Page 1 of 1
Life with some death
Posted: June 14th, 2018, 11:02 pm
by Redstoneboi
Turing complete?
Code: Select all
x = 136, y = 141, rule = B3/S0123456
23bo8$128bo4$78bo2$104bo20$135bo4$39bo32$35bo4$15bo31$43bo4$43bo5$8b3o
$7b4o$7b6o$7bobo2bo$6b5ob2o$7bo2bobo$6b2ob5o$7bobo2bo$6b2obo2b2o9$50bo
2$obobo$8o$4bob3o$3ob5o$2b3ob3o$2bo3bo$7o$obobo!
Re: Life with some death
Posted: June 15th, 2018, 8:33 am
by Naszvadi
Nice find!
A 2D tiling of the whole plane with gates/turners containing only
still lifes where each row simulates a generation of a
Rule 110 automata provides the desired result - proof for TCness. Its construction is up to the community.
Such
TWO-dimensional automata simulation should be enough:
Code: Select all
x = 1, y = 1, rule = MAPdgD//wAA//8AAP//AAD//wAA//8AAP//AAD//wAA//8AAP//AAD//wAA//8AAP//AAD//wAA//8AAP//AAD//w
o
Notes to the above rule: Basically this is Rule-110 unless I miscalculated something. First 8 bits were set to 76h (reverse ordered bits of decimal number 110), padded with zeroes up to 16 bits, extended with 1 bits (word 0xffff) to 32 bits, then bigendian 0x0000ffff appended 15 times. Done with unix CLI, printf -ed, then piped with base64, inserted 3 letter string 'MAP' before the encoded string, pasted here, profit, enjoy!
Re: Life with some death
Posted: June 15th, 2018, 10:48 am
by KittyTac
I was looking at relatives of LWOD, but didn't find those interactions. Nice job!
Re: Life with some death
Posted: June 15th, 2018, 9:29 pm
by Redstoneboi
since dupers, multiple turners, and ladder blocking exist, it should be possible to make a 110 unit cell.
Re: Life with some death
Posted: June 15th, 2018, 11:16 pm
by Redstoneboi
WAIT A MINUTE
all of these seem to work in LWoD!
(except the last reflector, that should go die)
Code: Select all
x = 136, y = 141, rule = B3/S012345678
23bo8$128bo4$78bo2$104bo20$135bo4$39bo32$35bo4$15bo31$43bo4$43bo5$8b3o
$7b4o$7b6o$7bobo2bo$6b5ob2o$7bo2bobo$6b2ob5o$7bobo2bo$6b2obo2b2o9$50bo
2$obobo$8o$4bob3o$3ob5o$2b3ob3o$2bo3bo$7o$obobo!
TC proved as corollaries then.
Code: Select all
x = 136, y = 141, rule = B38/S012345678
23bo8$128bo26$135bo4$39bo32$35bo4$15bo31$43bo4$43bo5$8b3o$7b4o$7b6o$7b
obo2bo$6b5ob2o$7bo2bobo$6b2ob5o$7bobo2bo$6b2obo2b2o9$50bo2$obobo$8o$4b
ob3o$3ob5o$2b3ob3o$2bo3bo$7o$obobo!