Alternating rules
Posted: August 21st, 2011, 6:57 pm
The set of 2-state Life-like CAs has a lot of "uninhabitable" space, since all ¬B0 + B1/B2 rules explode, with the former indeed all patterns. A large part of the B3 rules, too… This always seem'd like a shame to me.
The concept of Generations rules semi-salvages a lot of the B2 and B34 rules into at least cleaner explosions, but I thought of a simple way for alternate stabilization of these parts of the rule space: rather than applying birth and death simultaneously, apply them on alternating generations! So on the first tick, only birth occurs; on the 2nd, only death; etc. This opens some fresh new ground to discover… Has anyone else tried these? Seems like a pretty obvious thing to try; indeed whenever I explain CA to someone new, they commonly ask which of birth and death is applied first.
Some alternating rules to try out, from my first sweepthru around these parts:
B1/S578: stable with a large natural spaceship
B12/S2678: very slowly exploding, may be engineerable (funnily, all the "subrules" — S268 etc. — are stable)
B12/S4: exploding, but the universe seems to end up composed of nothing but diagonal replicators. Orthogonal growth is slow.
B2/S3: similar to the previous, but rotated 45°. Add S0 to gain some puffers and spaceships
B2/S24: stable, but has a few natural c/4 spaceships
B2/S1246: very slowly stabilizing; seems promising
B23/S47: stable, but has some longer-lasting activity and a natural spaceship
B3/S1234: appears to explode, but activity dies down eventually leaving large "corals". (An L-tetromino lasts for ~8725 gens, leaving a population of ~54710.) S01234 is similar.
B3/S235: fairly stable, small natural spaceship
(Counterparts of stable non-alternating rules seem to either die off or stabilize even faster than normally.)
A basic ruletable for messing around:
Quite a few of these actually remind me of the appearence of of some non-alternating B0 rules. Indeed, I would not be surprized if some number could be shown to be equivalent…
The concept of Generations rules semi-salvages a lot of the B2 and B34 rules into at least cleaner explosions, but I thought of a simple way for alternate stabilization of these parts of the rule space: rather than applying birth and death simultaneously, apply them on alternating generations! So on the first tick, only birth occurs; on the 2nd, only death; etc. This opens some fresh new ground to discover… Has anyone else tried these? Seems like a pretty obvious thing to try; indeed whenever I explain CA to someone new, they commonly ask which of birth and death is applied first.
Some alternating rules to try out, from my first sweepthru around these parts:
B1/S578: stable with a large natural spaceship
B12/S2678: very slowly exploding, may be engineerable (funnily, all the "subrules" — S268 etc. — are stable)
B12/S4: exploding, but the universe seems to end up composed of nothing but diagonal replicators. Orthogonal growth is slow.
B2/S3: similar to the previous, but rotated 45°. Add S0 to gain some puffers and spaceships
B2/S24: stable, but has a few natural c/4 spaceships
B2/S1246: very slowly stabilizing; seems promising
B23/S47: stable, but has some longer-lasting activity and a natural spaceship
B3/S1234: appears to explode, but activity dies down eventually leaving large "corals". (An L-tetromino lasts for ~8725 gens, leaving a population of ~54710.) S01234 is similar.
B3/S235: fairly stable, small natural spaceship
(Counterparts of stable non-alternating rules seem to either die off or stabilize even faster than normally.)
A basic ruletable for messing around:
Code: Select all
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}
# birth
# 0,1,0,0,0,0,0,0,0,2
# 0,1,1,0,0,0,0,0,0,2
0,1,1,1,0,0,0,0,0,2
# 0,1,1,1,1,0,0,0,0,2
# 0,1,1,1,1,1,0,0,0,2
# 0,1,1,1,1,1,1,0,0,2
# 0,1,1,1,1,1,1,1,0,2
# 0,1,1,1,1,1,1,1,1,2
# phase change
1,a,b,c,d,e,f,g,h,2
# survival
# 2,0,0,0,0,0,0,0,0,1
2,2,0,0,0,0,0,0,0,1
2,2,2,0,0,0,0,0,0,1
2,2,2,2,0,0,0,0,0,1
2,2,2,2,2,0,0,0,0,1
# 2,2,2,2,2,2,0,0,0,1
# 2,2,2,2,2,2,2,0,0,1
# 2,2,2,2,2,2,2,2,0,1
# 2,2,2,2,2,2,2,2,2,1
# death otherwise
2,a,b,c,d,e,f,g,h,0
Pteriforever's RLE above has "A" *and* "B", meaning a mix of state 1 and state 2 in the same generation! And I suspect that's why you're now confused.