Challenges

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
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testitemqlstudop
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Re: Challenges

Post by testitemqlstudop » June 6th, 2019, 4:47 am

Oh my... f(2, 2, 1) is

Code: Select all

2!+
3!+
9!+
25!+
49!+
48!+
48!+
2304!+
108288!+
4981248!+
224156160!+
9862871040!+
424103454720!+
17812345098240!+
730306149027840!+
29212245961113600!+
1139277592483430400!+
43292548514370355200!+
1601824295031703142400!+
57665674621141313126400!+
2018298611739945959424000!+
68622152799158162620416000!+
2264531042372219366473728000!+
72464993355911019727159296000!+
2246414794033241611541938176000!+
67392443820997248346258145280000!+
1954380870808920202041486213120000!+
54722664382649765657161613967360000!+
1477511938331543672743363577118720000!+
38415310396620135491327453005086720000!+
960382759915503387283186325127168000000!+
23049186237972081294796471803052032000000!+
530131283473357869780318851470196736000000!+
11662888236413873135167014732344328192000000!+
244920652964691335838507309379230892032000000!+
4898413059293826716770146187584617840640000000!+
93069848126582707618632777564107738972160000000!+
1675257266278488737135389996153939301498880000000!+
28479373526734308531301629934616968125480960000000!+
455669976427748936500826078953871490007695360000000!+
6835049646416234047512391184308072350115430400000000!+
95690695049827276665173476580313012901616025600000000!+
1243979035647754596647255195544069167721008332800000000!+
14927748427773055159767062346528830012652099993600000000!+
164205232705503606757437685811817130139173099929600000000!+
1642052327055036067574376858118171301391730999296000000000!+
14778470943495324608169391723063541712525578993664000000000!+
118227767547962596865355133784508333700204631949312000000000!+
827594372835738178057485936491558335901432423645184000000000!+
4965566237014429068344915618949350015408594541871104000000000!+
24827831185072145341724578094746750077042972709355520000000000!+
99311324740288581366898312378987000308171890837422080000000000!+
297933974220865744100694937136961000924515672512266240000000000!+
595867948441731488201389874273922001849031345024532480000000000!+
595867948441731488201389874273922001849031345024532480000000000!
EDIT: By Stirling approximation that's only 3.714691769685526e+64 digits, so no, it doesn't even exceed g_3.

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Moosey
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Re: Challenges

Post by Moosey » June 6th, 2019, 8:05 am

fluffykitty wrote:You can do exactly the same thing as ltr_n but with ltr_n(n,n,n) (or similar) as the base function instead of f. From there extension to w^2 should be easy.
Okay, so if I define ç_n(x,y,z) as

Code: Select all

ç_n-1(x,x,x)ç_(n)(ç_n-1(x,x,x),y-1,z), n >0, y>0
ç_n-1(x,x,x)ç_(n)(ç_n-1(x,x,x),x,z-1), n > 0, y = 0, z>0
ç_n-1(x,x,x)ç_(n-1)(ç_n-1(x,x,x),x,x), n > 0, z = 0,y=0
ltr_x(x,x,x), n=0
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Re: Challenges

Post by fluffykitty » June 6th, 2019, 12:50 pm

Looks good.

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Moosey
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Re: Challenges

Post by Moosey » June 6th, 2019, 1:01 pm

fluffykitty wrote:Looks good.
Good, then I think this is a way to allow for infinitely many Mltrs equivalents, based upon each other
http://www.conwaylife.com/forums/viewto ... 004#p77218

I did it by creating an analog of f where it uses the ç analog of σM instead of factorials
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Re: Challenges

Post by Moosey » June 6th, 2019, 3:30 pm

PkmnQ wrote:み(x,y,z) = (x+y)! + み(xz,y,z-1)
み(x,y,0) = x! + み(x,y-1,xy)
み(x,0,0) = x!

ミ(x) = み(x+1,x+1,x^2)

み(1,1,0) = 3

み(2,2,1) = 24 + 2 + 6 + 9! + 25! + 49! + 48! + み(48,0,48)

Yeah...even with 4 statements it's powerful.
Don't know how it compares to tree though.
Couldn’t you just remove the addition and replace it with multiplication? n! > 0 for any n => 0, so your result would be far larger. Not that you should edit that post— just make a new function.

That reminds me of my old f(x,y,z), by the way—
f(x,0,0)= 1
f(x,0,z)= z!f(z,x,z-1), for z >0
f(x,y,z)=x!f(x!,y-1,z), for y > 0 and any z

I modified the way I phrased my definition to emphasize the similarity
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Moosey
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Re: Challenges

Post by Moosey » June 8th, 2019, 8:08 am

Two challenges:
1:
Find the largest SL by cell count you can which fits in this area, without searching using LLS or something

Code: Select all

x = 20, y = 11, rule = LifeHistory
2.5F$.2F3.2F$2F2.C2.13F$F2.CDC13.F$F.DCDC2D2CD2CDCD2C.F$F.2CD4CD2CD3C
DC.F$F.16D.F$F.2CD2CD2CD2CD2CDC.F$F.2CDCD2CD2CD2CD2C.F$F18.F$20F!
2:
Find a function which returns large countable ordinals given finite number inputs. Try to make the returned ordinal as large as possible.
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Re: Challenges

Post by fluffykitty » June 8th, 2019, 3:01 pm

2. q(a)=FGHordinal(b=>f(a,b)) using my f function

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testitemqlstudop
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Re: Challenges

Post by testitemqlstudop » June 22nd, 2019, 2:51 am

Find a non-explosive rule where

Code: Select all

x = 3, y = 1, rule = B/S0123456789
obo!
evolves into

Code: Select all

x = 7, y = 7, rule = B/S0123456789
2obob2o$obobobo$bo3bo$o2bo2bo$bo3bo$obobobo$2obob2o!

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Macbi
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Re: Challenges

Post by Macbi » June 22nd, 2019, 5:23 am

testitemqlstudop wrote:Find a non-explosive rule where

Code: Select all

x = 3, y = 1, rule = B/S0123456789
obo!
evolves into

Code: Select all

x = 7, y = 7, rule = B/S0123456789
2obob2o$obobobo$bo3bo$o2bo2bo$bo3bo$obobobo$2obob2o!

Code: Select all

x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!

Code: Select all

x = 8, y = 130, rule = B2ce3a4aci5y8/S02-cn3cij4c
6bo8$6bo2$6bo4$o2$o6bo80$3bobo2$3bobo12$4bo2$4bo7$3bo$4bo$3bo$2bo$4bo$
3bobo$4bo$2bo$3bo$4bo$3bo!

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testitemqlstudop
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Re: Challenges

Post by testitemqlstudop » June 22nd, 2019, 7:49 am

Macbi wrote:

Code: Select all

x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!
That doesn't evolve into my still life.

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Saka
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Re: Challenges

Post by Saka » June 22nd, 2019, 8:02 am

testitemqlstudop wrote:
Macbi wrote:

Code: Select all

x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!
That doesn't evolve into my still life.
Look at generation 8, you didnt say it had to be a still life.

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Re: Challenges

Post by Gamedziner » June 22nd, 2019, 9:54 am

testitemqlstudop wrote:
Macbi wrote:

Code: Select all

x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!
That doesn't evolve into my still life.
Logical breakdown:
  • Because the target pattern is a still-life, none of the following birth transitions can exist: B012ac3eky5c

    On the other hand, the following survival conditions must exist: S02ce3cn

    Only one birth condition can change the state from the starting condition under these circumstances:B2i

    The first generation after the starting pattern, when using a correct rule, must be (3o!).


    The survival condition S1e is now necessary, as the pattern will return to a 90-degree rotated version of gen 0 (or, in the case where B2i is used, it'll be a blinker).

    Here's where things start getting complicated: There are two possibilities for gen 2,
    (bo$obo$bo!) and (bo$3o$bo!).

    If you do not have S2i, you get (bo$obo$bo!).




    If, on the other hand, you do have S2i, you get (bo$3o$bo!).

    ▓▓▓



    CASE 1: S2i does not exist.
    ░▓░
    ▓░▓
    ░▓░

    In this case, all live cells will remain in gen 3.




    Now, there are three possibilities for gen 3:

    You can have B2e without B4e, in which case you get (3o$obo$3o!).

    ▓░▓



    You can have B4e without B2e, in which case you get (bo$3o$bo!).
    ░▓░

    ░▓░

    (This is the same pattern as in the other possibility for gen 2, but with a different set of birth requirements.)

    You can have both B2e and B4e, in which case you get (3o$3o$3o!).





    CASE 2: S2i does exist.
    ░▓░
    ▓▓▓
    ░▓░

    In this case, none of the cells are required to survive if and only if B3a exists, which on its own gives you (obo2$obo!):

    ░░░

    If you have B3a, S4e, and not S3i, you'll need to have S1c and not have S4c, as you cannot have B3e. This leads back to the above pattern with a one-generation delay.





    If you have B3a and S3i, then you get (3o$obo$3o!):




    If you have B3a, S3i, and S4e, then you get (3o$3o$3o!):

    ▓▓▓


    If you do not have B3a, then you must have S3i and not S4e, leading to (bo$obo$bo!):
    ░▓░

    ░▓░

    The logic gets too complicated to enumerate in a single post at this point.
(I spent way too long making this post, and I don't plan on summarizing it.)

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!

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Re: Challenges

Post by Macbi » June 23rd, 2019, 4:06 am

testitemqlstudop wrote:still life.

Code: Select all

x = 471, y = 113, rule = B2ei3ai4ae5a8/S01e2cen3acejn4i
216b2o$214bo$210b3o2bo4bo$210b3o2bo2bobo$210b3o$213bo2bo4bo4bobobo$
214bo4bobo4bo3bo$80b2ob2o$79b2o3b2o127bobo6bo2bo5bo$81bo3bo2bo124bobo
2bo4bobob3obo$76bo7b2ob3o128bobo$75b2o4bo8bo121bo9b2o3b2o$75bobobo4bo
125b2obo16bo$83bobo3bobo118bo4bobo9bo2bo$75bo5bo2bo6bo117b2o2bobo7b2o$
75b2obobobo5bo121bo9bo10bo4bobobo$76b3o2bo12bo115b2obo2b2o6bo4bobo4bo
3bo$92bo119bo6b2o$78bo19b2o123bobo6bo2bo5bo$77b2o4bo6bo3bo127bo2bo2bo
4bobob3obo$78bo2bo8bo6bo130bobo163bo2b4ob3ob2ob5obo5bo5bob2o2b2o2b2obo
2b5obo3bo4b2ob4o2b2o$79bo7b2o3bo129b2o8b2o3b2o155bob3obobo2bob2o3bob6o
4bo5bo2b2obo2b3o2b2ob3ob3obo2b2o2bo2b3ob2o$81b2o12bo2bobo118b2o19bo
153bo2b5o6b2o3b3o2b2obo2bo4bob2obo2bob4o3bo2b2o2b5ob3ob5obo$85bo3bo10b
o121bo2bobo9bo2bo154b3obo2bob2o3b3o4bo3bo2b2ob3obob2ob2o2bo3b2o3bob3o
3b2obobo2b2ob4o$97bo121bobobobo7b2o159bob4ob3o2b3o2bo4b3obob2obo5bo2bo
bo2bob4obo2bobo2bo2bob2o2b3ob4o$84bo2bo15bo118bo7bo10bo4bobobo144bo2b
5ob2ob3ob3ob4ob6o2b2ob6ob2ob2o6bo2bo3b5ob6obo$90bo10bo117b2o5b2o6bo4bo
bo4bo3bo145bo2bob2obobo2bobo4bo3b3obobob2ob2ob3obo2b5o2bobo3bo2b2o7b3o
$107b2o113b2o5b2o163b2obo3b5o3b2obob4ob2o3bob2o2b2o4b2o2bo4bobo2bo2b4o
4bobo2bo2bo$88bo3bo6bo3bo129bobo6bo2bo5bo142bo3b2o5bo3b2o3bobo2bo5bo2b
4ob3o2bo4b2ob2o2b2o3bo3b5obob4o$86bo3bo8bo6bo125bo2bo2bo4bobob3obo142b
5ob5o6b2o4bobobobobobo2b8o2b2o4b2obob4o3bobob2o5b2o$86bo9b2o3bo136bobo
155b2ob2obo2bo3bobob2o4bobo3bobobobobo2b2o3bo4b2o4b2o3bobob2ob2obo$90b
2o12bo2bobo122b2o8b2o3b2o145bobobo2b2ob2obob2o2b2obo2bo2bobo6b2o2b3o2b
o2bo2b3obobo3b2o5b3o$94bo3bo10bo119b2o19bo146b3o4b2obo2bobo2bobob2obob
o2bo2bo4b3ob5o3b2ob2o3bo4b3ob3ob3o$106bo125bo2bobo9bo2bo144bo2b2o2bo2b
4ob10o2bobob2obo5b3ob5ob2o2bobob3o4b4o2bob2o$93bo2bo15bo116bobobobo7b
2o149b2ob2obo2bob2ob2ob3o2bob2o2b2obobo5bo3b3o3bo3b2ob4ob3o2b4obo4bo$
99bo10bo121bo7bo10bo4bobobo134bobobo5b3o2bobob4o3b4obob2o3bo2b3ob4o2b
3o6b2ob2o3bo3b4o$116b2o111b2o5b2o6bo4bobo4bo3bo134bob2obobo4b5obo4bo3b
ob5ob3o7b2obob2obo2bobob2o4b2o2b3o2bo$97bo3bo6bo3bo119b2o5b2o154bob3o
4b2obo4bob3o3b2obo4b2o3bo2bo4b3ob3o2b2o2b3o2b3o2bo2b2obo$95bo3bo8bo6bo
127bobo6bo2bo5bo132bob3obo2b2obo6b5ob3o4bo2bo4bo2bo3bobobob5o3b2o2bob
4o3b2o$95bo9b2o3bo131bo2bo2bo4bobob3obo133bobo6bo2bo3bo7bo2bo3b3o2b4o
2b2ob2o2bob3obo2bobo5bobo2b2ob2o$99b2o12bo2bobo129bobo143b2o3bo8b2obo
2bobo2bo4bob4obo2b2o3b3ob3o2bo2bob2o5b4ob3o2bo$103bo3bo10bo123b2o8b2o
3b2o135bobo4b2ob4o2bob9obobobo2b2o2bob2o3bob4ob2obo3b2ob6o2bobobo$115b
o123b2o19bo136bo3b3obob2o2b2obo3bo2b2ob4o3b2ob3ob3o2bo2b4obo3b3o3b2o4b
3o$102bo2bo15bo120bo2bobo9bo2bo134bo2b2obo3b4ob2o2b2o4b2o3bobo2b2ob2ob
o5b2o3bo2bo4bob8ob2obo$108bo10bo119bobobobo7b2o139bo10b3obo4b8ob2o2bob
o3b4o2b2ob4o3bo2b2ob3ob4ob2o2bo$125b2o115bo7bo10bo4bobobo126bo3b3ob4o
2bobobo3b3obo2b5obobobo2bo2bob9o2bo4b2ob3ob2obo$106bo3bo6bo3bo117b2o5b
2o6bo4bobo4bo3bo123bob3o2b3obobob3o5bob2o3bob2ob2o4bo3bob5obo2b5ob2ob
3ob3o$104bo3bo8bo6bo117b2o5b2o143b2o4b4ob2o4bo3b6obob4o3bo5bobob2o7b
10ob2o5b2o$104bo9b2o3bo133bobo6bo2bo5bo122bo2b3o3bobo3b2o2bob2ob2o5b3o
2b3obob2obobo2bo5bo2bo3b2obob3obob3o$108b2o12bo2bobo124bo2bo2bo4bobob
3obo122b4ob4ob2o2bobo4b2ob2o2bobo3b5o2b2o3bob2obo2bobobobobo6b2obo2bo$
112bo3bo10bo130bobo134b4o3b3o2b2o5b3ob4obo6b7obo4b4o2b2ob2o2bob8ob3o$
124bo127b2o8b2o3b2o126b2o2bo2bobo2b2obobo4b4o4b3o5b2o4bob2obo4bo2b8o3b
obo3b2o$111bo2bo15bo118b2o19bo123bo2b2obob2o2b2o2bo2b3obo3bo3bob2obob
2obo3b5o4bo3bob6obo4b2obo$117bo10bo123bo2bobo9bo2bo123bob2ob2o2bob2ob
2ob2obobobo2b2obobob3obo2bo2bo3b6obob4obo2b4o2b3o$134b2o113bobobobo7b
2o131b3o2b2o2bobobo2b2o4bob2ob2obobob2obobo2b4obobobo3bo2b4o3b3o2bob2o
$115bo3bo6bo3bo121bo7bo10bo4bobobo113b4obo2b3o7b3obo6bo5bob2obob3o2b2o
3b2obobo4b7obo$113bo3bo8bo6bo115b2o5b2o6bo4bobo4bo3bo115bo2bob5ob2o2b
4ob2o2b3o2b7ob3o2bo2bo3b2o3b2o4bob4o8bo$113bo9b2o3bo123b2o5b2o134bobob
5o2b2o6bobobobob2o2bob2o4bo2b2o4b3ob2ob2ob4o4b2obo3b2o$117b2o12bo2bobo
126bobo6bo2bo5bo112bo2bobob2obo2b5obob3obo4bo6b8o6b3o3bob2o2bobob2o2b
3o$obo118bo3bo10bo125bo2bo2bo4bobob3obo113bob4ob3obob4obo2bo2b3ob4o5bo
b3o2bo2b2o4bo3bobobo3bobob3ob2o$133bo134bobo123bobob3obob3ob2o2bobob3o
2b2ob2obobo2bob5o2b2ob3o2b4o3bo3b2o2bobobobo$120bo2bo15bo122b2o8b2o3b
2o115bo3b2obob4ob3o5bo2bob3o4bo3b5o4bob3o4b7o6bob2o2bo$126bo10bo121b2o
19bo113b2ob2ob5o2bo3b3ob2obobo2bob3o4bo3b2o6b7ob5o4b2o2b2obobo$143b2o
117bo2bobo9bo2bo116bo2b9obo3b2o2bobob2ob3o3bob3ob5obobobo3b2obo6bo4b2o
b2o$124bo3bo6bo3bo119bobobobo7b2o119bobobobobo2bo3bo2b3ob2o3b7o2b2ob4o
bob3ob2ob3o3b3obobo3b2obo2b2o$122bo3bo8bo6bo119bo7bo10bo4bobobo106b2o
2b2ob2o3bobo2b4o2bobobo3bobobob7o3bo3bo3b2ob2o9bo$122bo9b2o3bo121b2o5b
2o6bo4bobo4bo3bo104b4o2bobob2ob5ob2o2b12o2b2o2bo3bo3b3obob3obo2b2o3b2o
b2obo$126b2o12bo2bobo116b2o5b2o124bobobob6o2bo3b3obobobo3b2o2b3ob6obob
ob2o2b2o2b2o4bobo2b2o4b2o$130bo3bo10bo127bobo6bo2bo5bo104bobo2bob2o3b
3obobo3b4o4b2ob3o3b2o3b4obob2o3b2ob2obo4b2o2bob2o$142bo129bo2bo2bo4bob
ob3obo104b5obob2ob3ob2obob3obo4b3o5b2o2bobo9b3o3bob4ob3ob4o$129bo2bo
15bo129bobo113b4o4bobo5b2obobobo3b2o2bo2b2o7b3obobo3b6o4b2ob2obobob3o$
135bo10bo125b2o8b2o3b2o105b2obob2o3b5ob5ob6o3b2o2bob2obo3b2o3b3o3b2ob
3o2bobobob2o2b2obo$152b2o115b2o19bo103bo2b5o2b4o3b3ob4o2bo2bobo2bobob
2obobob4o3bo3bobobo2b3o3bo2b2o$133bo3bo6bo3bo123bo2bobo9bo2bo103b2o2b
3obob3ob3ob2ob2o7b5ob4obo2b2o2b4ob2ob2o3b2ob2obobo3bo2bo$131bo3bo8bo6b
o117bobobobo7b2o109b2o2bo4bob2o2bob6o2bo3b3o2bobob3o2b2o2b2obo2bob2o2b
2o2b2o2bobob3obo$131bo9b2o3bo125bo7bo10bo4bobobo93b2o2bobo5b2o3bob2o2b
2o2bob3obob6o4bobobo3bo2b8ob2o2bob5o$135b2o12bo2bobo114b2o5b2o6bo4bobo
4bo3bo93bobobo2b3obo7b4ob5o6b6obo3bo4bobob4obo2b2o2b4o$139bo3bo10bo
117b2o5b2o113bobob3o2bob3obobobobob2obo2bo3b3o6b2ob4o2b3ob2o2bobo2bo6b
2obo$151bo131bobo6bo2bo5bo92bobobobo3bo5bo2bob2obo4bobo3b3o2bobo2b2o4b
o2bob2ob2o3b2ob9o$138bo2bo15bo124bo2bo2bo4bobob3obo96bobobo2bobo3b2o2b
o3b3ob2o4b2o2bob2o2bo2b3o6b4obob4ob4o2b2o$144bo10bo132bobo105bob3o2b2o
3bo3b2o2bob2o3b2o2b2obob4o2b2obo3b3ob2ob4o2bobob5ob3o$161b2o119b2o8b2o
3b2o95bob5o6b4obobo2bo2b6o3b5o2bobobo3bob2o3b2ob3ob5obobo2b2o$142bo3bo
6bo3bo121b2o19bo93b8o4bo2bo2bobo3bo6bo6b3o2b2ob2obob2obo2bob2o2b2obo4b
2obo$140bo3bo8bo6bo121bo2bobo9bo2bo93bobob3o2b2ob2o2bob2ob6o2b2ob3ob4o
3bo4bobob2o2bobobobo2bo2b5o2bo$140bo9b2o3bo123bobobobo7b2o100bob5ob3o
2bo5bo3bob2obo2bobob2o2b6o2b3o5bo6bob4ob2obo$144b2o12bo2bobo118bo7bo
10bo4bobobo83b3o2b3ob4o2bo3b3o3bob5o2b2obo2b2o3b3o3bob3o6b2o7bo2b3o$
148bo3bo10bo115b2o5b2o6bo4bobo4bo3bo83b2o4bobobo2bo2b2ob2ob2o3bobo2b3o
2b3ob3ob2ob5o4b2ob6ob2obo2bo2bo$160bo121b2o5b2o104b2o2b2o2b2obob6obob
3ob2o2b3o4bo2bo2bobo4b4o2b4obo3bo3bo3bo$147bo2bo15bo126bobo6bo2bo5bo
82b3ob2o2b2obob2o3bobo2bob5ob2obo2b2o4bo3bo2b3obobo2b2o2bobob2o2b4obo$
153bo10bo127bo2bo2bo4bobob3obo82bo2b2o2bo4bo2b2obob2o3bo2b2ob4o4bobo3b
ob2obo4b3o6bobobo3b2o2bo$170b2o126bobo93bo2bobo4b3obo2bobo3bo2b3obobo
2b4ob5o4bob3obo5bob2o3b2o2b2ob2o$151bo3bo6bo3bo125b2o8b2o3b2o87b2ob3o
2bo2b6o2b2obo3bobo6bobo5b2o3b5o2bo2b2ob2o6bo3b2o$149bo3bo8bo6bo119b2o
19bo83b3o3bob4o2b2o4b2obo5b3ob2ob4ob2ob6o10b3o5bo2b2obo$149bo9b2o3bo
127bo2bobo9bo2bo84b4ob5ob2o2bobobo2b2obobo3bobobobobo4bo4b2o4bob3o3bob
obo2bo2bo$153b2o12bo2bobo116bobobobo7b2o89b3ob2obobob2ob2o3bo2b8obo3bo
b2obobo2b3obob4ob3o5bobo5b4o$157bo3bo10bo119bo7bo10bo4bobobo73bobo5bo
2bo2b5o3b2obobobo3b2ob3obobo2b2ob2o2bob2ob4o2bo5bobob2o$169bo119b2o5b
2o6bo4bobo4bo3bo74b5o3bobob5o5bo2b5o3b3o2b3ob5o5b2o3b3ob3o2b4obobobo$
156bo2bo15bo116b2o5b2o93bobob3obo6b2ob4o2bo2bobo2bobo2b2o2b3o4bobo5bob
2o3b2o2bo6b2o$162bo10bo129bobo6bo2bo5bo72bo2bo5b2o3b4o5bo2b2obobo2b2ob
3obo3bobobo3bob2obo2b2ob5o4b3o$302bo2bo2bo4bobob3obo73bo5bo3b3o4bobo4b
obob2ob3o3b2ob5ob2o2bob4ob2obob2obobo2b3o2bo$160bo3bo6bo3bo132bobo84bo
bobob2o5bobo3b3o5bo3b5obobobo2b2ob3ob3o7b3ob2obo2b5o$158bo3bo8bo130b2o
8b2o3b2o77b5ob3ob4o3bo4b2obo2bo2bob5ob5obob2o3bo4b4obo2b2o2bob3o$158bo
9b2o3bo125b2o19bo74b2o2b2obobobobob2ob2o3b2o2bob4o2b3o5b2obo3bo5bob2o
2bo2bobob2ob4o$162b2o138bo2bobo9bo2bo73b2obo4b2obobob2o2b4obo3bob6ob2o
2bobo2b3o2bo4b2ob3ob2o5b3o2bo$166bo3bo128bobobobo7b2o$302bo7bo10bo4bob
obo$165bo2bo130b2o5b2o6bo4bobo4bo3bo$302b2o5b2o$313bobo6bo2bo5bo$312bo
2bo2bo4bobob3obo$318bobo$312b2o8b2o3b2o$309b2o19bo!

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Re: Challenges

Post by Moosey » July 7th, 2019, 1:08 pm

Define the largest countable ordinal you can.
Disclaimer: fluffykitty is probably really good at this, though I imagine a lot of you are.
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Re: Challenges

Post by testitemqlstudop » July 21st, 2019, 11:38 pm

Find a larger "still life tree" than this:

Code: Select all

x = 18, y = 40, rule = B3/S23
4b2o$4b2o3$5bo$5bo3$4b2o$4bobo$5bo2$4bo2bo$3bo4bo$2bo6bo2$bo8bo$obo6bo
bo$bobo5bobo$2bo7bo3$10bo$10bo3$10bo$9bobo$9bo2bo$10b2o2$8bo4bo$7bo6bo
$6bo8bo3$4b2o9b2o$3bo2bo7bo2bo$4bo2bo6bo2bo$5b2o8b2o!

(A "still life tree" is created by repeating the following process on a starting still life as many times as possible:

1. Take an ON cell of the current still life.
2. Set it to OFF and set any two adjacent OFF cells (Von-Neumman neighborhood) to ON, ensuring the resulting pattern is a still life.
3. Find all the still lives that can be possibly made from step 2, and do step 1 on all these still lives.

)

Soon, this process will construct a "tree". Find the largest possible such "tree", or prove that it can be infinite.

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Re: Challenges

Post by toroidalet » July 22nd, 2019, 12:27 am

It's more of a directed acyclic graph, but:

Code: Select all

x = 100, y = 140, rule = LifeHistory
39.2A$38.A.A$39.A$36.A5.A$36.7A2$36.7A$36.A5.A$34.D4.A$31.D.D4.A.A$
31.2D6.2A$31.3D2$39.D$39.D$37.D.D.D$38.3D$39.D3$22.A16.A$21.A.A14.A.A
$20.A.A15.A.A$21.A17.A$18.A5.A11.A5.A$18.7A11.7A2$18.7A11.7A3.2D$18.A
5.A11.A5.A5.2D$21.A17.A10.2D$20.A.A15.A.A4.D6.2D2.D$15.D5.2A12.D3.2A
5.D7.2D.D$14.D19.D12.D8.3D$13.D7.D11.D14.D.D5.3D$10.D.D8.D8.D.D6.D9.
2D$10.2D9.D8.2D5.D.D.D6.3D$10.3D6.D.D.D6.3D5.3D$20.3D16.D$21.D$5.A72.
A$4.A.A70.A.A$3.A.A16.A16.2A17.2A17.A.A$4.A16.A.A14.A2.A15.A2.A17.A$.
A5.A12.A.A15.A.A17.A.A14.A5.A$.7A13.A17.A19.A15.7A$18.A5.A11.A5.A13.A
5.A$.7A10.7A11.7A13.7A12.7A$.A5.A67.A5.A$4.A13.7A11.7A13.7A15.A$3.A.A
12.A5.A11.A5.A13.A5.A14.A.A$4.A.A14.A17.A19.A17.A.A$5.A14.A.A15.A.A
17.A.A17.A$20.A.A16.2A18.2A$15.D5.A56.D$14.D24.D16.4D18.D$13.D7.D15.
3D11.5D22.D$10.D.D6.D.D.D9.4D2.D9.2D25.D.D.D$10.2D8.3D5.5D6.D6.3D28.
3D$10.3D8.D4.2D11.D2.4D32.D$25.D12.DE2D$21.4D11.2D.D$15.6D14.D3.D$13.
3D17.2D2.D.D.D$10.D.D19.D5.3D$4.A5.2D10.A8.D7.D38.2A$3.A.A4.3D8.A.A4.
D.D46.A2.A$2.A.A15.A.A5.2D27.A19.A.A$3.A17.A6.3D25.A.A19.A$A5.A11.A5.
A14.A16.A2.A15.A5.A$7A11.7A13.A.A16.A.A15.7A$37.A2.A17.A$7A11.7A12.A.
A15.A5.A13.7A$A5.A11.A5.A13.A16.7A13.A5.A$3.A17.A13.A5.A36.A$2.A.A15.
A.A12.7A13.7A15.A.A$2.A2.A13.A2.A2.D29.A5.A12.D2.A.A3.D$3.2A2.D12.2A
4.D.D6.7A16.A14.D4.A5.D$8.D.D16.2D6.A5.A12.D2.A.A10.D.D12.D.D$9.2D15.
3D9.A12.D.D4.2A10.2D14.2D$8.3D26.A.A11.2D17.3D5.D6.3D$34.D3.2A11.3D
22.D.D.D$33.D43.3D$30.D.D45.D$30.2D$30.3D2$79.A$78.A.A15.2A$21.A16.A
19.2A17.A2.A14.A2.A$20.A.A14.A.A17.A2.A16.A.A15.A.A$19.A.A14.A.A18.A.
A18.A17.A$20.A16.A20.A16.A5.A11.A5.A$17.A5.A10.A5.A14.A5.A13.7A11.7A$
17.7A10.7A14.7A$75.7A11.7A$17.7A10.7A14.7A13.A5.A11.A5.A$17.A5.A10.A
5.A14.A5.A16.A17.A$20.A16.A20.A18.A.A15.A.A$19.A.A14.A.A18.A.A17.A.A
14.A2.A$19.A2.A12.A2.A18.A2.A17.A16.2A$20.A.A12.A.A20.2A$21.A14.A44.D
13.D$56.D.D.D14.D6.D10.D.D.D$57.3D14.D8.D10.3D$58.D12.D.D10.D.D8.D$
71.2D12.2D$59.A11.3D10.3D8.A$58.A.A33.A.A$57.A2.A33.A2.A$57.A.A35.A.A
$58.A37.A$55.A5.A31.A5.A$55.7A31.7A2$55.7A31.7A$55.A5.A31.A5.A$58.A
37.A$57.A.A35.A.A$57.A2.A34.A2.A$58.2A36.2A$96.D$56.D37.D.D.D$54.D.D.
D36.3D$55.3D38.D$56.D$59.A35.A$58.A.A33.A.A$57.A2.A33.A2.A$57.A.A35.A
.A$58.A37.A$55.A5.A31.A5.A$55.7A31.7A2$55.7A31.7A$55.A5.A31.A5.A$58.A
37.A$57.A.A35.A.A$57.A2.A34.A2.A$58.A.A35.A.A$59.A37.A!
Chain them together with a beehive of length 5 to increase the possibilities.
EDIT: Skewing them allows for even more still lives to be derived; I won't draw a tree for this one.
EDIT2: Then you can chain those 7-tables and add 2 bookends on each end (whose hooks can be turned into tubs)
Any sufficiently advanced software is indistinguishable from malice.

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Re: Challenges

Post by testitemqlstudop » July 22nd, 2019, 12:35 am

ArGGGGH I DID NOT MEAN COMBINATIONS

Define an "elementary still life" as a still life whose islands are not still lives. For example table-on-table is elementary but block-on-table is not. TWIT is elementary since it is one island.

Find an elementary still life tree

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Re: Challenges

Post by toroidalet » July 22nd, 2019, 12:44 am

Y O U C A N N O T W I N

Code: Select all

x = 91, y = 76, rule = LifeHistory
18.2A5.2A$18.A.A3.A.A$19.A.A.A.A$21.A.A$21.A.A$22.A6$18.A$17.A.A5.2A
7.2A5.2A$18.A.A3.A.A7.A.A3.A2.A$19.A.A.A.A9.A.A.A.2A$21.A.A13.A.A$21.
A.A13.A.A$22.A15.A7$2.A7.A7.A37.A$.A.A5.A.A5.A.A5.2A7.2A5.2A5.2A5.A.A
4.2A5.2A$2.A.A3.A.A7.A.A3.A2.A6.A.A3.A2.A4.A.A3.A2.A3.A2.A3.A2.A$3.A.
A.A.A9.A.A.A.2A8.A.A.A.A.A5.A.A.A.2A5.2A.A.A.2A$5.A.A13.A.A13.A.A2.A
8.A.A11.A.A$5.A.A13.A.A13.A.A11.A.A11.A.A$6.A15.A15.A13.A13.A6$.A15.A
7.A16.2A$A.A5.2A6.A.A5.A.A7.2A5.A2.A29.A$.A.A3.A2.A6.A.A3.A2.A7.A.A3.
A2.A6.2A5.2A7.2A5.A.A5.2A5.2A$2.A.A.A.A.A7.A.A.A.2A9.A.A.A.2A7.A.A3.A
2.A5.A2.A3.A2.A4.A2.A3.A2.A$4.A.A2.A10.A.A14.A.A11.A.A.A.A2.A5.2A.A.A
.2A6.2A.A.A.A.A$4.A.A13.A.A14.A.A13.A.A2.2A9.A.A12.A.A2.A$5.A15.A16.A
14.A.A13.A.A12.A.A$54.A15.A14.A3$89.A$42.2A22.A7.A6.2A5.A.A$.A16.A7.
2A6.2A5.A2.A5.2A5.2A6.A.A5.A.A4.A2.A3.A2.A$A.A5.2A7.A.A5.A2.A4.A2.A3.
A2.A5.A2.A3.A2.A5.A2.A3.A2.A4.A.A.A.A.2A$.A.A3.A2.A7.A.A3.A2.A6.2A.A.
A.2A7.2A.A.A.A2.A5.2A.A.A.2A6.A2.A.A$2.A.A.A.A2.A7.A.A.A.2A10.A.A13.A
.A2.2A9.A.A12.A.A$4.A.A2.2A10.A.A13.A.A13.A.A13.A.A13.A$4.A.A14.A.A
14.A15.A15.A$5.A16.A3$59.2A$34.A7.2A7.2A5.A2.A$33.A.A5.A2.A5.A2.A3.A
2.A$33.A2.A3.A2.A6.A.A.A.A.2A$34.2A.A.A.2A8.A2.A.A$37.A.A14.A.A$37.A.
A15.A$38.A5$32.2A7.2A16.2A$31.A2.A5.A2.A7.2A5.A2.A$32.A2.A3.A2.A7.A2.
A3.A2.A$33.2A.A.A.2A7.A2.A.A.A.2A$36.A.A11.2A2.A.A$36.A.A15.A.A$37.A
17.A!
Draw the arrows if you want.
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Re: Challenges

Post by testitemqlstudop » July 22nd, 2019, 1:17 am

Flpppt.

Find a still life tree where every still life cannot "contain" 2 or more smaller still lives.

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Re: Challenges

Post by Moosey » July 22nd, 2019, 7:47 am

testitemqlstudop wrote:Flpppt.

Find a still life tree where every still life cannot "contain" 2 or more smaller still lives.
If your rules were a little different and allowed for setting a cell to ON:

Code: Select all

x = 45, y = 12, rule = LifeHistory
21.6D$11.8D2.D4.D$11.D6.D2.D3.3D$2.6D3.D5.3D.D4.D$2.D4.D3.D6.D2.D22.D
$2.D3.3D2.D9.D4.A11.D$2.D4.D3.D6.A6.A.A4.D$9.A7.A.A5.A.A$2.A5.A.A6.A.
A4.2A.2A$.A.A4.A.A5.2A.2A$.A.A3.2A.2A$2A.2A!
EDIT: different SL tree type--:
Every arrow represents a way to cleanly get exactly one copy of their target by adding/removing one cell from the source

Code: Select all

x = 26, y = 31, rule = LifeHistory
6.7D$6.D5.D$6.D5.D$6.D4.3D$6.D5.D$6.D$6.5D.2A$12.2A2$12.D2.D$.11DE3DE
7D$.D10.D4.D.D3.D$.D9.3D4.2D2.3D$.D10.D4.3D3.D$22.A$.A3.D2.D3.A5.D2.A
.A$A.A.6D.A.A.5D.A.A$.A3.D2.D3.2A4.D3.A2$12.D2.D$11.3D2.D$12.D4.D.D$
12.D5.2D$11.3D3.3D$12.D$23.2A$22.A2.A$23.A.A$11.2A3.D2.D4.A$11.A.A.6D
$12.2A2.D2.D!
Here's a larger tree than yours by edges:

Code: Select all

x = 18, y = 40, rule = LifeHistory
4.2A$4.2A3$5.D$5.D3$4.2A$4.A.A$5.A2$4.D2.D$3.D4.D$2.D6.D2$.A8.A$A.A6.
A.A$.A.A5.A.A$2.A7.A$4.D$5.D$6.D3.D$7.D2.D$8.D2$10.A$9.A.A$9.A2.A$10.
2A2$8.D4.D$7.D6.D$6.D8.D3$4.2A9.2A$3.A2.A7.A2.A$4.A2.A6.A2.A$5.2A8.2A
!

It's valid all right.
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Re: Challenges

Post by testitemqlstudop » July 27th, 2019, 2:51 am

Here's a difficult challenge: complete any of the following almost-reflectors. -Not in Life-

(AbphzTa!)

Code: Select all

x = 69, y = 21, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
2o$2o3$5b2o50b2o$5b2o50b2o9$14b2o50b2o$16bo51bo$15bo51bo$11b3o49b3o$
11bo2bo48bo2bo$11bobo49bobo$12b2o50b2o!

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Re: Challenges

Post by Moosey » July 27th, 2019, 7:12 am

testitemqlstudop wrote:Here's a difficult challenge: complete any of the following almost-reflectors. -Not in Life-

(AbphzTa!)

Code: Select all

x = 69, y = 21, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
2o$2o3$5b2o50b2o$5b2o50b2o9$14b2o50b2o$16bo51bo$15bo51bo$11b3o49b3o$
11bo2bo48bo2bo$11bobo49bobo$12b2o50b2o!
That isn't... is it...? Is it the dreaded X3VI?
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Re: Challenges

Post by testitemqlstudop » July 27th, 2019, 10:36 pm

pretends i didn't hear anything

THE FIRST SEMI-REFLECTOR IS EDGY

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Re: Challenges

Post by Moosey » July 28th, 2019, 7:25 am

testitemqlstudop wrote:pretends i didn't hear anything

THE FIRST SEMI-REFLECTOR IS EDGY
Unfortunately it's edgy in the wrong direction; the input would hit it
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Re: Challenges

Post by testitemqlstudop » July 28th, 2019, 8:42 am

Beg pardon?

Code: Select all

x = 29, y = 43, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
10b2o$10b2o3$15b2o$15b2o5$2o$2o19b2o$23bo$22bo$5b2o11b3o$5b2o11bo2bo$
18bobo$19b2o19$26b2o$28bo$27bo$23b3o$23bo2bo$23bobo$24b2o!

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