Generations rules, as you all know, work by having "dying" cells, such that they count as off for the purposes of survival/birth counts, but will only become vacuum after a delay.
There are however three other cell type options transitional between vacuum and fully live:
• "Nascent": Newborn cell, counts as off, will become fully live in X ticks.
• "Young": Newborn cell, counts as on, will become fully live in X ticks.
• "Sick": Dead cell, counts as on, will become vacuum in X ticks.
CA using these six cell types (vacuum, nascent, young, live, sick, dying) can be considered united by the feature that birth and survival of live cells is determined only according to a single set of 16 B/S conditions. All transitional cells evolve independantly of their environment; live and vacuum cells according to the sum of their "on" neighbors.
There's further expansion potential too: while including multiple kinds of a transitional cell type in the rules is obvious, we might also consider using multiple kinds of vacuum and live cells: eg. B3 turns Vacuum1 into Vacuum2 etc, and finally VacuumX into Live1; or D8 turns Live1 into Live2 etc, until LiveY becomes dead. (Transitional states could be injected at any point here, too.)
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Adding one sick stage is a boost in the growth rate of a rule (unlike the kick downward that adding one dying stage is): all of B34/S, B35/S, B3/S01, B3/S2, B3/S3 and B3/S4 are explosiv rules. The last three all support a multitude of replicators and spaceships. Adding two, even B3/S explodes. So rules with only vacuum, live and sick states don't seem to hold too much to discover.
However, these are perfectly mixable, let's say using one sick + one dying stage…
Some initial results:
B3/S2 is now a stable rule; this and B3/S1 support P4 versions of simple P2 ocillators of Life-like rules
B3/S3 remains replicator-dominated
B3/S4 as well, but B3/S24 turns into a CA resembling a sparser version of the "MilhinSA" rule.
B34/S and B35/S are now stable
B36/S24 has a strange "self-puffer" pattern. This initially looks like an obliq linear-growth replicator stream, but it actually generates a 6c/218 rake:
Code: Select all
x = 3, y = 4, rule = sick+dying
AC$2A$ACA$AC!Code: Select all
n_states:4
neighborhood:Moore
symmetries:permute
var a={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={0,1,2,3}
var j={i}
var k={i}
var l={i}
var m={i}
var n={i}
var o={i}
var p={i}
var q={0,3}
var r={q}
var s={q}
var t={q}
var u={q}
var v={q}
var w={q}
var x={q}
#birth
0,a,b,c,t,u,v,w,x,1
#0,a,b,c,d,u,v,w,x,1
#0,a,b,c,d,e,v,w,x,1
0,a,b,c,d,e,f,w,x,1
#0,a,b,c,d,e,f,g,x,1
#0,a,b,c,d,e,f,g,h,1
#survival
1,q,r,s,t,u,v,w,x,2
1,a,r,s,t,u,v,w,x,2
1,a,b,s,t,u,v,w,x,1
1,a,b,c,t,u,v,w,x,2
1,a,b,c,d,u,v,w,x,1
1,a,b,c,d,e,v,w,x,2
1,a,b,c,d,e,f,w,x,2
1,a,b,c,d,e,f,g,x,2
1,a,b,c,d,e,f,g,h,2
#death
2,i,j,k,l,m,n,o,p,3
3,i,j,k,l,m,n,o,p,0Adding a young stage is similarly a growth rate booster. Over here, B3/S4 is a highly stable rule; B3/S1 however explodes, B3/S2, B3/S3, B34/S, and B35/S still as well. These seem for some reason yet more chaotic than their sick-stage counterparts, creating an expanding mess rather than replicators. Not going to look more here (and this also predicts using two live states + no dead-transition states is not going to do anything useful either). Combining with dying or nascent stages needs checking out.
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Last area tonight: using 2 vacuum states. This approach is quite strongly growth-retarding; even B3/S01345 is stable. B2 rules also have the potential to not explode (as this works rather similarly to the "Bx2" approach), there is a lightspeed growth engine in B1 tho.
B2/S23, B2/S13, B24/S03 and B24/S12 do explode. B23/S2 and B234/S are only weakly explosiv; B23/S0, B23/S34 and B24/S345 wholly stable.
Also as a more general observation, the (pseudo)random sprinkling of Vacuum1 and Vacuum2 states left behind by live areas seems like an obstacle for anything structured to occur under this subspace.