x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
x = 0, y = 0, rule = B3/S23
!
blah wrote:I don't think your maths is correct. I don't know where you got the factorial from, and I think you put the exponent on the wrong end; there are 2^18 = 262,144 lifelike rules, and 2^58 (58 being 8+the number of modifiers if I counted them right) isotropic rules.
Anyway, this oscillator is pretty universal:Code: Select allx = 0, y = 0, rule = B3/S23
!
I call it "Empty Space". It's a p1 oscillator in 50% of rules (anything without B0), a p2 oscillator in 25% of rules (with B0 but without S8), and the immediate predecessor of a still life in the other 25% of rules (with B0 and S8).
You never said it couldn't be trivial. :^)
Gamedziner wrote:Except a so called "p1 oscillator" is actually a still life and nothing more.
x = 2, y = 2, rule = B2/S
bo$o!
x = 16, y = 16, rule = B7/S01234578
16o$16o$16o$16o$16o$16o$16o$7ob8o$8ob7o$16o$16o$16o$16o$16o$16o$16o!
A for awesome wrote:BlinkerSpawn wrote:The most universal oscillator would be the p2 doublet, which only requires B2e and prohibits B01/S1c.
A single dot is a p1 oscillator requiring S0 and prohibiting B01. A block is a p1 oscillator requiring S3a and prohibiting B01c2a. Both work in 1/16 of all rules, whereas the duoplet works in only 1/32 of all rules.
I recognize that p1 oscillators might not count, though.
EDIT: For p3 oscillators the best I can find is requiring B2i3a4e/S2c and prohibiting B012ce4c/S03i4e:Code: Select allx = 3, y = 3, rule = B2i3a4e/S2c
bo$obo$bo!
(1/8192)
For p4s it requires B2k3a/S0 and prohibits B012a/S2a3j:Code: Select allx = 3, y = 2, rule = B2k3a/S0
o$2bo!
(1/512)
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
83bismuth38 wrote:Ooh a new twist: what is the most universal RULE? (it has the most oscillators, ships, guns, still lifes, replicators, agars, etc.)
x = 1, y = 1, rule = B1357/S1357
1000o!
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
Saka wrote:The most unuversal rule would be b3/s23 because it has been studied the most
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
Sphenocorona wrote:the list of all possible [insert object here] has a cardinality of ℵ₀
A for awesome wrote:Sphenocorona wrote:the list of all possible [insert object here] has a cardinality of ℵ₀
Are you sure? It seems like in some rules, some categories of objects may have cardinalities of ℵ₀, but wouldn't cardinalities more commonly be finite or ℵ₁?
Sphenocorona wrote:One issue with rule universality is that of defining when a rule has 'more' of some type of object than another when both have infinitely many objects of that type.
dvgrn wrote:Seems like you can't put any set of CA objects in one-to-one correspondence with real numbers, unless 100% of the objects have infinite population (ugh).
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
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