This morning, after coming back from holiday, I proved greycells/OffNeutronium/ExtendedLifeButNotAsGood omniperiodic. I'm quite happy with this result, especially considering the time I spent soup searching, and considering how close this rule is to Life - maybe some of the higher period oscillators can be stabilised without using grey cells. Every oscillator that works in regular Life also works in greycells, so we only need to find oscillators of period 19, 23, 34, 38 and 41:
I've been keeping two stamp collections, one for every oscillator I find and one for the smallest oscillator of each period. Both of them are in a custom rule I made named findosc, which is basically LifeHistory for greycells.
Code: Select all
@RULE findosc
Grey cells never die, and do not create life
All birth/death conditions become marked, including grey cells
Oscillator stators will be marked with state 6.
state 0: OFF
state 1: ON
state 2: GREY
state 3: OFF M (ROTOR)
state 4: ON M (ROTOR)
state 5: GREY M
state 6: ON S (STATOR)
@TABLE
n_states:7
neighborhood:Moore
symmetries:rotate8
var a={0,2,3,5}
var b={0,2,3,5}
var c={0,2,3,5}
var d={0,2,3,5}
var e={0,2,3,5}
var f={0,2,3,5}
var g={0,2,3,5}
var h={0,1,2,3,4,5,6}
var i={0,1,2,3,4,5,6}
var j={0,1,2,3,4,5,6}
var k={0,1,2,3,4,5,6}
var l={0,1,2,3,4,5,6}
var m={0,1,2,3,4,5,6}
var n={0,1,2,3,4,5,6}
var o={0,1,2,3,4,5,6}
var p={0,1,2,3,4,5,6}
var Q={1,4,6}
var R={1,4,6}
var S={1,4,6}
var T={1,4,6}
var u={2,5}
var W={1,6}
var aa={3,4,6}
var ra={4,6}
var rb={4,6}
var rc={4,6}
var sa={0,1,2,3,5}
var sb={0,1,2,3,5}
var sc={0,1,2,3,5}
var sd={0,1,2,3,5}
var se={0,1,2,3,5}
var z={3,6}
# grey cell becomes marked with 3 stator/rotor neighbours
u,ra,rb,rc,sa,sb,sc,sd,se,5
u,ra,rb,sa,rc,sb,sc,sd,se,5
u,ra,rb,sa,sb,rc,sc,sd,se,5
u,ra,rb,sa,sb,sc,rc,sd,se,5
u,ra,rb,sa,sb,sc,sd,rc,se,5
u,ra,sa,rb,sb,rc,sc,sd,se,5
u,ra,sa,rb,sb,sc,rc,sd,se,5
# otherwise it stays grey
u,h,i,j,k,l,m,n,o,u
# dead cell turns to OFF M with 3 stator/ON M neighours and at least 1 live neighbour:
0,ra,rb,rc,1,sb,sc,sd,se,3
0,ra,rb,rc,sa,1,sc,sd,se,3
0,ra,rb,rc,sa,sb,1,sd,se,3
0,ra,rb,rc,sa,sb,sc,1,se,3
0,ra,rb,rc,sa,sb,sc,sd,1,3
0,ra,rb,1,rc,sb,sc,sd,se,3
0,ra,rb,sa,rc,1,sc,sd,se,3
0,ra,rb,sa,rc,sb,1,sd,se,3
0,ra,rb,sa,rc,sb,sc,1,se,3
0,ra,rb,sa,rc,sb,sc,sd,1,3
0,ra,rb,1,sb,rc,sc,sd,se,3
0,ra,rb,sa,1,rc,sc,sd,se,3
0,ra,rb,sa,sb,rc,1,sd,se,3
0,ra,rb,sa,sb,rc,sc,1,se,3
0,ra,rb,sa,sb,rc,sc,sd,1,3
0,ra,rb,1,sb,sc,rc,sd,se,3
0,ra,rb,sa,1,sc,rc,sd,se,3
0,ra,rb,sa,sb,1,rc,sd,se,3
0,ra,rb,sa,sb,sc,rc,1,se,3
0,ra,rb,sa,sb,sc,rc,sd,1,3
0,ra,rb,1,sb,sc,sd,rc,se,3
0,ra,rb,sa,1,sc,sd,rc,se,3
0,ra,rb,sa,sb,1,sd,rc,se,3
0,ra,rb,sa,sb,sc,1,rc,se,3
0,ra,rb,sa,sb,sc,sd,rc,1,3
0,ra,1,rb,sb,rc,sc,sd,se,3
0,ra,sa,rb,1,rc,sc,sd,se,3
0,ra,sa,rb,sb,rc,1,sd,se,3
0,ra,sa,rb,sb,rc,sc,1,se,3
0,ra,sa,rb,sb,rc,sc,sd,1,3
0,ra,1,rb,sb,sc,rc,sd,se,3
0,ra,sa,rb,1,sc,rc,sd,se,3
0,ra,sa,rb,sb,1,rc,sd,se,3
0,ra,sa,rb,sb,sc,rc,1,se,3
0,ra,sa,rb,sb,sc,rc,sd,1,3
# spread stator only if 2/3 neighbours 2:
1,R,S,aa,a,b,c,d,e,6
1,6,S,f,a,b,c,d,e,6
1,R,6,f,a,b,c,d,e,6
1,R,S,a,aa,b,c,d,e,6
1,6,S,a,f,b,c,d,e,6
1,R,6,a,f,b,c,d,e,6
1,R,S,a,b,aa,c,d,e,6
1,6,S,a,b,f,c,d,e,6
1,R,6,a,b,f,c,d,e,6
1,R,S,a,b,c,aa,d,e,6
1,6,S,a,b,c,f,d,e,6
1,R,6,a,b,c,f,d,e,6
1,R,S,a,b,c,d,aa,e,6
1,6,S,a,b,c,d,f,e,6
1,R,6,a,b,c,d,f,e,6
1,R,S,a,b,c,d,e,aa,6
1,6,S,a,b,c,d,e,f,6
1,R,6,a,b,c,d,e,f,6
1,R,aa,S,a,b,c,d,e,6
1,6,f,S,a,b,c,d,e,6
1,R,f,6,a,b,c,d,e,6
1,R,a,S,aa,b,c,d,e,6
1,6,a,S,f,b,c,d,e,6
1,R,a,6,f,b,c,d,e,6
1,R,a,S,b,aa,c,d,e,6
1,6,a,S,b,f,c,d,e,6
1,R,a,6,b,f,c,d,e,6
1,R,a,S,b,c,aa,d,e,6
1,6,a,S,b,c,f,d,e,6
1,R,a,6,b,c,f,d,e,6
1,R,aa,a,S,b,c,d,e,6
1,6,f,a,S,b,c,d,e,6
1,R,f,a,6,b,c,d,e,6
1,R,a,aa,S,b,c,d,e,6
1,6,a,f,S,b,c,d,e,6
1,R,a,f,6,b,c,d,e,6
1,R,a,b,S,aa,c,d,e,6
1,6,a,b,S,f,c,d,e,6
1,R,a,b,6,f,c,d,e,6
1,R,a,b,S,c,aa,d,e,6
1,6,a,b,S,c,f,d,e,6
1,R,a,b,6,c,f,d,e,6
1,R,a,b,S,c,d,aa,e,6
1,6,a,b,S,c,d,f,e,6
1,R,a,b,6,c,d,f,e,6
1,R,a,b,S,c,d,e,aa,6
1,6,a,b,S,c,d,e,f,6
1,R,a,b,6,c,d,e,f,6
1,R,aa,a,b,S,c,d,e,6
1,6,f,a,b,S,c,d,e,6
1,R,f,a,b,6,c,d,e,6
1,R,a,aa,b,S,c,d,e,6
1,6,a,f,b,S,c,d,e,6
1,R,a,f,b,6,c,d,e,6
#d:
1,aa,R,b,S,c,d,e,f,6
1,aa,6,b,S,c,d,e,f,6
1,aa,R,b,6,c,d,e,f,6
1,a,R,aa,S,c,d,e,f,6
1,a,6,aa,S,c,d,e,f,6
1,a,R,aa,6,c,d,e,f,6
1,a,R,b,S,aa,d,e,f,6
1,a,6,b,S,aa,d,e,f,6
1,a,R,b,6,aa,d,e,f,6
1,a,R,b,S,c,aa,e,f,6
1,a,6,b,S,c,aa,e,f,6
1,a,R,b,6,c,aa,e,f,6
1,a,R,b,S,c,d,aa,f,6
1,a,6,b,S,c,d,aa,f,6
1,a,R,b,6,c,d,aa,f,6
1,a,R,b,S,c,d,e,aa,6
1,a,6,b,S,c,d,e,aa,6
1,a,R,b,6,c,d,e,aa,6
1,aa,R,b,c,d,S,e,f,6
1,aa,6,b,c,d,S,e,f,6
1,aa,R,b,c,d,6,e,f,6
1,a,R,aa,c,d,S,e,f,6
1,a,6,aa,c,d,S,e,f,6
1,a,R,aa,c,d,6,e,f,6
1,a,R,b,aa,d,S,e,f,6
1,a,6,b,aa,d,S,e,f,6
1,a,R,b,aa,d,6,e,f,6
1,a,R,b,c,aa,S,e,f,6
1,a,6,b,c,aa,S,e,f,6
1,a,R,b,c,aa,6,e,f,6
1,a,R,b,c,d,S,aa,f,6
1,a,6,b,c,d,S,aa,f,6
1,a,R,b,c,d,6,aa,f,6
1,a,R,b,c,d,S,e,aa,6
1,a,6,b,c,d,S,e,aa,6
1,a,R,b,c,d,6,e,aa,6
#3:
1,R,S,T,3,a,b,c,d,6
1,R,S,T,a,3,b,c,d,6
1,R,S,T,a,b,3,c,d,6
1,R,S,T,a,b,c,3,d,6
1,R,S,T,a,b,c,d,3,6
1,R,S,3,T,b,c,d,e,6
1,R,S,a,T,3,c,d,e,6
1,R,S,a,T,b,3,d,e,6
1,R,S,a,T,b,c,3,e,6
1,R,S,a,T,b,c,d,3,6
1,R,S,3,b,c,T,d,e,6
1,R,S,a,3,c,T,d,e,6
1,R,S,a,b,3,T,d,e,6
1,R,S,a,b,c,T,3,e,6
1,R,S,a,b,c,T,d,3,6
1,R,S,3,b,c,d,T,e,6
1,R,S,a,3,c,d,T,e,6
1,R,S,a,b,3,d,T,e,6
1,R,S,a,b,c,3,T,e,6
1,R,S,a,b,c,d,T,3,6
1,3,R,b,S,c,T,d,e,6
1,a,R,3,S,c,T,d,e,6
1,a,R,b,S,3,T,d,e,6
1,a,R,b,S,c,T,3,e,6
1,a,R,b,S,c,T,d,3,6
# marked 3-neighbour birth
a,R,S,T,f,b,c,d,e,4
a,R,S,f,T,b,c,d,e,4
a,R,S,f,b,T,c,d,e,4
a,R,S,f,b,c,T,d,e,4
a,R,S,f,b,c,d,T,e,4
a,R,f,S,b,T,c,d,e,4
a,R,f,S,b,c,T,d,e,4
# 3-neighbour survival
Q,R,S,T,f,b,c,d,e,Q
Q,R,S,f,T,b,c,d,e,Q
Q,R,S,f,b,T,c,d,e,Q
Q,R,S,f,b,c,T,d,e,Q
Q,R,S,f,b,c,d,T,e,Q
Q,R,f,S,b,T,c,d,e,Q
Q,R,f,S,b,c,T,d,e,Q
# 2-neighbour survival
Q,R,S,a,b,c,d,e,f,Q
Q,R,a,S,b,c,d,e,f,Q
Q,R,a,b,S,c,d,e,f,Q
Q,R,a,b,c,S,d,e,f,Q
# otherwise DIE
Q,h,i,j,k,l,m,n,o,3
@COLORS
1 255 255 255
2 96 96 96
3 0 0 96
4 255 0 0
5 0 255 0
6 255 255 0
The 2nd column contains the smallest oscillator by population. State 3 cells are not counted as alive, which is probably cheating, but I couldn't think of a better metric at the time.
The 4th column contains the oscillators with the lowest population of state 3 cells, which is only relevant for 19, 23, 34, 38 and 41.