wwei23 wrote:Find one of those that uses a replicator not based on this one.
Do we have to use 2-sate isotropic, or can we do a non-symmetric rule with this behavior?
wwei23 wrote:Find one of those that uses a replicator not based on this one.
AforAmpere wrote:wwei23 wrote:Find one of those that uses a replicator not based on this one.
Do we have to use 2-sate isotropic, or can we do a non-symmetric rule with this behavior?
AforAmpere wrote:wwei23 wrote:Find one of those that uses a replicator not based on this one.
Do we have to use 2-sate isotropic, or can we do a non-symmetric rule with this behavior?
x = 143, y = 86, rule = LifeHistory
54.4B50.B$55.4B48.2B$56.4B46.3B$57.4B44.4B$58.4B42.4B$59.4B40.4B$60.
4B38.4B$61.4B36.4B$62.4B34.4B$63.4B32.4B$64.4B30.4B$65.4B28.4B$36.2A
11.A16.4B4.B21.4B$35.B2AB9.A.A16.4B2.3B19.4B$36.3B9.A.A17.9B5.2A10.4B
$35.B.B9.2A.3A2.2A12.9B4.A10.4B$35.5B8.B4.A2.A13.8B.BA.A9.4B$35.6B6.
2AB3A3.A.AB2.4B3.9B.B2A9.4B$35.8B4.2A.A6.2AB2.5B2.11B10.4B$36.13B10.
8B2.11B9.4B$34.13B12.21B8.4B$33.15B12.19B8.4B$33.15B10.B2.19B6.4B$32.
17B.B5.26B3.4B$32.51B.4B$31.13B2A13B2A21B.4B$30.14B2A13B2A25B$29.2AB
3.50B$28.A2.A4.48B$27.A.2A5.6B3.B2.2B2.33B$27.A7.6B13.4B2.7B2.16B$26.
2A6.9B17.6B3.18B$33.4B4.2A19.3B5.18B$32.4B5.A21.B4.3B.9B3.B2CB$31.4B
7.3A23.2A3.8B4.BC3B6.B$30.4B10.A24.A6.4B5.BCBC2B4.3B$29.4B33.3A5.4B6.
3B2C5B.3B$28.4B34.A7.2A8.18B$27.4B44.A8.19B$26.4B42.3A10.18B$25.4B43.
A10.19B$24.4B55.7B2C12B$23.4B56.7B2C6B.3B2C$22.3CB58.8B2.4B2.2B2C$22.
2BC61.6B9.4B$23.C62.5B11.4B$86.5B12.4B$87.3B14.4B$88.B16.4B$106.3B$
107.2B$108.B11$116.4B19.B$117.4B6.E10.2B$.2A115.4B5.3E7.4B$A.A116.4B
7.E5.4B$2.A117.4B5.2E4.4B$121.4B4.9B$122.4B5.6B$123.4B2.8B$124.15B$
125.14B$126.13B$127.10B.B2E$129.3B2EB3.BE.E$129.3B2EB6.E$131.4B6.2E$
131.3B$128.EB.2B$127.E.EB2EB$127.E.EBEBEB$124.2E.E.E.E.E2.E$124.E2.E
2.2E.4E$126.2E4.E$132.E.E$133.2E!
#C [[ THUMBNAIL THUMBSIZE 2 Z 4 ]]
x = 88, y = 47, rule = LifeHistory
32.4B50.B$33.4B48.2B$34.4B46.3B$35.4B44.4B$36.4B42.4B$37.4B40.4B$38.
4B38.4B$39.4B36.4B$40.4B34.4B$41.4B32.4B$42.4B30.4B$43.4B28.4B$14.2A
11.A16.4B4.B21.4B$13.B2AB9.A.A16.4B2.3B19.4B$14.3B9.A.A17.9B5.2A10.4B
$13.B.B9.2A.3A2.2A12.9B4.A10.4B$13.5B8.B4.A2.A13.8B.BA.A9.4B$13.6B6.
2AB3A3.A.AB2.4B3.9B.B2A9.4B$13.8B4.2A.A6.2AB2.5B2.11B10.4B$14.13B10.
8B2.11B9.4B$12.13B12.21B8.4B$11.15B12.19B8.4B$11.15B10.B2.19B6.4B$10.
17B.B5.26B3.4B$10.51B.4B$9.13B2A13B2A21B.4B$8.14B2A13B2A25B$7.2AB3.
50B$6.A2.A4.48B$5.A.2A5.6B3.B2.2B2.33B$5.A7.6B13.4B2.7B2.16B$4.2A6.9B
17.6B3.16B$11.4B4.2A19.3B5.14B$10.4B5.A21.B4.3B.9B4.2C$9.4B7.3A23.2A
3.8B3.C2.C$8.4B10.A24.A6.4B4.C2.C$7.4B33.3A5.4B7.2C$6.4B34.A7.2A$5.4B
44.A$4.4B42.3A$3.4B43.A14.2C9.2C$2.4B59.C.C8.2C$.4B61.C$3CB$2BC$.C!
x = 87, y = 46, rule = LifeHistory
32.4B50.B$33.4B48.2B$34.4B46.3B$35.4B44.4B$36.4B42.4B$37.4B40.4B$38.
4B38.4B$39.4B36.4B$40.4B34.4B$41.4B32.4B$42.4B30.4B$43.4B28.4B$14.2A
11.A16.4B4.B21.4B$13.B2AB9.A.A16.4B2.3B19.4B$14.3B9.A.A17.9B5.2A10.4B
$13.B.B9.2A.3A2.2A12.9B4.A10.4B$13.5B8.B4.A2.A13.8B.BA.A9.4B$13.6B6.
2AB3A3.A.AB2.4B3.9B.B2A9.4B$13.8B4.2A.A6.2AB2.5B2.11B10.4B$14.13B10.
8B2.11B9.4B$12.13B12.21B8.4B$11.15B12.19B8.4B$11.15B10.B2.19B6.4B$10.
17B.B5.26B3.4B$10.51B.4B$9.13B2A13B2A21B.4B$8.14B2A13B2A25B$7.2AB3.
50B$6.A2.A4.48B$5.A.2A5.6B3.B2.2B2.33B$5.A7.6B13.4B2.7B2.16B$4.2A6.9B
17.6B3.16B$11.4B4.2A19.3B5.14B$10.4B5.A21.B4.3B.9B4.C$9.4B7.3A23.2A3.
8B3.C.C$8.4B10.A24.A6.4B4.C2.C$7.4B33.3A5.4B7.2C$6.4B34.A7.2A$5.4B44.
A$4.4B42.3A$3.4B43.A11.2C$2.4B55.C.C$.4B56.2C$3CB$2BC$.C!
dvgrn wrote:I'm in need of a one-time attachment to a Scorbie Splitter that gets an extra glider out, but only the first time the circuit is used.
x = 87, y = 46, rule = LifeHistory
32.4B50.B$33.4B48.2B$34.4B46.3B$35.4B44.4B$36.4B42.4B$37.4B40.4B$38.
4B38.4B$39.4B36.4B$40.4B34.4B$41.4B32.4B$42.4B30.4B$43.4B28.4B$14.2A
11.A16.4B4.B21.4B$13.B2AB9.A.A16.4B2.3B19.4B$14.3B9.A.A17.9B5.2A10.4B
$13.B.B9.2A.3A2.2A12.9B4.A10.4B$13.5B8.B4.A2.A13.8B.BA.A9.4B$13.6B6.
2AB3A3.A.AB2.4B3.9B.B2A9.4B$13.8B4.2A.A6.2AB2.5B2.11B10.4B$14.13B10.
8B2.11B9.4B$12.13B12.21B8.4B$11.15B12.19B8.4B$11.15B10.B2.19B6.4B$10.
17B.B5.26B3.4B$10.51B.4B$9.13B2A13B2A21B.4B$8.14B2A13B2A25B$7.2AB3.
50B$6.A2.A4.48B$5.A.2A5.6B3.B2.2B2.33B$5.A7.6B13.4B2.7B2.14B$4.2A6.9B
17.6B3.14B7.2A$11.4B4.2A19.3B5.13B7.A.A$10.4B5.A21.B4.3B.9B10.A$9.4B
7.3A23.2A3.8B3.2A$8.4B10.A24.A6.4B3.A2.A$7.4B33.3A5.4B6.2A$6.4B34.A7.
2A$5.4B44.A$4.4B42.3A$3.4B43.A$2.4B$.4B$3CB$2BC$.C!
x = 87, y = 46, rule = LifeHistory
32.4B50.B$33.4B48.2B$34.4B46.3B$35.4B44.4B$36.4B42.4B$37.4B40.4B$38.
4B38.4B$39.4B36.4B$40.4B34.4B$41.4B32.4B$42.4B30.4B$43.4B28.4B$14.2A
11.A16.4B4.B21.4B$13.B2AB9.A.A16.4B2.3B19.4B$14.3B9.A.A17.9B5.2A10.4B
$13.B.B9.2A.3A2.2A12.9B4.A10.4B$13.5B8.B4.A2.A13.8B.BA.A9.4B$13.6B6.
2AB3A3.A.AB2.4B3.9B.B2A9.4B$13.8B4.2A.A6.2AB2.5B2.11B10.4B$14.13B10.
8B2.11B9.4B$12.13B12.21B8.4B$11.15B12.19B8.4B$11.15B10.B2.19B6.4B$10.
17B.B5.26B3.4B$10.51B.4B$9.13B2A13B2A21B.4B$8.14B2A13B2A25B$7.2AB3.
50B$6.A2.A4.48B$5.A.2A5.6B3.B2.2B2.33B$5.A7.6B13.4B2.7B2.14B$4.2A6.9B
17.6B3.14B$11.4B4.2A19.3B5.13B3.A$10.4B5.A21.B4.3B.9B4.A.A$9.4B7.3A
23.2A3.8B4.A.A$8.4B10.A24.A6.4B6.A$7.4B33.3A5.4B$6.4B34.A7.2A$5.4B44.
A$4.4B42.3A$3.4B43.A$2.4B57.A$.4B57.A.A$3CB59.2A$2BC$.C!
chris_c wrote:You don't state how useful a glider heading NW would be. Maybe because it is useless or maybe it didn't occur to you as an option (like me)...
dvgrn wrote:A glider-to-c/3-spaceship converter whose RLE fits in a forum posting and so can be run in LifeViewer.
aforampere sort of wrote:Either way, it’s rather nontrivial to devise a computable system which exceeds TREE(3)
fluffykitty wrote:Here's a somewhat boring entry:
f(0,x)=x
f(a,x)=f(g(a,a,x),x+1)
g(4b+2,x,n)=b
g(a,x,0)=0
g(4b+1,x,n+1)=2^g(x,x,n)*(4b+2)
g(2^a*(4b+2),x,n+1)=2^g(a,a,n+1)*(4*g(2^a*(4b+2),x,n)+2)
g(2^a*(4b+2)-1,x,n+1)=2^g(a,x,n+1)*(4*g(2^a*(4b+2)-1,x,n)+2)-1
Submit f(2^2^16,n)
If you want to test this function, use something like f(8,n) since even f(2^2^16,1) is massive.
Approximations of other functions:
Successor: f(2,n)
Weak Goodstein sequences/Ackermann function: f(512,n)
Strong Goodstein sequences/Simple hydras/tree: f(4,n)
TREE: f(2^(2^2046-1),n)
Something stronger than TREE: f(2^2^16,n)
Odd first arguments of f are not guaranteed to work correctly.
fluffykitty wrote:Done, but you won't like it
σM(δM(m-1,σM(n))), m>0
σM(n), m=0
δM(δM(δM(σM(σM(10^100)),σM(σM(10^100))),σM(σM(10^100))),δM(δM(σM(σM(10^100)),σM(σM(10^100))),σM(σM(10^100))))
fluffykitty wrote:deltmoose only adds 1 more FGH level (w+3), so your number is easily beaten by f_(w+4)(4) or f(2^2219,4) in my function. To gain more power, you need to do something like Mltrs again.
δM(δME_(n-1)(p,q),δME_(n-1)(p,q)), n > 0
δM(p,q), n = 0
δME_(Mgltrs(n-1,p,q))(p,q), n > 0
δΜ(p,q), n = 0
Mgltrs(дM(n-1),дM(n-1),дM(n-1)), n>0
Mgltrs(googol,googol,googol), n=0
дM(дME_(m-1)(n)) n > 0
дM(n), n = 0
дME_(Mcltrs(n-1))(m), n>0
дM(googol,googol,googol), n = 0
fluffykitty wrote:δME is FGH level w+4, Mgltrs is FGH level w+5, дM is FGH level w+6, дME is infinite but if defined correctly would be FGH level w+7, Mcltrs would be w+8, and the diagonalizer of M*ltrs would be w2. Try comparing the definitions of Mlrts and Mgltrs to see why one is a much larger step up than the other.
fluffykitty wrote:The problem is each function is nesting the previous function in a simple fashion, so each step adds 1 to the FGH level. However, the ltr_n function adds 2 to the FGH level for each increment of n, so something like ltr_n(4,4,4) has FGH level w.
fluffykitty wrote:Well first you need an analog of ltr_n at the f_(w+n) level. Then you can nest that to get a much stronger Mgltrs function, make another ltr_n analog... and then diagonalize over all of these levels to reach w^2.
x = 3, y = 3, rule = B26/S2|B358/S3
2o$2bo$obo!
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