"Smallest" INT rules supporting particular speeds

[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

[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!

[Heavpoot]

Thank you, Hunting!
I've updated the original thread. I'll see if I can find a proper place to put these soon.

[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!

[Hunting]

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

[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)

[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.

[yujh]

(4,0)c/4,2:

Code: Select all

x=0,y=0,rule=B2ac/S
obo$2bo!

[FWKnightship]

(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!

[Hunting]

(4,0)c/4,2:

Code: Select all

x=0,y=0,rule=B2ac/S
obo$2bo!

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!

(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!

[FWKnightship]

(3,0)c/3,2:

Code: Select all

x = 10, y = 7, rule = B2ac/S
8b2o$2o2b2o2$2o2b2o$4b2o$3bo$3bo5bo!

[Hunting]

(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!

[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!

[yujh]

(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.

[Hunting]

(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.

[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!

[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.

[Hunting]

(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.

(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.)

[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.

(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.

[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.

[Hunting]

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!

[Heavpoot]

Please add a mirror version, I can't access google because I'm in mainland China.

I'm not sure how to do this.

[Hunting]

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.

[Heavpoot]

Here you go!

Smallest INT rules public spreadsheet - Sheet1.csv

(4.13 KiB) Downloaded 177 times

[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