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toroidalet

Off-topic, but here's a repeat time 51 electron-G converter: x = 25, y = 30, rule = WW_LIFE 12.D$12.D$12.D$12.D.D$12.D$12.D$12.D$12.D$12.D$12.D$10.D.D$12.D$6.D4. D$6.D4.D3$11.2A5.2D$2.2D6.A2.A4D.2DBCD$.D9.2A5.2D.B2.D$.D19.D2.D$.D 17.2D3.D$2.D3.D4.D6.D5.D$3.D2.D4.D7.3D2.D$4.D9.2D6.D.D$5.9D.7D2.D$14. ...

toroidalet

If for you, universes mean what I think they mean (each universe is a copy of the "dimension ascend" structure with the power to oracle any lower universe), then it would only be ω_(ω^(ω+1))^CK (in the future, I'll ignore the ω_^CK bit for convenience). Of course, you can add dimensions of universes...

toroidalet

I'm pretty sure that "tape ascend" is ω_ω^CK (but much faster than the diagonal busy beaver), since it can access an arbitrary but finite (otherwise it would never halt) oracle level, making it the limit of all the oracle Turing machine functions. Similarly, "plane ascend" is ω_(ω^2)^CK,"space ascen...

toroidalet

Is the well ordering of w_1 provable? Isn't well-orderedness part of the definition of an ordinal? If I'm missing something, then see this proof (set X to be the set of natural numbers to get the conclusion that ω_1 exists and is well-ordered) Thanks now I understand everything. But what about w-1?...

toroidalet

This is sort of a stupid question, but why isn't ε_1=ε_0^ω?

toroidalet

x = 256, y = 256, rule = B1357/S02468:T256,256 b2ob2ob2ob2ob2obob2ob2ob2ob2ob2ob3o3b3o3b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o b2ob3o3b3o3b3o5b3o3b3o3b3ob2ob2ob2ob2ob3ob2ob2ob2ob2ob3o3b3o3b3o5b3o3b 3o3b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3o3b3o3b3ob2ob2ob2ob2ob2obob2ob2o b2ob2ob2o$bo3bobo3bobo5bobo3bobo3bo5bo5...

toroidalet

x = 256, y = 256, rule = B1357/S02468:T256,256 bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo bobobobobobobobobobobobobobobobobobobob...

toroidalet

All the buzz has been about colliding gliders to cleanly make a Sir Robin. But is it possible for a finite amount of Sir Robins to cleanly make a single glider? After all, the knightship's so big it's hard to clean any reaction up. Colliding 35 pairs of Sir Robins like this can create any 35-glider...

toroidalet

#C [[ PASTET EVERY 41 ]] #C [[ PASTE bo$obo$bo! 0 12 ]] #C [[ PASTE bo$obo$bo! 134 12 ]] x = 137, y = 27, rule = B3/S23 4bo127bo$4b3o123b3o$7bo121bo$6b2o12bo31bo31bo31bo12b2o$20bo31bo31bo31b o$2o18bo31bo31bo31bo18b2o$bo133bo$bobo129bobo$2b2o129b2o2$16bo7bo23bo 7bo23bo7bo23bo7bo$14b2ob2o3b2ob2o19b2o...

toroidalet

Rules that start with R are still displayed as 2-state rules, and patterns in invalid rules are not displayed at all at zoom levels below -1.0 (zoomed out more than 1 pixel/cell). Test cases: x = 2, y = 1, rule = Rule ABC! x = 2, y = 1, rule = R5B3C3 ABC! This variant is a fringe bug of little impor...

toroidalet

Can you fix the bug where only state 1 shows up for patterns in invalid rules, or is that one of those "me bugs"?

toroidalet

p268 18c/54 gun: x = 150, y = 15, rule = WWEJ3 2.C$.C.C$C$.C$2.13CGBCHB2CFBCEBCEBCEBCEBCEBCEBCEBCFB5CEBCEBCEBCIB14CK BCLB3CFBCEBCHBCFBCFBCFBCEBCLBCHBCFBCFBCEBCLBCFBCHBCFBCFBCFBCFBCLBCHB 2C$.C9.C3.G133.F$C10.C3.13CBECBHCBFCBFCBHCBFCBLCBFCBHCBFCBKCBECBECBFC BFCBFCBHCBKCBFCBFCBFCBFCBHCBFCBKCBECBFCBFCBH...

toroidalet

The paper Transfinite Game Values in Infinite Chess (which also provides an infinite 2D chess position with a value of ω^3) proves that with infinite configurations, the ordinal of 3d chess (it also works on 3D chess with finite but sufficiently large thickness) is ω_1 (first uncountable ordinal). W...

toroidalet

652: x = 254, y = 249, rule = B3/S23 50b2o33bob2o15b2obo26b2o$5b2ob2o15b2ob2o19bob3o30b2obo17bob2o23b3obo$ 6bobo17bobo20bobo2bo32bo17bo25bo2bobo$8bo17bo21b2o2b2obo31b2o15b2o24bo b2o2b2o$8b2o15b2o24bob2o7b2o20bo37b2o7b2obo$15b2ob2o12b3o8bo4b2obo7bob o2bo18bobo6bob2ob2obo7bobo10bo2bobo7bob2o3bo$3bobo7...

toroidalet

Here's a mediocre rule with a p330 binary counter: x = 3, y = 4, rule = B2-ak3ai4n5/S2i3-i4-q5iq8 obo3$obo! p330*2^n oscillators (and probably guns) can be constructed fairly trivially. Here are some hassler-based guns for a small 2c/6 ship: p63: x = 35, y = 14, rule = B2-ak3ai4n5/S2i3-i4-q5iq8 18b2...

toroidalet

Dani posted a comment about the tube replicator a while ago. Binary counter (sort of) based on it: x = 71, y = 66, rule = B3-ckq4z/S2-c3-a4iq5k6k 14b3ob3o11b3ob3o11b3ob3o$14bobobobo11bobobobo11bobobobo63$3ob3o57b3ob 3o$obobobo57bobobobo! 12c/168 (c/14) ship: x = 372, y = 192, rule = B3-ckq4z/S2-c3-a...

toroidalet

11G synthesis of Saka's pattern: x = 71, y = 60, rule = Polystate_B3S23_3 4$61.B$60.B$60.3B7$4.B$5.B$3.3B$7.B$6.B$6.3B2$.2A$.2A4$3.2A2.2B50.A$ 2.A.A2.B.B48.A$4.A2.B50.3A4$35.2B$30.2A3.2B$30.2A3$33.2A2B$33.2A2B3$ 36.2A$37.2A$36.A6.3A$43.A$44.A4$50.2A$50.A.A$50.A! Cool catalysis: x = 7, y = 7, rule = ...

toroidalet

101: x = 14, y = 15, rule = LifeHistory 6.2E$6.E$2E5.3E$E.A.3A2.E$2.A.A2.E$.EA2.A.2E$E2.2A.A2.E$.E.A2.ADE.A$ 2.A2.A.ED.A$3.EA2.A.2A.2E$4.E.2A4.E$2.E2.A2.3A.E$2.2E.E.E2.E.2E$5.E.E $5.2E! EDIT: 98 x = 16, y = 15, rule = LifeHistory 3.2E$4.E$3.E$2.A.3A$2.A.A2.E.2E$.EA2.A.E.E.E$E2.2A.A2.E2.E.2E$.E.A2.A ...

toroidalet

There are total functions based on intermediate Turing degrees (r.e. sets that aren't universal or recursive) that dominate every computable function but are dominated by the busy beaver function, i.e. f M (n)=(the maximum time Turing machine M takes to accept a string of length n), where M is any T...

toroidalet

90: x = 16, y = 9, rule = LifeHistory 9.2E$5.E2.E2.E$.A2.A.A2.2E.A.2E$.AE2A2.2A3.A.E$3.D.2A.DA.A2.A$.AEA.E 2.2A.E2A$E2.E.E$2E2.E3.4E$8.E2.E! Here are 2 others: x = 16, y = 10, rule = LifeHistory 10.2E$2E8.E.E$E.E5.2E2.E$2.A2.D.A2.2E.AE$.EA.2A2.2A3.A.E$2.E.A.2A.DA. A2.A$2.A.A4.2A.E2A$3.2E$9.4E$9.E2.E...

toroidalet

This is the l‮esimorp I eno t‮sa wrote:
December 4th, 292277026596, 11:30 am
Is 922‭3372036854775807 some kind of power?

toroidalet

x = 5, y = 5, rule = B/S012345678 5o$2bo$2bo$2bo$2bo! [[ RLE e 5o$o$5o$o$5o! ]] [[ RLE s 5o$o$5o$4bo$5o! ]] [[ PASTEMODE COPY ]] [[ PASTET 1 ]] [[ PASTE e 0 0 ]] [[ PASTET 2 ]] [[ PASTE s 0 0 ]] [[ LOOP 3 ]] [[ AUTOSTART ]] [[ GPS 2 ]] This is the longest necropost on the forums. This is the shorte...

toroidalet

Saka wrote: ↑

December 31st, 1969, 8:00 pm

Code: Select all

x = 5, y = 5, rule = B/S012345678
5o$2bo$2bo$2bo$2bo!
[[ RLE e 5o$o$5o$o$5o! ]]
[[ RLE s 5o$o$5o$4bo$5o! ]]
[[ PASTEMODE COPY ]]
[[ PASTET 1 ]]
[[ PASTE e 0 0 ]]
[[ PASTET 2 ]]
[[ PASTE s 0 0 ]]
[[ LOOP 3 ]]
[[ AUTOSTART ]]
[[ GPS 2 ]]

This is the longest necropost on the forums.

toroidalet

2-engine ship: x = 22, y = 92, rule = B3/S2-in3-ace4ikqz 17b3o$16bo3bo$19b2o$14bo6bo$13bo2bobobo$13bo3b2o$13b3o2$18bobo$8bo$7bo $11bo$9bobo$8bo2bo$2b5o3bo$2bo2bobo$2bobob3o$3b2o54$2b3o$2bobo$bo2b2o$ o2bo2$b2o$2bo$2bo6$2bo$2bo$b2o2$o2bo$bo2b2o$2bobo$2b3o! There's probably a slower B-based ship moving...

toroidalet

Infinite periodic patterns in B2a/S are Turing complete. This makes it the simplest universal rule. Here is an ANDNOT gate: x = 217, y = 155, rule = B2a/S 108bo105bo$108bo105bo$106b2o107b2o$161bo31bo$111b2o48bo31bo16b2o$110bo 101bo$110bo101bo11$108bo105bo$108bo105bo$106b2o107b2o$145bo$111b2o32bo 64b...

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