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"Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 11:56 am
by Heavpoot
Inspired by 5s.
"Smallest" here is defined by transition count of the rule (e.g B/S1 actually counts as 2 transitions, S1c and S1e, B2a/S counts as 1 transition).
Spaceships do not have to be optimized for bounding box or cell count.
For example: (1,0)c/1 is 2 (B2ae/S):
Code: Select all
x = 2, y = 4, rule = B2ae/S
o$bo$bo$o!
No official spreadsheet or place to put these yet, but these would be interesting to find:
UPDATE: I have created a spreadsheet that is able to be edited by anyone. It can be found here: https://docs.google.com/spreadsheets/d/ ... sp=sharing
Re: "Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 12:20 pm
by Hunting
I strongly supports this thread.
(1,0)c/2, 5:
Code: Select all
x = 2, y = 3, rule = B2e3i/S1c2ec
o$bo$o!
(1,1)c/4, 4:
Code: Select all
x = 2, y = 3, rule = B2ce/S1
o$bo$bo!
will surely post more tomorrow.
I know there's no point to optimize the spaceship size, but smaller size generally takes less transistions. Also glide symmetric spaceships takes less transistions.
EDIT: Just relized (1,0)c/2 can be done with in 4 transistions:
Code: Select all
x = 5, y = 2, rule = B2k3ai/S0
o3bo$2bo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 5:35 pm
by Heavpoot
Thank you, Hunting!
I've updated the original thread. I'll see if I can find a proper place to put these soon.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 6:05 pm
by dani
B2ce/S0 (3 transitions) contains the following ships:
c/2 (AforAmpere, beats the old record):
Code: Select all
x = 3, y = 23, rule = B2ce/S0
bo$2bo$bo$o$o$bo$2bo$bo3$bo$2bo$bo$o$o$bo$2bo$bo$o$o$bo$2bo$bo!
2c/4 (2718281828):
Code: Select all
x = 29, y = 17, rule = B2ce/S0
7$10bobo2bobo$6bobo10bobo2$7b2o10b2o!
c/7 (2718281828):
Code: Select all
x = 19, y = 12, rule = B2ce/S0
4bo9bo$bo5bo3bo5bo2$9bo$2bo5bobo5bo$4bobo5bobo$9bo2$3bobo7bobo$o6bo3bo
6bo2$2bo2bo7bo2bo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 7:18 pm
by Hunting
dani wrote: March 18th, 2020, 6:05 pm
B2ce/S0 (3 transitions) contains the following ships:
c/2 (AforAmpere, beats the old record):
Code: Select all
x = 3, y = 23, rule = B2ce/S0
bo$2bo$bo$o$o$bo$2bo$bo3$bo$2bo$bo$o$o$bo$2bo$bo$o$o$bo$2bo$bo!
2c/4 (2718281828):
Code: Select all
x = 29, y = 17, rule = B2ce/S0
7$10bobo2bobo$6bobo10bobo2$7b2o10b2o!
c/7 (2718281828):
Code: Select all
x = 19, y = 12, rule = B2ce/S0
4bo9bo$bo5bo3bo5bo2$9bo$2bo5bobo5bo$4bobo5bobo$9bo2$3bobo7bobo$o6bo3bo
6bo2$2bo2bo7bo2bo!
Wow! Turns out directly optimizing the rule is better than optimizing the spaceship.
@Heavpoot please update
(Thinking) We'll need one bounding-box breaking transistion and one bounding-diamond transistion
Oh wait I'm still in non-B2a mode
Re: "Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 8:02 pm
by Heavpoot
Wow, thanks everyone! Updated. I really ought to find a better place to post these (where i can nicely post RLEs in bulk and collapse them, etc)
Re: "Smallest" INT rules supporting particular speeds
Posted: March 18th, 2020, 8:07 pm
by Hunting
Ridiculous baseline, (1,0)c/3, 7:
Code: Select all
x = 3, y = 2, rule = B2-cn3e/S2c3i
bo$obo!
(1,1)c/6, 7:
Code: Select all
x = 2, y = 3, rule = B2ce/S12aek
o$bo$bo!
Even more ridiculous, (1,1)c/8, 10:
Code: Select all
x = 4, y = 3, rule = B2ce3aijqr/S02ak
o$3bo$bobo!
(1,1)c/7, 10:
Code: Select all
x = 2, y = 4, rule = B2ce3aiqr/S02aek
bo$o2$bo!
Less ridiculous HuntingFinds:
(2,0)c/6, 5:
Code: Select all
x = 2, y = 3, rule = B2ce3n/S1
o$bo$bo!
(1,0)c/4, 9:
Code: Select all
x = 5, y = 2, rule = B2ek3ai4i5y/S03jk
2bo$o3bo!
(1,0)c/5, 9:
Code: Select all
x = 5, y = 2, rule = B2ek3i4i/S02a3j4iw
2bo$o3bo!
(4,0)c/8, 5:
Code: Select all
x = 5, y = 2, rule = B2ck3ai/S0
2bo$o3bo!
Meanwhile, directly optimizing the rule, (3,0)c/6, 5:
Code: Select all
x = 2, y = 8, rule = B2ce3n/S1
bo$o$bo3$bo$o$bo!
(10,0)c/24, 5:
Code: Select all
x = 14, y = 11, rule = B2ce3c/S1
o2bo6bo2bo$6b2o$o2bo6bo2bo2$13bo2$13bo2$o2bo6bo2bo$6b2o$o2bo6bo2bo!
I tried looking for (2,1)c/6s. Obviously no luck. 15:
Code: Select all
x = 3, y = 3, rule = B2ce3aiq4j/S012cek3jq5i
2bo$o$o!
(2,1)c/3, 15:
Code: Select all
x = 7, y = 3, rule = B2ac3q4an5kn/S1e3ar4iqr5ij
o2bo2bo$b2o$b5o!
I tried my best.
EDIT: (1, 1)c/2, 9:
Code: Select all
x = 4, y = 4, rule = B2a3a4r6e/S02e3ir4q
o2bo$b2o$b3o$obo!
EDIT: (2, 0)c/3, 10:
Code: Select all
x = 5, y = 3, rule = B2ack3ey/S02-ei
o3bo$bobo$bobo!
EDIT: (2, 0)c/2, 2:
Code: Select all
x = 2, y = 3, rule = B2ae/S
o$bo$bo!
EDIT: (1, 1)c/2 can be done with 8 transistions:
Code: Select all
x = 3, y = 3, rule = B2a3a4r5c/S3ai4er
3o$b2o$obo!
I'm not familiar with B2a rules, maybe someone can do better than me.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:08 am
by yujh
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:13 am
by FWKnightship
Hunting wrote: March 18th, 2020, 8:07 pm
(10,0)c/24, 5:
Code: Select all
x = 14, y = 11, rule = B2ce3c/S1
o2bo6bo2bo$6b2o$o2bo6bo2bo2$13bo2$13bo2$o2bo6bo2bo$6b2o$o2bo6bo2bo!
4:
Code: Select all
x = 24, y = 18, rule = B2ce/S1
o$23bo$o$o22bo$23bo$o$23bo$o$o22bo$23bo$o$23bo$o$o22bo$4bobo2bo3bo9bo$
o2bo10bo2bobo$4bobo2bo10bo2bo$10bo3bo2bobo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:17 am
by Hunting
yujh wrote: March 19th, 2020, 5:08 am
(4,0)c/4,2:
Good. (Trying to find a p3 photon)
EDIT: Oh, yep.
(3,0)c/3
Code: Select all
x = 3, y = 2, rule = B2ace/S
o$b2o!
FWKnightship wrote: March 19th, 2020, 5:13 am
Hunting wrote: March 18th, 2020, 8:07 pm
(10,0)c/24, 5:
Code: Select all
x = 14, y = 11, rule = B2ce3c/S1
o2bo6bo2bo$6b2o$o2bo6bo2bo2$13bo2$13bo2$o2bo6bo2bo$6b2o$o2bo6bo2bo!
4:
Code: Select all
x = 24, y = 18, rule = B2ce/S1
o$23bo$o$o22bo$23bo$o$23bo$o$o22bo$23bo$o$23bo$o$o22bo$4bobo2bo3bo9bo$
o2bo10bo2bobo$4bobo2bo10bo2bo$10bo3bo2bobo!
How did I miss that?
EDIT: (1,1)c/3
Code: Select all
x = 3, y = 3, rule = B2c3ar5k/S02a5a
3o$2o$o!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:24 am
by FWKnightship
(3,0)c/3,2:
Code: Select all
x = 10, y = 7, rule = B2ac/S
8b2o$2o2b2o2$2o2b2o$4b2o$3bo$3bo5bo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:32 am
by Hunting
FWKnightship wrote: March 19th, 2020, 5:24 am
(3,0)c/3,2:
Code: Select all
x = 10, y = 7, rule = B2ac/S
8b2o$2o2b2o2$2o2b2o$4b2o$3bo$3bo5bo!
Very clever.
Unrelated:
(1,0)c/4, 9:
Code: Select all
x = 3, y = 3, rule = B2ei3iy4a5y/S02ak
bo2$obo!
(2,0)c/4, 9:
Code: Select all
x = 3, y = 2, rule = B2ce3ae/S1c2c3e5i6c
bo$obo!
(2,1)c/4, 13 (didn't try hard):
Code: Select all
x = 5, y = 3, rule = B2-in3ekqr/S2k3a4eqr
bo2bo$3o$bobo!
Pure accidental (8,0)c/8, 4 - not even close to optimal:
Code: Select all
x = 11, y = 13, rule = B2ack3q/S
2b2o3b2o4$o9bo4$2b2o3b2o4$4bobo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:37 am
by FWKnightship
(6,0)c/6,2:
Code: Select all
x = 7, y = 13, rule = B2ac/S
b2o2b2o6$o2bob2o6$bo!
(8,0)c/8,2:
Code: Select all
x = 8, y = 16, rule = B2ac/S
3b2o$2o$3b2o$2o6$2o2$o2$6b2o2$5bo!
(12,0)c/12,2:
Code: Select all
x = 10, y = 19, rule = B2ac/S
b2o3b2o2$4bo2$4bo2$o7bo8$4bo2$4bo3b2o2$9bo!
(16,0)c/16,2:
Code: Select all
x = 8, y = 24, rule = B2ac/S
3b2o$2o$3b2o$2o14$2o2$o2$6b2o2$5bo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:45 am
by yujh
FWKnightship wrote: March 19th, 2020, 5:37 am
(6,0)c/6,2:
Code: Select all
x = 7, y = 13, rule = B2ac/S
b2o2b2o6$o2bob2o6$bo!
(8,0)c/8,2:
Code: Select all
x = 8, y = 16, rule = B2ac/S
3b2o$2o$3b2o$2o6$2o2$o2$6b2o2$5bo!
(12,0)c/12,2:
Code: Select all
x = 10, y = 19, rule = B2ac/S
b2o3b2o2$4bo2$4bo2$o7bo8$4bo2$4bo3b2o2$9bo!
(16,0)c/16,2:
Code: Select all
x = 8, y = 24, rule = B2ac/S
3b2o$2o$3b2o$2o14$2o2$o2$6b2o2$5bo!
Wow! That’s (8+4n,0)c/8+4n,2.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 5:50 am
by Hunting
yujh wrote: March 19th, 2020, 5:45 am
FWKnightship wrote: March 19th, 2020, 5:37 am
(6,0)c/6,2:
Code: Select all
x = 7, y = 13, rule = B2ac/S
b2o2b2o6$o2bob2o6$bo!
(8,0)c/8,2:
Code: Select all
x = 8, y = 16, rule = B2ac/S
3b2o$2o$3b2o$2o6$2o2$o2$6b2o2$5bo!
(12,0)c/12,2:
Code: Select all
x = 10, y = 19, rule = B2ac/S
b2o3b2o2$4bo2$4bo2$o7bo8$4bo2$4bo3b2o2$9bo!
(16,0)c/16,2:
Code: Select all
x = 8, y = 24, rule = B2ac/S
3b2o$2o$3b2o$2o14$2o2$o2$6b2o2$5bo!
Wow! That’s (8+4n,0)c/8+4n,2.
Yep. That's very impressive, and immediately beats the 8c/8 I just found.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 6:28 am
by FWKnightship
(4,4)c/8,4:
Code: Select all
x = 14, y = 18, rule = B2ac/S01e
bo$bo$o$bo2$3bob2o$6bo$5bo2bo4$12bo$8bo$8bo$7bo$8bo4bo2$10bo!
(4,0)c/5,5:
Code: Select all
x = 7, y = 10, rule = B2ac5a/S01e
bo3bo$bo3bo2$o5bo3$b5o$bo3bo$bo3bo$2bobo!
(8,0)c/10,5:
Code: Select all
x = 32, y = 37, rule = B2ac5a/S01e
3b2ob2o14b2ob2o$4bobo16bobo$o2b2ob2o2bo8bo2b2ob2o2bo$4bobo16bobo$o3bob
o3bo8bo3bobo3bo$o9bo8bo9bo2$5bo18bo2$14b2o5$24b2ob2o$25bobo$21bo2b2ob
2o2bo$13bo2bo8bobo$14b2o5bo3bobo3bo$21bo9bo2$26bo4$17bo5$15bo$16bo$15b
o$12bobo$15bo$16bo$15bo!
(48,0)c/60,5:
Code: Select all
x = 26, y = 53, rule = B2ac5a/S01e
16bo3bo$16bo3bo2$15bo5bo3$16b5o$16bo3bo$16bo3bo$17bobo$18bo5$12b2o11$b
o3bo14bo3bo$bo3bo6b2o6bo3bo2$o5bo12bo5bo3$b5o14b5o$bo3bo5bo2bo5bo3bo$b
o3bo14bo3bo$2bobo16bobo$3bo18bo6$2bo3bo12bo3bo$2bo3bo12bo3bo2$bo5bo10b
o5bo3$2b5o12b5o$2bo3bo12bo3bo$2bo3bo12bo3bo$3bobo14bobo$4bo16bo!
(96,0)c/120,5:
Code: Select all
x = 28, y = 300, rule = B2ac5a/S01e
17bo3bo$17bo3bo2$16bo5bo3$17b5o$17bo3bo$17bo3bo$18bobo$19bo11$13b2o10$
12bo2bo$11bob2obo$12bo2bo36$10bo6bo36$12bo2bo12$13b2o12$13b2o30$10bo6b
o6$10bo6bo6$12bo2bo12$10bo6bo36$12bo2bo6$13b2o6$10bo6bo6$13b2o18$12bo
2bo6$10bo6bo4$bo3bo16bo3bo$bo3bo16bo3bo$12bo2bo$o5bo14bo5bo3$b5o16b5o$
bo3bo16bo3bo$bo3bo16bo3bo$2bobo18bobo$3bo20bo14$3bo3bo12bo3bo$3bo3bo
12bo3bo2$2bo5bo10bo5bo3$3b5o12b5o$3bo3bo12bo3bo$3bo3bo12bo3bo$4bobo14b
obo$5bo16bo!
(4,0)c/8,5:
Code: Select all
x = 3, y = 21, rule = B2a3e/S1c2c3e
obo$bo5$2o13$3o$bo!
(8,0)c/16,5:
Code: Select all
x = 3, y = 36, rule = B2a3e/S1c2c3e
obo$bo8$2o25$3o$bo!
(2,0)c/6,7:
Code: Select all
x = 4, y = 16, rule = B2-cn3e/S2c3i
bo$obo6$2o6$bobo2$2bo!
(4,0)c/12,7:
Code: Select all
x = 4, y = 25, rule = B2-cn3e/S2c3i
obo2$bo4$2o17$2bo$bobo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 6:34 am
by yujh
(1,1)6,8
Code: Select all
x=0,y=0,rule=B2ce/S12kean
bo$bo$o!
This might need to be improved.
Searching in the SSSSS database.
I’m not good at rules.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 7:12 am
by Hunting
yujh wrote: March 19th, 2020, 6:34 am
(1,1)6,8
Code: Select all
x=0,y=0,rule=B2ce/S12kean
bo$bo$o!
This might need to be improved.
Searching in the SSSSS database.
I’m not good at rules.
Hunting wrote: March 18th, 2020, 8:07 pm
(1,1)c/6, 7:
Code: Select all
x = 2, y = 3, rule = B2ce/S12aek
o$bo$bo!
Uh?
(And yes, that ship comes from Just Friends.)
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 7:17 am
by yujh
Hunting wrote: March 19th, 2020, 7:12 am
yujh wrote: March 19th, 2020, 6:34 am
(1,1)6,8
Code: Select all
x=0,y=0,rule=B2ce/S12kean
bo$bo$o!
This might need to be improved.
Searching in the SSSSS database.
I’m not good at rules.
Hunting wrote: March 18th, 2020, 8:07 pm
(1,1)c/6, 7:
Code: Select all
x = 2, y = 3, rule = B2ce/S12aek
o$bo$bo!
Uh?
Hmm...
Maybe I haven’t noticed it.
Sorry.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 7:36 am
by Heavpoot
This has gotten an overwhelming amount of replies! Nice job everyone!
I have created a spreadsheet to put these in, it is in the original post. I will work on adding these, however feel free to contribute if you wish!
Update: Added all of them! That took a while. Be careful though, I had to skip over a few because they didn't improve on existing ones and were already there.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 7:46 am
by Hunting
Heavpoot wrote: March 19th, 2020, 7:36 am
This has gotten an overwhelming amount of replies! Nice job everyone!
I have created a spreadsheet to put these in, it is in the original post. I will work on adding these, however feel free to contribute if you wish!
Please add a mirror version, I can't access google because I'm in mainland China.
EDIT: Obviously not optimized (but is probably the best (3,1)c/4 that fits in a 5*6 box) but (3,1)c/4, 16:
Code: Select all
x = 4, y = 4, rule = B2ack3qr4an/S1e2ek3enq4ai5c
o2bo$2b2o$b3o$2bo!
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 8:09 am
by Heavpoot
Hunting wrote: March 19th, 2020, 7:46 am
Please add a mirror version, I can't access google because I'm in mainland China.
I'm not sure how to do this.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 8:20 am
by Hunting
Heavpoot wrote: March 19th, 2020, 8:09 am
Hunting wrote: March 19th, 2020, 7:46 am
Please add a mirror version, I can't access google because I'm in mainland China.
I'm not sure how to do this.
Can you give a text version of the spreadshit? Like using the CSV format.
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 8:26 am
by Heavpoot
Re: "Smallest" INT rules supporting particular speeds
Posted: March 19th, 2020, 8:29 am
by Hunting
Thank you.
Also unoptimized (3,0)c/5
Code: Select all
x = 3, y = 5, rule = B2aci4knty6a/S02-an3iq4j
o$b2o$2bo$3o$bo!
EDIT: For the spreadsheet I would say using 5S-like format (like: three columns - dx, dy and period for the speed) is better
The scoreand the rule should be seperated