Page 8 of 16
Re: Challenges
Posted: June 6th, 2019, 4:47 am
by testitemqlstudop
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.
Re: Challenges
Posted: June 6th, 2019, 8:05 am
by Moosey
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
Re: Challenges
Posted: June 6th, 2019, 12:50 pm
by fluffykitty
Looks good.
Re: Challenges
Posted: June 6th, 2019, 1:01 pm
by Moosey
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
Re: Challenges
Posted: June 6th, 2019, 3:30 pm
by Moosey
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
Re: Challenges
Posted: June 8th, 2019, 8:08 am
by Moosey
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$20F!
2:
Find a function which returns large countable ordinals given finite number inputs. Try to make the returned ordinal as large as possible.
Re: Challenges
Posted: June 8th, 2019, 3:01 pm
by fluffykitty
2. q(a)=FGHordinal(b=>f(a,b)) using my f function
Re: Challenges
Posted: June 22nd, 2019, 2:51 am
by testitemqlstudop
Find a non-explosive rule where
Code: Select all
x = 3, y = 1, rule = B/S0123456789
obo!
evolves into
Code: Select all
x = 7, y = 7, rule = B/S0123456789
2obob2o$obobobo$bo3bo$o2bo2bo$bo3bo$obobobo$2obob2o!
Re: Challenges
Posted: June 22nd, 2019, 5:23 am
by Macbi
testitemqlstudop wrote:Find a non-explosive rule where
Code: Select all
x = 3, y = 1, rule = B/S0123456789
obo!
evolves into
Code: Select all
x = 7, y = 7, rule = B/S0123456789
2obob2o$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$3bo!
Re: Challenges
Posted: June 22nd, 2019, 7:49 am
by testitemqlstudop
Macbi wrote:Code: Select all
x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!
That doesn't evolve into my still life.
Re: Challenges
Posted: June 22nd, 2019, 8:02 am
by Saka
testitemqlstudop wrote:Macbi wrote:Code: Select all
x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!
That doesn't evolve into my still life.
Look at generation 8, you didnt say it had to be a still life.
Re: Challenges
Posted: June 22nd, 2019, 9:54 am
by Gamedziner
testitemqlstudop wrote:Macbi wrote:Code: Select all
x = 3, y = 1, rule = B2ce3a4aci5y8/S02-cn3cij4c
obo!
That doesn't evolve into my still life.
Logical breakdown:
- Because the target pattern is a still-life, none of the following birth transitions can exist: B012ac3eky5c
On the other hand, the following survival conditions must exist: S02ce3cn
Only one birth condition can change the state from the starting condition under these circumstances:B2i
The first generation after the starting pattern, when using a correct rule, must be (3o!).
▓▓▓
The survival condition S1e is now necessary, as the pattern will return to a 90-degree rotated version of gen 0 (or, in the case where B2i is used, it'll be a blinker).
Here's where things start getting complicated: There are two possibilities for gen 2,
(bo$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.)
Re: Challenges
Posted: June 23rd, 2019, 4:06 am
by Macbi
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!
Re: Challenges
Posted: July 7th, 2019, 1:08 pm
by Moosey
Define the largest countable ordinal you can.
Disclaimer: fluffykitty is probably really good at this, though I imagine a lot of you are.
Re: Challenges
Posted: July 21st, 2019, 11:38 pm
by testitemqlstudop
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.
Re: Challenges
Posted: July 22nd, 2019, 12:27 am
by toroidalet
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)
Re: Challenges
Posted: July 22nd, 2019, 12:35 am
by testitemqlstudop
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
Re: Challenges
Posted: July 22nd, 2019, 12:44 am
by toroidalet
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.
Re: Challenges
Posted: July 22nd, 2019, 1:17 am
by testitemqlstudop
Flpppt.
Find a still life tree where every still life cannot "contain" 2 or more smaller still lives.
Re: Challenges
Posted: July 22nd, 2019, 7:47 am
by Moosey
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.
Re: Challenges
Posted: July 27th, 2019, 2:51 am
by testitemqlstudop
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!
Re: Challenges
Posted: July 27th, 2019, 7:12 am
by Moosey
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?
Re: Challenges
Posted: July 27th, 2019, 10:36 pm
by testitemqlstudop
pretends i didn't hear anything
THE FIRST SEMI-REFLECTOR IS EDGY
Re: Challenges
Posted: July 28th, 2019, 7:25 am
by Moosey
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
Re: Challenges
Posted: July 28th, 2019, 8:42 am
by testitemqlstudop
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!