Yesterday I looked for the first time into your rule and realized that I was recently playing independently with a very large rule space of similar rules. Not yours though and with a different style of computer generated rule tables. My main interest are 4-state tamed rules with speed of light spaceships based on Seeds and augmented with still lifes.
In my
cyclical notation, your rule would be denoted as
D3a-01a2n3n4z4n5z5n6z6n7z7n8z8n (I made all such 3-state rules red and blue because it resembles standard electric wire coloring in some countries):
Code: Select all
@RULE Symbiosis
# D3a-01a2n3n4z4n5z5n6z6n7z7n8z8n
@COLORS
0 0 0 0
1 255 0 0
2 0 0 255
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var A={0,1,2}
var B=A
var C=A
var D=A
var E=A
var F=A
var G=A
var H=A
var I=A
var a={1,2}
var b=a
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i=a
0,i,i,i,0,0,0,0,0,i
1,2,0,0,0,0,0,0,0,1
2,1,0,0,0,0,0,0,0,2
i,a,b,0,0,0,0,0,0,i
i,a,b,c,0,0,0,0,0,i
i,i,i,i,i,0,0,0,0,0
i,a,b,c,d,0,0,0,0,i
i,i,i,i,i,i,0,0,0,0
i,a,b,c,d,e,0,0,0,i
i,i,i,i,i,i,i,0,0,0
i,a,b,c,d,e,f,0,0,i
i,i,i,i,i,i,i,i,0,0
i,a,b,c,d,e,f,g,0,i
i,i,i,i,i,i,i,i,i,0
i,a,b,c,d,e,f,g,h,i
I,A,B,C,D,E,F,G,H,0
The head and the final line of this table is my standard wrapper for such rules. I used rules similar to yours for testing my rule table generator written in Common Lisp.
I am very glad that someone else had realized the great potential of such state-symmetrical rules! You undoubtedly created this rule, but I invented the generalization of such cyclical rules (looking from a different perspective though) and the corresponding notation system (not exactly perfect yet)!
Now, among the rules I've recently looked into, the closest to yours in the rule structure and general behavior seems to be
D14a3a-2n3n4zr4n5zr5n6zr6n7zr7n8zr8n (stored as 2Life18 on my computer):
Code: Select all
@RULE 2Life18
# D14a3a-2n3n4zr4n5zr5n6zr6n7zr7n8zr8n
@COLORS
0 0 0 0
1 255 0 0
2 0 0 255
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var A={0,1,2}
var B=A
var C=A
var D=A
var E=A
var F=A
var G=A
var H=A
var I=A
var a={1,2}
var b=a
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i=a
0,1,2,2,2,2,0,0,0,1
0,2,1,1,1,1,0,0,0,2
0,i,i,i,0,0,0,0,0,i
i,a,b,0,0,0,0,0,0,i
i,a,b,c,0,0,0,0,0,i
i,1,1,1,1,0,0,0,0,0
i,2,2,2,2,0,0,0,0,0
i,a,b,c,d,0,0,0,0,i
i,1,1,1,1,1,0,0,0,0
i,2,2,2,2,2,0,0,0,0
i,a,b,c,d,e,0,0,0,i
i,1,1,1,1,1,1,0,0,0
i,2,2,2,2,2,2,0,0,0
i,a,b,c,d,e,f,0,0,i
i,1,1,1,1,1,1,1,0,0
i,2,2,2,2,2,2,2,0,0
i,a,b,c,d,e,f,g,0,i
i,1,1,1,1,1,1,1,1,0
i,2,2,2,2,2,2,2,2,0
i,a,b,c,d,e,f,g,h,i
I,A,B,C,D,E,F,G,H,0
I wanted to add an extra "symbiotic" birth rule and didn't think that surviving something like solid 2-color lines and 100% dense agars would not lead to a complete freeze.
For somewhat similar 4-state rules (3-color, as I call) with "Go boards", look at
SeaLife and
Triple_Swamps.
I also thought of symbiosis, because some similar rules grow very much like lichens. For example:
Code: Select all
@RULE 2Life22
# D12b3a-2n3n4zr4n5zr5n
@COLORS
0 0 0 0
1 255 0 0
2 0 0 255
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var A={0,1,2}
var B=A
var C=A
var D=A
var E=A
var F=A
var G=A
var H=A
var I=A
var a={1,2}
var b=a
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i=a
0,1,2,2,0,0,0,0,0,2
0,2,1,1,0,0,0,0,0,1
0,i,i,i,0,0,0,0,0,i
i,a,b,0,0,0,0,0,0,i
i,a,b,c,0,0,0,0,0,i
i,1,1,1,1,0,0,0,0,0
i,2,2,2,2,0,0,0,0,0
i,a,b,c,d,0,0,0,0,i
i,1,1,1,1,1,0,0,0,0
i,2,2,2,2,2,0,0,0,0
i,a,b,c,d,e,0,0,0,i
I,A,B,C,D,E,F,G,H,0
Code: Select all
x = 19, y = 19, rule = 2Life22
$12.B$11.B$11.3B8$5.A$5.2A$4.A.A!
Some "symbiotic" rules also exhibit a "galaxy" behavior by producing stable cores or glider emitters or mutating extra-large period guns that turn almost any 2-color pattern into a methuselah or an oscillator with an astronomical period, while some others explode in very different ways, or are stable, but have crazy long average lives. I guess I should categorize them at some time. I didn't really expect much from such rules, besides radical changes in Life's general behavior. I'll gonna look, if some of your cool oscillators work in other related rules.
Many thanks for great discoveries!
BTW, does anyone know other interesting "symbiotic" rules? I honestly didn't know that at least this rule has been already explored.
