3,one4,17
one,off1,off2,off3,two4,18
one,off1,off2,one3,one4,19
one,off1,off2,one3,two4,20
one,off1,off2,two3,two4,21
one,off1,one2,one3,one4,22
one,off1,one2,one3,two4,23
one,off1,one2,two3,two4,24
one,off1,two2,two3,two4,25
one,one1,one2,one3,one4,26
one,one1,one2,one3,two4,27
one,one1,one2,two3,two4,28
one,one1,two2,two3,two4,29
one,two1,two2,two3,two4,30

two,off1,off2,off3,off4,31
two,off1,off2,off3,one4,32
two,off1,off2,off3,two4,33
two,off1,off2,one3,one4,34
two,off1,off2,one3,two4,35
two,off1,off2,two3,two4,36
two,off1,one2,one3,one4,37
two,off1,one2,one3,two4,38
two,off1,one2,two3,two4,39
two,off1,two2,two3,two4,40
two,one1,one2,one3,one4,41
two,one1,one2,one3,two4,42
two,one1,one2,two3,two4,43
two,one1,two2,two3,two4,44
two,two1,two2,two3,two4,45

@ICONS
XPM

"7 315 14 1"

". c #000000"
"D c #F4592D"
"E c #EDA667"
"F c #FAF03E"
"G c #5FB319"
"H c #8EEDE2"
"I c #0568E3"
"J c #49207C"
"K c #FF00FF"
"S c #333333"
"T c #666666"
"U c #999999"
"V c #CCCCCC"
"W c #FFFFFF"

"FFFFFFF"
"FWFFFFF"
"FWFFFFF"
"FWWWWFF"
"FWFFFWF"
"FWWWWFF"
"FFFFFFF"

"FFFFFFF"
"FVVVVFF"
"FVFFFVF"
"FVVVVFF"
"FVFFFFF"
"FVFFFFF"
"FFFFFFF"

"FFFFFFF"
"FFTFTFF"
"FTFTFTF"
"FTFTFTF"
"FTFTFTF"
"FTFFFTF"
"FFFFFFF"

"FFFFFFF"
"FUFFFUF"
"FUFUFUF"
"FUFUFUF"
"FUFUFUF"
"FFUFUFF"
"FFFFFFF"

"DDDDDDD"
"DDDDDWD"
"DDDDDWD"
"DDDDDWD"
"DDDDDWD"
"DWWWWDD"
"DDDDDDD"

"DDDDDDD"
"DDVVVDD"
"DVDDDVD"
"DVDVDVD"
"DVDDVDD"
"DDVVDVD"
"DDDDDDD"

"DDDDDDD"
"DVDDDVD"
"DDVDVDD"
"DDDVDDD"
"DDVDVDD"
"DVDDDVD"
"DDDDDDD"

"DDDDDDD"
"DUDDDUD"
"DDUDUDD"
"DDDUDDD"
"DDDUDDD"
"DDDUDDD"
"DDDDDDD"

"DDDDDDD"
"DTTTTDD"
"DTDDDTD"
"DTDDDTD"
"DTDDDTD"
"DTDDDTD"
"DDDDDDD"

"JJJJJJJ"
"JWWWWWJ"
"JJJJWJJ"
"JJJWJJJ"
"JJWJJJJ"
"JWWWWWJ"
"JJJJJJJ"

"JJJJJJJ"
"JVVVVVJ"
"JJJJJVJ"
"JJVVVJJ"
"JVJJJJJ"
"JJVVVVJ"
"JJJJJJJ"

"JJJJJJJ"
"JJVVVVJ"
"JVJJJJJ"
"JJVVVJJ"
"JJJJJVJ"
"JVVVVJJ"
"JJJJJJJ"

"JJJJJJJ"
"JUUUUJJ"
"JUJJJUJ"
"JUUUUJJ"
"JUJJJUJ"
"JUJJJUJ"
"JJJJJJJ"

"JJJJJJJ"
"JTJJJJJ"
"JTJJJJJ"
"JTTTTTJ"
"JTJJJJJ"
"JTJJJJJ"
"JJJJJJJ"

"GGGGGGG"
"GGGGGTG"
"GGGGGTG"
"GTTTTTG"
"GTGGGGG"
"GTGGGGG"
"GGGGGGG"

"GGGGGGG"
"GTGGGGG"
"GTGGGGG"
"GTGGGGG"
"GTGGGGG"
"GGTTTTG"
"GGGGGGG"

"GGGGGGG"
"GWWWWGG"
"GGWGGWG"
"GGWGGWG"
"GGWGGWG"
"GWWWWGG"
"GGGGGGG"

"GGGGGGG"
"GVVVVVG"
"GGGVGGG"
"GGGVGGG"
"GGGVGGG"
"GGGVGGG"
"GGGGGGG"

"GGGGGGG"
"GGWWWGG"
"GWGGGGG"
"GWGGWWG"
"GWGGGWG"
"GGWWWGG"
"GGGGGGG"

"GGGGGGG"
"GVGGGVG"
"GVGGVGG"
"GVVVGGG"
"GVGGVGG"
"GVGGGVG"
"GGGGGGG"

"GGGGGGG"
"GVGGGVG"
"GVGGGVG"
"GVVVVVG"
"GVGGGVG"
"GVGGGVG"
"GGGGGGG"

"GGGGGGG"
"GGGGUGG"
"GGGUUGG"
"GGUGUGG"
"GUUUUUG"
"GGGGUGG"
"GGGGGGG"

"EEEEEEE"
"ETEEEEE"
"ETEEEEE"
"ETTTTTE"
"EEEEETE"
"EEEEETE"
"EEEEEEE"

"EEEEEEE"
"ETEEETE"
"ETEEETE"
"EETETEE"
"EETETEE"
"EEETEEE"
"EEEEEEE"

"EEEEEEE"
"EWWWWWE"
"EEEEEWE"
"EEWWWWE"
"EEEEEWE"
"EEEEEWE"
"EEEEEEE"

"EEEEEEE"
"EVVVVEE"
"EEEEEVE"
"EEEEEVE"
"EEEEEVE"
"EEEEEVE"
"EEEEEEE"

"EEEEEEE"
"EWWWWEE"
"EWEEEWE"
"EWWWWEE"
"EWEEEWE"
"EWWWWEE"
"EEEEEEE"

"EEEEEEE"
"EEVVVVE"
"EVEEEEE"
"EVEEEEE"
"EVEEEEE"
"EEVVVVE"
"EEEEEEE"

"EEEEEEE"
"EVVVVVE"
"EVFFFFE"
"EVVVVFE"
"EVFFFFE"
"EVFFFFE"
"EEEEEEE"

"EIEIEIE"
"IUIEIUI"
"EUEIEUE"
"IUIEIUI"
"EUEIEUE"
"IEUUUEI"
"EIEIEIE"

"IIIIIII"
"IIDDDII"
"IDIIIDI"
"IDIIIDI"
"IDDDDDI"
"IDIIIDI"
"IIIIIII"

"IIIIIII"
"IIFFFII"
"IFIIIFI"
"IFIIIFI"
"IFIIIFI"
"IIFFFII"
"IIIIIII"

"IIIIIII"
"IIGGGII"
"IGIIIGI"
"IGGGGGI"
"IGIIIII"
"IIGGGII"
"IIIIIII"

"IIIIIII"
"IIUUUUI"
"IUIIIII"
"IIUUUII"
"IUIIIII"
"IIUUUUI"
"IIIIIII"

"IIIIIII"
"IEIIIEI"
"IEEEEEI"
"IEIIIEI"
"IEIIIEI"
"IIEEEII"
"IIIIIII"

"HHHHHHH"
"HGGHGGH"
"HHHGHHH"
"HHGHGHH"
"HGHHHGH"
"HHGGGHH"
"HHHHHHH"

"HHHHHHH"
"HFFFHHH"
"HHHHFHH"
"HHHFHFH"
"HHFHHFH"
"HFHHHFH"
"HHHHHHH"

"HHHHHHH"
"HHEEEHH"
"HEHHHHH"
"HEEEEHH"
"HEHHHEH"
"HHEEEHH"
"HHHHHHH"

"HHHHHHH"
"HHTTTHH"
"HHHHHTH"
"HTTTTTH"
"HTHHHTH"
"HHTTTHH"
"HHHHHHH"

"HHHHHHH"
"HHTTTHH"
"HTHHHTH"
"HTTTTTH"
"HTHHHTH"
"HHTTTHH"
"HHHHHHH"

"HHHHHHH"
"HHTTTTH"
"HTHHHTH"
"HHTTTTH"
"HTHHHTH"
"HHTTTTH"
"HHHHHHH"

"HHHHHHH"
"HTTTTHH"
"HHHHHTH"
"HHTTTHH"
"HHHHHTH"
"HTTTTHH"
"HHHHHHH"

"HHHHHHH"
"HHHUHHH"
"HHHUHHH"
"HHHUHHH"
"HHUHUHH"
"HUHHHUH"
"HHHHHHH"

"IIIIIII"
"IIIJIII"
"IIJJIII"
"IIIJIII"
"IIIJIII"
"IIIJIII"
"IIIIIII"

"DIDIDID"
"IUUUUUI"
"DIDUDID"
"IDIUIDI"
"DIDUDID"
"IUUUUUI"
"DIDIDID"
Here is a Python script that generates such rules.

Code: Select all

#C Distribute the numbers 1 through 45 between these three sets

offq=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
oneq=[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
twoq=[31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]

print("""@RULE OTVN3GBT-template

Hibiscus's OTVN3 Rulespace Graded By Transition

(Compare [[Rule:LGBT|Life Graded By Transition]], which doesn't grade dead cells)

@TABLE

n_states:49
neighborhood:vonNeumann
symmetries:permute""")

print("var offq={",','.join([str(k)for k in offq]),end="}\n")
print("var oneq={",','.join([str(k)for k in oneq]),end="}\n")
print("var twoq={",','.join([str(k)for k in twoq]),end="}\n")

print("""var offp={48,offq}
var off={0,offp}
var one={46,oneq}
var two={47,twoq}

var off1=off
var off2=off
var off3=off
var off4=off

var one1=one
var one2=one
var one3=one
var one4=one

var two1=two
var two2=two
var two3=two
var two4=two

offp,off1,off2,off3,off4,1
off,off1,off2,off3,one4,2
off,off1,off2,off3,two4,3
off,off1,off2,one3,one4,4
off,off1,off2,one3,two4,5
off,off1,off2,two3,two4,6
off,off1,one2,one3,one4,7
off,off1,one2,one3,two4,8
off,off1,one2,two3,two4,9
off,off1,two2,two3,two4,10
off,one1,one2,one3,one4,11
off,one1,one2,one3,two4,12
off,one1,one2,two3,two4,13
off,one1,two2,two3,two4,14
off,two1,two2,two3,two4,15

one,off1,off2,off3,off4,16
one,off1,off2,off3,one4,17
one,off1,off2,off3,two4,18
one,off1,off2,one3,one4,19
one,off1,off2,one3,two4,20
one,off1,off2,two3,two4,21
one,off1,one2,one3,one4,22
one,off1,one2,one3,two4,23
one,off1,one2,two3,two4,24
one,off1,two2,two3,two4,25
one,one1,one2,one3,one4,26
one,one1,one2,one3,two4,27
one,one1,one2,two3,two4,28
one,one1,two2,two3,two4,29
one,two1,two2,two3,two4,30

two,off1,off2,off3,off4,31
two,off1,off2,off3,one4,32
two,off1,off2,off3,two4,33
two,off1,off2,one3,one4,34
two,off1,off2,one3,two4,35
two,off1,off2,two3,two4,36
two,off1,one2,one3,one4,37
two,off1,one2,one3,two4,38
two,off1,one2,two3,two4,39
two,off1,two2,two3,two4,40
two,one1,one2,one3,one4,41
two,one1,one2,one3,two4,42
two,one1,one2,two3,two4,43
two,one1,two2,two3,two4,44
two,two1,two2,two3,two4,45

@ICONS
XPM

"7 315 14 1"

". c #000000"
"D c #F4592D"
"E c #EDA667"
"F c #FAF03E"
"G c #5FB319"
"H c #8EEDE2"
"I c #0568E3"
"J c #49207C"
"K c #FF00FF"
"S c #333333"
"T c #666666"
"U c #999999"
"V c #CCCCCC"
"W c #FFFFFF"

"FFFFFFF"
"FWFFFFF"
"FWFFFFF"
"FWWWWFF"
"FWFFFWF"
"FWWWWFF"
"FFFFFFF"

"FFFFFFF"
"FVVVVFF"
"FVFFFVF"
"FVVVVFF"
"FVFFFFF"
"FVFFFFF"
"FFFFFFF"

"FFFFFFF"
"FFTFTFF"
"FTFTFTF"
"FTFTFTF"
"FTFTFTF"
"FTFFFTF"
"FFFFFFF"

"FFFFFFF"
"FUFFFUF"
"FUFUFUF"
"FUFUFUF"
"FUFUFUF"
"FFUFUFF"
"FFFFFFF"

"DDDDDDD"
"DDDDDWD"
"DDDDDWD"
"DDDDDWD"
"DDDDDWD"
"DWWWWDD"
"DDDDDDD"

"DDDDDDD"
"DDVVVDD"
"DVDDDVD"
"DVDVDVD"
"DVDDVDD"
"DDVVDVD"
"DDDDDDD"

"DDDDDDD"
"DVDDDVD"
"DDVDVDD"
"DDDVDDD"
"DDVDVDD"
"DVDDDVD"
"DDDDDDD"

"DDDDDDD"
"DUDDDUD"
"DDUDUDD"
"DDDUDDD"
"DDDUDDD"
"DDDUDDD"
"DDDDDDD"

"DDDDDDD"
"DTTTTDD"
"DTDDDTD"
"DTDDDTD"
"DTDDDTD"
"DTDDDTD"
"DDDDDDD"

"JJJJJJJ"
"JWWWWWJ"
"JJJJWJJ"
"JJJWJJJ"
"JJWJJJJ"
"JWWWWWJ"
"JJJJJJJ"

"JJJJJJJ"
"JVVVVVJ"
"JJJJJVJ"
"JJVVVJJ"
"JVJJJJJ"
"JJVVVVJ"
"JJJJJJJ"

"JJJJJJJ"
"JJVVVVJ"
"JVJJJJJ"
"JJVVVJJ"
"JJJJJVJ"
"JVVVVJJ"
"JJJJJJJ"

"JJJJJJJ"
"JUUUUJJ"
"JUJJJUJ"
"JUUUUJJ"
"JUJJJUJ"
"JUJJJUJ"
"JJJJJJJ"

"JJJJJJJ"
"JTJJJJJ"
"JTJJJJJ"
"JTTTTTJ"
"JTJJJJJ"
"JTJJJJJ"
"JJJJJJJ"

"GGGGGGG"
"GGGGGTG"
"GGGGGTG"
"GTTTTTG"
"GTGGGGG"
"GTGGGGG"
"GGGGGGG"

"GGGGGGG"
"GTGGGGG"
"GTGGGGG"
"GTGGGGG"
"GTGGGGG"
"GGTTTTG"
"GGGGGGG"

"GGGGGGG"
"GWWWWGG"
"GGWGGWG"
"GGWGGWG"
"GGWGGWG"
"GWWWWGG"
"GGGGGGG"

"GGGGGGG"
"GVVVVVG"
"GGGVGGG"
"GGGVGGG"
"GGGVGGG"
"GGGVGGG"
"GGGGGGG"

"GGGGGGG"
"GGWWWGG"
"GWGGGGG"
"GWGGWWG"
"GWGGGWG"
"GGWWWGG"
"GGGGGGG"

"GGGGGGG"
"GVGGGVG"
"GVGGVGG"
"GVVVGGG"
"GVGGVGG"
"GVGGGVG"
"GGGGGGG"

"GGGGGGG"
"GVGGGVG"
"GVGGGVG"
"GVVVVVG"
"GVGGGVG"
"GVGGGVG"
"GGGGGGG"

"GGGGGGG"
"GGGGUGG"
"GGGUUGG"
"GGUGUGG"
"GUUUUUG"
"GGGGUGG"
"GGGGGGG"

"EEEEEEE"
"ETEEEEE"
"ETEEEEE"
"ETTTTTE"
"EEEEETE"
"EEEEETE"
"EEEEEEE"

"EEEEEEE"
"ETEEETE"
"ETEEETE"
"EETETEE"
"EETETEE"
"EEETEEE"
"EEEEEEE"

"EEEEEEE"
"EWWWWWE"
"EEEEEWE"
"EEWWWWE"
"EEEEEWE"
"EEEEEWE"
"EEEEEEE"

"EEEEEEE"
"EVVVVEE"
"EEEEEVE"
"EEEEEVE"
"EEEEEVE"
"EEEEEVE"
"EEEEEEE"

"EEEEEEE"
"EWWWWEE"
"EWEEEWE"
"EWWWWEE"
"EWEEEWE"
"EWWWWEE"
"EEEEEEE"

"EEEEEEE"
"EEVVVVE"
"EVEEEEE"
"EVEEEEE"
"EVEEEEE"
"EEVVVVE"
"EEEEEEE"

"EEEEEEE"
"EVVVVVE"
"EVFFFFE"
"EVVVVFE"
"EVFFFFE"
"EVFFFFE"
"EEEEEEE"

"EIEIEIE"
"IUIEIUI"
"EUEIEUE"
"IUIEIUI"
"EUEIEUE"
"IEUUUEI"
"EIEIEIE"

"IIIIIII"
"IIDDDII"
"IDIIIDI"
"IDIIIDI"
"IDDDDDI"
"IDIIIDI"
"IIIIIII"

"IIIIIII"
"IIFFFII"
"IFIIIFI"
"IFIIIFI"
"IFIIIFI"
"IIFFFII"
"IIIIIII"

"IIIIIII"
"IIGGGII"
"IGIIIGI"
"IGGGGGI"
"IGIIIII"
"IIGGGII"
"IIIIIII"

"IIIIIII"
"IIUUUUI"
"IUIIIII"
"IIUUUII"
"IUIIIII"
"IIUUUUI"
"IIIIIII"

"IIIIIII"
"IEIIIEI"
"IEEEEEI"
"IEIIIEI"
"IEIIIEI"
"IIEEEII"
"IIIIIII"

"HHHHHHH"
"HGGHGGH"
"HHHGHHH"
"HHGHGHH"
"HGHHHGH"
"HHGGGHH"
"HHHHHHH"

"HHHHHHH"
"HFFFHHH"
"HHHHFHH"
"HHHFHFH"
"HHFHHFH"
"HFHHHFH"
"HHHHHHH"

"HHHHHHH"
"HHEEEHH"
"HEHHHHH"
"HEEEEHH"
"HEHHHEH"
"HHEEEHH"
"HHHHHHH"

"HHHHHHH"
"HHTTTHH"
"HHHHHTH"
"HTTTTTH"
"HTHHHTH"
"HHTTTHH"
"HHHHHHH"

"HHHHHHH"
"HHTTTHH"
"HTHHHTH"
"HTTTTTH"
"HTHHHTH"
"HHTTTHH"
"HHHHHHH"

"HHHHHHH"
"HHTTTTH"
"HTHHHTH"
"HHTTTTH"
"HTHHHTH"
"HHTTTTH"
"HHHHHHH"

"HHHHHHH"
"HTTTTHH"
"HHHHHTH"
"HHTTTHH"
"HHHHHTH"
"HTTTTHH"
"HHHHHHH"

"HHHHHHH"
"HHHUHHH"
"HHHUHHH"
"HHHUHHH"
"HHUHUHH"
"HUHHHUH"
"HHHHHHH"

"IIIIIII"
"IIIJIII"
"IIJJIII"
"IIIJIII"
"IIIJIII"
"IIIJIII"
"IIIIIII"

"DIDIDID"
"IUUUUUI"
"DIDUDID"
"IDIUIDI"
"DIDUDID"
"IUUUUUI"
"DIDIDID"

@COLORS
0 0 0 0
46 255 136 0
47 0 136 255
""")

for i in range(1,46):
 if i in offq:
  print(i,0,0,0)
 elif i in oneq:
  print(i,255,136,0)
 elif i in twoq:
  print(i,0,136,255)

Re: Three-state outer-totalistic von Neumann rules

Posted: October 25th, 2025, 4:46 am
by hibiscus
A Golly script to generate ruletables for the rules in this space:

Code: Select all

import golly as g
rule=g.getstring("Rule?","")
trans=["0,0,0,0,", "1,0,0,0,", "1,1,0,0,", "1,1,1,0,", "1,1,1,1,", "2,0,0,0,", "2,1,0,0,", "2,1,1,0,", "2,1,1,1,", "2,2,0,0,", "2,2,1,0,", "2,2,1,1,", "2,2,2,0,", "2,2,2,1,", "2,2,2,2,"]
with open(g.getdir("rules") + rule + ".rule", "w") as file:
    file.write("@RULE " + rule + "\n@TABLE\nn_states:3\nneighborhood:vonNeumann\nsymmetries:permute\nvar a 0 1 2\nvar b a\nvar c a\nvar d a\nvar e a\n")
    for x in range(6,53):
        if (rule[x] != "-") and (rule[x] != "0"):
            state = ("0" if x<=20 else ("1" if x<=36 else "2"))
            tran=(trans[(x-6)%15] if state=="0" else (trans[(x-7)%15] if state=="1" else trans[(x-8)%15]))
            file.write(state + "," + tran + rule[x] + "\n")
    file.write("a,b,c,d,e,0") 
g.setrule(rule)
Using this script, I've determined that the rulestring I manually wrote for the 5c/29o is incorrect (021010000000112 instead of 021010000000212). It's been fixed now.

p314 and p1536 in OTVN3-021000000002212-010010000000000-010001000100000:

Code: Select all

x = 117, y = 6, rule = OTVN3-021000000002212-010010000000000-010001000100000
A4.A85.A.A19.A.A2$90.A3.A17.A3.A$A4.A84.A3.A17.A3.A2$91.A.A19.A.A!
@RULE OTVN3-021000000002212-010010000000000-010001000100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,1,1,2
0,2,2,2,0,2
0,2,2,2,1,1
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,1,1,1
2,1,0,0,0,1
2,2,0,0,0,1
2,2,2,0,0,1
a,b,c,d,e,0
Edit (2025/10/25 10:58): The rulestring for vNtest was also wrong. Corrected.
Edit 2 (2025/12/16 16:19): Notation changed.

Re: Three-state outer-totalistic von Neumann rules

Posted: October 25th, 2025, 7:55 am
by Naszvadi
Well, nice idea!
I would tihnk about a python/lua code that converts from/to 2-state rules, especially B0 blinking rules as a 3-state automaton with 0-0000-0 nonflipping term.

Adding something to the notations: it would be fine if regarding to the ${\mathbb{Z}}^2$ grid with JvN neighbourhood with countable states, only the flipping terms are stored in the rulestring without the number of states due to redundancy, like this p.ex: "PERMUTE/010001-011001-111000" is "B12/S2V" and so on. I do not known whether golly has support for the latter proposed standard.

Re: Three-state outer-totalistic von Neumann rules

Posted: October 26th, 2025, 5:12 am
by hibiscus
p16, p23, p40, and p74 in vNtest:

Code: Select all

x = 73, y = 27, rule = vNtest
5.A18.A24.A22.A$3.B19.AB24.B19.A2B$4.B19.B.2A19.A.B.A18.2B$.B20.A5B.A
19.B21.2A$2.B19.A7BA17.BAB17.A.BA$A22.5B20.3B17.A.BA$20.A7BA18.A3.A
19.2A$7.B13.A.5BA41.2B$23.2A.B22.A19.A2B$14.A11.BA20.ABA21.A$12.B13.A
22.A$13.B24.A3.A6.A6.A3.A$10.B29.2B3.A3.B3.A3.2B$11.B24.A3BAB2.AB2AB.
B2ABA2.BA3BA$9.A30.2B3.A3.B3.A3.2B$38.A3.A6.A6.A3.A$49.A$48.ABA$49.A
2$47.A3.A$48.3B$48.BAB$49.B$47.A.B.A$49.B$49.A!
RT 37 reflector in another rule:

Code: Select all

x = 26, y = 4, rule = OTVN3-020000000002002-011000010101000-010000100220020
.B22.2B$B.A17.AB2.2B$B.A17.AB$.B!
@RULE OTVN3-020000000002002-011000010101000-010000100220020
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,2,2,1,1,2
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,0,0,1
1,2,1,1,0,1
1,2,2,0,0,1
1,2,2,1,1,1
2,1,0,0,0,1
2,2,1,0,0,1
2,2,2,0,0,2
2,2,2,1,0,2
2,2,2,2,1,2
a,b,c,d,e,0
Edit (2025/12/16 16:20): Notation changed.

Re: Three-state outer-totalistic von Neumann rules

Posted: December 15th, 2025, 3:12 pm
by hibiscus
3c/38d ship in OTVN3-021000000002212-010010000000000-010001000100000:

Code: Select all

x = 15, y = 15, rule = OTVN3-021000000002212-010010000000000-010001000100000
11.B.B$10.B3.B$11.B.B$11.B.B$12.B6$.B$B.2B$4.B$B.2B$.B!
@RULE OTVN3-021000000002212-010010000000000-010001000100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,1,1,2
0,2,2,2,0,2
0,2,2,2,1,1
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,1,1,1
2,1,0,0,0,1
2,2,0,0,0,1
2,2,2,0,0,1
a,b,c,d,e,0
Edit (2025/12/15 22:43): p1536 gun

Code: Select all

x = 94, y = 117, rule = OTVN3-021000000002212-010010000000000-010001000100000
6.B.B19.B.B$5.B.A.B17.B.A.B$6.B.B19.B.B$2A3.A.B.A3.2A7.2A3.A.B.A3.2A$
B13.B7.B13.B5$B13.B7.B13.B$2A3.A.B.A3.2A7.2A3.A.B.A3.2A$6.B.B19.B.B$
5.B.A.B17.B.A.B$6.B.B19.B.B77$90.2A$88.A4.A2$88.A4.A$90.2A18$90.2A$
88.A4.A2$88.A4.A$90.2A!
@RULE OTVN3-021000000002212-010010000000000-010001000100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,1,1,2
0,2,2,2,0,2
0,2,2,2,1,1
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,1,1,1
2,1,0,0,0,1
2,2,0,0,0,1
2,2,2,0,0,1
a,b,c,d,e,0
A collision with a p1536 leads to the formation of two p96 c/4d puffers:

Code: Select all

x = 278, y = 200, rule = OTVN3-021000000002212-010010000000000-010001000100000
5.B2$4.ABA2$2.A.BA$B.B.A$2.A188$252.A.A19.A.A2$251.A3.A17.A3.A$251.A
3.A17.A3.A2$252.A.A19.A.A!
@RULE OTVN3-021000000002212-010010000000000-010001000100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,1,1,2
0,2,2,2,0,2
0,2,2,2,1,1
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,1,1,1
2,1,0,0,0,1
2,2,0,0,0,1
2,2,2,0,0,1
a,b,c,d,e,0
Edit (2025/12/16 16:21): Notation changed.

Re: Three-state outer-totalistic von Neumann rules

Posted: December 19th, 2025, 4:59 pm
by hibiscus
Ship collection in a rule one transition away from OTVN3-021000000002212-010010000000000-010001000100000:
2c/4o (c/2o), 3c/19o, 5c/32o, 8c/264o (c/33o), c/4d and 2c/10d (c/5d) ships

Code: Select all

x = 121, y = 10, rule = OTVN3-021000000002212-010010000001000-010001000100000
A.A12.A5.A19.2A25.2A21.B2A17.A3.A$A.A36.B4.B27.A$16.A3.A20.2A52.A15.A
3.A$A.A12.A5.A73.A19.A$B.B69.A22.B15.A$117.2A.A$40.B2AB67.A3$114.A.A.
A.A!
@RULE OTVN3-021000000002212-010010000001000-010001000100000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,1,1,2
0,2,2,2,0,2
0,2,2,2,1,1
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,1,1,1
1,2,2,1,1,1
2,1,0,0,0,1
2,2,0,0,0,1
2,2,2,0,0,1
a,b,c,d,e,0

Re: Three-state outer-totalistic von Neumann rules

Posted: February 3rd, 2026, 12:48 pm
by hibiscus
14c/229o ship (28c/458o) found on 28 January 2026:

Code: Select all

x = 10, y = 3, rule = OTVN3-021000000002212-010020010000102-010011000102000
A2.4A2.A$3.B2.B$3.A2.A!
@RULE OTVN3-021000000002212-010020010000102-010011000102000
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a 0 1 2
var b a
var c a
var d a
var e a
0,1,0,0,0,2
0,1,1,0,0,1
0,2,2,1,1,2
0,2,2,2,0,2
0,2,2,2,1,1
0,2,2,2,2,2
1,1,0,0,0,1
1,1,1,1,1,2
1,2,1,1,0,1
1,2,2,2,0,1
1,2,2,2,2,2
2,1,0,0,0,1
2,1,1,1,1,1
2,2,0,0,0,1
2,2,2,0,0,1
2,2,2,1,1,2
a,b,c,d,e,0
I've got a page at https://iniquity816.github.io/vn.html which I plan to update with the newest discoveries.

Re: Three-state outer-totalistic von Neumann rules

Posted: February 7th, 2026, 1:45 pm
by hibiscus
p1536 3c/38d gun in OTVN3-021000000002212-010010000000000-010001000100000:

Code: Select all

x = 927, y = 689, rule = OTVN3-021000000002212-010010000000000-010001000100000
605.2A$603.B$604.A$603.B$605.2A7$613.A3.A$613.A3.A$615.A$614.B.B105$
486.B$477.B5.B$482.A2.A.A$476.A.A2.BABA2.A$476.A2.3B$481.BA3.A$480.A
2.A$481.BA3.A$476.A2.3B$476.A.A2.BABA.BA$482.A$477.B5.B2.AB.A5.2A$
487.A.B.A.A4.B$496.A$489.A5.A$487.B.B2.A2.B.B$488.2A.A.A.2A$489.3B.3B
$490.B.A.B$490.B3.B$489.A5.A$487.B9.B$489.2A3.2A103$396.2B$395.BA.A$
386.A7.B.2B$384.B.B.A4.BAB$386.A.BA3.B.B$394.A$388.ABA2$389.B3$350.B
2A2$354.A$354.A30.2B$354.B29.BA.A$383.B.2B$382.BAB$382.B.B$383.A12.2A
B2$394.A$394.A$394.B90$554.B.B63.B.B$553.B.A.B61.B.A.B$554.B.B11.A4.B
29.B4.A11.B.B$550.A.A5.A.A7.B3.A.B27.B.A3.B7.A.A5.A.A$548.A2.A2.A.A2.
A2.A2.A3.B37.B3.A2.A2.A2.A.A2.A2.A$565.A.B2ABA.A.A25.A.A.AB2AB.A$567.
A2.A3.B.B23.B.B3.A2.A$567.A2.A3.B.B23.B.B3.A2.A$565.A.B2ABA.A.A25.A.A
.AB2AB.A$548.A2.A2.A.A2.A2.A2.A3.B37.B3.A2.A2.A2.A.A2.A2.A$550.A.A5.A
.A7.B3.A.B27.B.A3.B7.A.A5.A.A$554.B.B11.A4.B29.B4.A11.B.B$553.B.A.B
61.B.A.B$554.B.B63.B.B13$319.B2.B7.B2.B$318.B.2B.B5.B.2B.B$316.B2.B2.
B7.B2.B2.B$315.B.A17.A.B$304.A11.A.B15.B.A11.A$303.B.B10.2B17.2B10.B.
B$303.3A6.2B.B.AB.B.A7.A.B.BA.B.2B6.3A$302.B3.B4.4A.4A3.B5.B3.4A.4A4.
B3.B$303.3A4.B4AB.2B.B.B3.A3.B.B.2B.B4AB4.3A$303.3A4.B4AB.2B.B.B3.A3.
B.B.2B.B4AB4.3A$302.B3.B4.4A.4A3.B5.B3.4A.4A4.B3.B$303.3A6.2B.B.AB.B.
A7.A.B.BA.B.2B6.3A$303.B.B10.2B17.2B10.B.B$304.A11.A.B15.B.A11.A$315.
B.A17.A.B$316.B2.B2.B7.B2.B2.B$318.B.2B.B5.B.2B.B$319.B2.B7.B2.B24$
503.A4.A$503.2A2.2A2$503.2A2.2A$503.A4.A9$226.2B4.2B$225.B2AB2.B2AB
270.2A$227.B4.B270.A4.A$226.A6.A$499.2ABA2.2A2.AB2A$225.ABA4.ABA264.B
12.B$500.B10.B$226.A6.A267.A3.2B3.A$227.B4.B268.BA.B2.B.AB$225.B2AB2.
B2AB$226.2B4.2B$502.2B4.2B$501.B2AB2.B2AB$502.2B4.2B8$224.B10.B$40.A.
A33.A.A143.2B.A8.A.2B$220.2B.B2.B6.B2.B.2B$219.B.BA.A.B2.2A2.B.A.AB.B
417.B.B33.B.B$220.2B2.A2.A4.A2.A2.2B417.B.A.B31.B.A.B$55.B2A3.2AB160.
A4.2A4.A422.B.B33.B.B$55.2A5.2A163.A4.A$224.A4.2A4.A$220.2B2.A2.A4.A
2.A2.2B433.2B5.2B$56.A.B.B.A156.B.BA.A.B2.2A2.B.A.AB.B431.A.AB3.BA.A$
4.B22.B2AB26.B3.B26.B2AB22.B105.2B.B2.B6.B2.B.2B262.2B4.2B161.B.2A.B.
B.2A.B$.B.B.B.B20.B29.A.A29.B20.B.B.B.B104.2B.A8.A.2B263.B2AB2.B2AB
161.AB.5A.BA$B.5B.B19.A61.A19.B.5B.B105.B10.B266.2B4.2B136.2B23.B2.BA
.A.AB2.B23.2B$.2B.A.2B20.B.A57.A.B20.2B.A.2B527.B2AB23.B2.5A2.B23.B2A
B$.B.B.B.B25.A.A17.B.B7.B.B17.A.A25.B.B.B.B500.A.BA.AB.A19.2B28.B.B
28.2B19.A.BA.AB.A$B7.B20.B22.B.A.B5.B.A.B22.B20.B7.B382.BA.B2.B.AB
110.A.A23.2B57.2B23.A.A$28.A2B2.A2.A16.B.B7.B.B16.A2.A2.2BA410.A3.2B
3.A107.2A5.2A19.A2.A55.A2.A19.2A5.2A$28.A2B2.A2.A16.B.B7.B.B16.A2.A2.
2BA409.B10.B105.B.AB3.BA.B23.B.B47.B.B23.B.AB3.BA.B$B7.B20.B22.B.A.B
5.B.A.B22.B20.B7.B380.B12.B105.B2.B.B2.B19.B3.B.A.B45.B.A.B3.B19.B2.B
.B2.B$.B.B.B.B25.A.A17.B.B7.B.B17.A.A25.B.B.B.B381.2ABA2.2A2.AB2A132.
BA.A2.B.B17.A.A7.A.A17.B.B2.A.AB$.2B.A.2B20.B.A57.A.B20.2B.A.2B527.BA
.A2.B.B17.A.A7.A.A17.B.B2.A.AB$B.5B.B19.A61.A19.B.5B.B384.A4.A109.B2.
B.B2.B19.B3.B.A.B45.B.A.B3.B19.B2.B.B2.B$.B.B.B.B20.B29.A.A29.B20.B.B
.B.B387.2A110.B.AB3.BA.B23.B.B47.B.B23.B.AB3.BA.B$4.B22.B2AB26.B3.B
26.B2AB22.B111.2B4.2B384.2A5.2A19.A2.A55.A2.A19.2A5.2A$56.A.B.B.A162.
B2AB2.B2AB386.A.A23.2B57.2B23.A.A$227.B4.B385.A.BA.AB.A19.2B28.B.B28.
2B19.A.BA.AB.A$226.A6.A411.B2AB23.B2.5A2.B23.B2AB$55.2A5.2A582.2B23.B
2.BA.A.AB2.B23.2B$55.B2A3.2AB161.ABA4.ABA437.AB.5A.BA$671.B.2A.B.B.2A
.B$226.A6.A438.A.AB3.BA.A$227.B4.B440.2B5.2B$40.A.A33.A.A146.B2AB2.B
2AB268.A4.A$226.2B4.2B269.2A2.2A$658.B.B33.B.B90.4B$503.2A2.2A148.B.A
.B31.B.A.B88.BA2.AB$503.A4.A149.B.B33.B.B91.2B12$788.2B$786.BA2.AB$
787.4B7$141.2B$138.B.B2AB.B641.B2AB$135.B.B.B.2B.B.B.B$134.B3.B.B2.B.
B3.B$135.A.A.B.2A.B.A.A635.B2.B2.B2.B$136.A.A.4A.A.A445.4A186.B2.B4.B
2.B$135.B.A3.2B3.A.B440.ABA6.ABA185.B4.B$134.B2A3.B2.B3.2AB441.B.4A.B
186.B6.B$135.2B2.B.2B.B2.2B439.A2.A6.A2.A$140.B2.B444.A4.B2.B4.A2$
590.AB2.2A2.BA$589.AB8.BA4$783.B10.B$780.B.B.B3.2A3.B.B.B$140.A2.A
635.B.B.B2.B4.B2.B.B.B$780.2B6.2A6.2B$140.A2.A636.B.2B10.2B.B$140.B2.
B450.2B185.A2.B8.B2.A$593.A2.A179.B2A.A.A4.4A4.A.A.2AB$139.A4.A449.2B
185.A14.A$788.2B$139.A4.A448.B2.B190.B2AB$141.2A449.B.2B.B180.2B8.2B
8.2B$593.A2.A180.B2AB16.B2AB$592.B.2B.B180.2B18.2B$593.B2.B190.B2.B$
788.2B2$784.A2.4B2.A$785.A.B2AB.A$787.B2AB$786.2B2A2B$126.A30.A630.2B
2$126.A30.A421.B30.B176.4B$141.2B435.B.B28.B.B174.BA2.AB$139.2B2A2B
434.A30.A176.4A$138.B.B2AB.B432.B.B28.B.B174.BA2.AB$139.2B2A2B434.B
30.B162.A13.4B13.A2$137.ABA.2A.ABA446.4A176.A30.A$137.A8.A$137.BAB.2A
.BAB640.4B$591.B.B2.B.B187.BA2.AB$139.A4.A445.B2A.2B.2AB187.4A$136.AB
8.BA442.B.A4BA.B186.B4.B$592.B4AB178.A9.B4AB9.A$138.BA4.AB445.A2.2A2.
A188.B2.B$136.A10.A444.6B178.A10.B2.B10.A$589.B2.2B2A2B2.B185.B.2B.B$
589.B4.2B4.B186.B2.B$590.B8.B3$136.A10.A$138.BA4.AB2$136.AB8.BA442.B
8.B$139.A4.A444.B4.2B4.B$589.B2.2B2A2B2.B$137.BAB.2A.BAB445.6B$137.A
8.A444.A2.2A2.A$137.ABA.2A.ABA445.B4AB$590.B.A4BA.B$139.2B2A2B445.B2A
.2B.2AB187.B2.B$138.B.B2AB.B445.B.B2.B.B187.B.2B.B$139.2B2A2B631.A10.
B2.B10.A$141.2B644.B2.B$126.A30.A435.4A179.A9.B4AB9.A$786.B4.B$126.A
30.A421.B30.B176.4A$578.B.B28.B.B174.BA2.AB$579.A30.A176.4B$578.B.B
28.B.B$579.B30.B162.A30.A2$773.A13.4B13.A$786.BA2.AB$787.4A$786.BA2.A
B$141.2A644.4B$139.A4.A$788.2B$139.A4.A448.B2.B189.2B2A2B$592.B.2B.B
189.B2AB$140.B2.B449.A2.A188.A.B2AB.A$140.A2.A448.B.2B.B186.A2.4B2.A$
593.B2.B$140.A2.A644.2B$594.2B191.B2.B$593.A2.A181.2B18.2B$594.2B181.
B2AB16.B2AB$778.2B8.2B8.2B$787.B2AB$788.2B$781.A14.A$776.B2A.A.A4.4A
4.A.A.2AB$140.B2.B637.A2.B8.B2.A$135.2B2.B.2B.B2.2B631.B.2B10.2B.B$
134.B2A3.B2.B3.2AB630.2B6.2A6.2B$135.B.A3.2B3.A.B440.AB8.BA178.B.B.B
2.B4.B2.B.B.B$136.A.A.4A.A.A442.AB2.2A2.BA180.B.B.B3.2A3.B.B.B$135.A.
A.B.2A.B.A.A634.B10.B$134.B3.B.B2.B.B3.B438.A4.B2.B4.A$135.B.B.B.2B.B
.B.B439.A2.A6.A2.A$138.B.B2AB.B445.B.4A.B$141.2B446.ABA6.ABA$593.4A4$
785.B6.B$786.B4.B$783.B2.B4.B2.B$784.B2.B2.B2.B3$787.B2AB11$780.2AB2$
778.A$778.A$778.B6$842.A.A33.A.A3$850.A.A17.A.A5$832.2B55.2B$804.B3.B
22.B2AB53.B2AB22.B3.B$803.B.B.B.B22.2A55.2A22.B.B.B.B$797.B2.B30.B2AB
14.3B19.3B14.B2AB30.B2.B$796.B.2B.B.B.2B25.2B14.B2.AB17.BA2.B14.2B25.
2B.B.B.2B.B$797.B2.B3.2B.B41.A23.A41.B.2B3.B2.B$799.B6.B22.B.B2.B.B
17.B13.B17.B.B2.B.B22.B6.B$807.A.A18.B3A2B3AB16.A13.A16.B3A2B3AB18.A.
A$807.A.A18.B3A2B3AB16.A13.A16.B3A2B3AB18.A.A$799.B6.B22.B.B2.B.B17.B
13.B17.B.B2.B.B22.B6.B$797.B2.B3.2B.B41.A23.A41.B.2B3.B2.B$796.B.2B.B
.B.2B25.2B14.B2.AB17.BA2.B14.2B25.2B.B.B.2B.B$797.B2.B30.B2AB14.3B19.
3B14.B2AB30.B2.B$803.B.B.B.B22.2A55.2A22.B.B.B.B$804.B3.B22.B2AB53.B
2AB22.B3.B$832.2B55.2B5$850.A.A17.A.A3$842.A.A33.A.A!
Edit (2026/02/07 20:22): Much smaller 3c/38d gun:

Code: Select all

x = 237, y = 237, rule = OTVN3-021000000002212-010010000000000-010001000100000
104.A24.A2$104.A24.A$110.B2.B6.B2.B$109.B.2B.A4.A.2B.B$110.B4.A2.A4.B
$111.B2.A.2B.A2.B$110.B.A.2B2.2B.A.B$111.B.B2.2A2.B.B$111.B10.B$110.B
2.2A.2A.2A2.B$111.A.AB4.BA.A$110.B2.2A.2A.2A2.B$111.B10.B$111.B.B2.2A
2.B.B$110.B.A.2B2.2B.A.B$111.B2.A.2B.A2.B$110.B4.A2.A4.B$109.B.2B.A4.
A.2B.B$110.B2.B6.B2.B$104.A24.A2$104.A24.A60$8.B.B33.B.B$7.B.A.B31.B.
A.B$8.B.B33.B.B$16.B.B17.B.B$15.B.A.B15.B.A.B$16.B.B17.B.B3$5.2A19.B.
B19.2A$A2.B4.B16.B.A.B16.B4.B2.A$A4.2A17.B.B.B.B17.2A4.A$23.B.2B.2B.B
$15.B4.A3.2B.A.2B3.A4.B$19.B6.B.B6.B$10.2B.B4.2B15.2B4.B.2B$4.A4.B2AB
.A2.B2A3.B7.B3.2AB2.A.B2AB4.A$3.B.B4.2B.BAB.B.A.AB9.BA.A.B.BAB.2B4.B.
B$3.B.B4.2B.BAB.B.A.AB9.BA.A.B.BAB.2B4.B.B$4.A4.B2AB.A2.B2A3.B7.B3.2A
B2.A.B2AB4.A$10.2B.B4.2B15.2B4.B.2B$19.B6.B.B6.B$15.B4.A3.2B.A.2B3.A
4.B$23.B.2B.2B.B$A4.2A17.B.B.B.B17.2A4.A$A2.B4.B16.B.A.B16.B4.B2.A$5.
2A19.B.B19.2A164.A.A17.A.A3$16.B.B17.B.B$15.B.A.B15.B.A.B$16.B.B17.B.
B66.2A3.2A106.B13.B$8.B.B33.B.B56.B9.B103.B.B.B2.B.B2.B.B.B$7.B.A.B
31.B.A.B57.A5.A106.B.B.2B.A.2B.B.B$8.B.B33.B.B59.B3.B107.B2.A7.A2.B$
106.B.A.B106.B4.B.3A.B4.B$105.3B.3B106.A.AB2.ABA2.BA.A$104.2A.A.A.2A
106.A.B7.B.A$103.B.B2.A2.B.B106.B.A.A.A.A.B$105.A5.A108.B.A.A.A.A.B$
104.A114.A.B7.B.A$102.B4.A.A.B.A104.A.AB2.ABA2.BA.A$104.2A5.A.BA2.B5.
B93.B4.B.3A.B4.B$118.A99.B2.A7.A2.B$113.AB.ABAB2.A.A93.B.B.2B.A.2B.B.
B$119.3B2.A92.B.B.B2.B.B2.B.B.B$114.A3.AB98.B13.B$117.A2.A$114.A3.AB$
119.3B2.A$113.A2.ABAB2.A.A$113.A.A2.A95.A.A17.A.A$117.B5.B$114.B48$
130.2A12.2A3$130.B6.2B6.B$136.A2.A$129.A.A5.2B5.A.A$129.A.A12.A.A$
122.B30.B$121.B.B6.B14.B6.B.B$122.A13.B2.B13.A$121.B.B11.BA2BAB11.B.B
$122.B12.BA2BAB12.B$136.B2.B$135.B.2B.B$136.4A$125.B7.B3.2B3.B7.B$
124.B.B22.B.B$125.A10.4B10.A$124.B.B8.BA2.AB8.B.B$125.B8.2B4A2B8.B$
133.A8.A$137.2A$137.2B$132.B3.B2.B3.B$131.B.B8.B.B$130.B.2B8.2B.B$
129.B.2B.B6.B.2B.B$130.A2.A8.A2.A$129.B.2B.B6.B.2B.B$130.B.2B8.2B.B$
131.B.B8.B.B$132.B3.B2.B3.B$137.2B$137.2A$133.A8.A$125.B8.2B4A2B8.B$
124.B.B8.BA2.AB8.B.B$125.A10.4B10.A$124.B.B22.B.B$125.B7.B3.2B3.B7.B$
136.4A$135.B.2B.B$136.B2.B$122.B12.BA2BAB12.B$121.B.B11.BA2BAB11.B.B$
122.A13.B2.B13.A$121.B.B6.B14.B6.B.B$122.B30.B$129.A.A12.A.A$129.A.A
5.2B5.A.A$136.A2.A$130.B6.2B6.B3$130.2A12.2A!

Re: Three-state outer-totalistic von Neumann rules

Posted: June 4th, 2026, 9:23 am
by hibiscus
The rule B1x2/S23V is in this space (and can be written in my notation as OTVN3-020000200020020-001100011001000-010020100010010):

Code: Select all

x = 0, y = 0, rule = B1x2_S23V
!
[[ RANDOMIZE2 ]]
I am planning to write a LifeWiki article on it, since it is notable (or at least historically significant, having been discovered in 2007). However, the Rule infobox template doesn't seem well-equipped to handle anything other than typical OT, INT, Generations, HROT, and BSFKL rules.

Re: Three-state outer-totalistic von Neumann rules

Posted: September 13th, 2026, 4:24 pm
by unname4798
A very simple, Brian's Brain-like rule with chevron arrows as the most common spaceships:

Code: Select all

x = 1, y = 1, rule = ChevronArrows:T256,256
!
[[ RANDOMIZE2 RANDWIDTH 256 RANDHEIGHT 256 RANDFILL 1 ]]
@RULE ChevronArrows
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
0,1,2,0,0,2
0,1,0,0,0,1
0,1,1,0,0,2
0,1,1,2,0,2
a,b,c,d,e,0
All times are UTC-04:00
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