Outrunning the Glider

[Hdjensofjfnen]

Post any diagonal spaceships (EDIT: preferably in non-B0 rules) that can outrun the glider (c/4) below!
For starters:
2c/7d, one transition from Life: (EDIT: Shown with glider)

Code: Select all

x = 11, y = 11, rule = B3/S234w
9bo$10bo$8b3o4$bo2bo$o3bo$4bo$3bo$3o!

c/3d, a lot of transitions from Life:

Code: Select all

x = 3, y = 3, rule = B2e3-j4a/S2-k3-ry4q5i
obo$2bo$3o!

[muzik]

This rule also has a c/3d: viewtopic.php?f=11&t=3194&p=54127#p54076

[PkmnQ]

Here's an alternating rule that has a c/2 that I call "Slider":

Code: Select all

@RULE B26S2B358S3

@TABLE
n_states:3
neighborhood:Moore
symmetries:permute

#B26S2
0,1,1,0,0,0,0,0,0,2
0,1,1,1,1,1,1,0,0,2
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,1,1,0,0,0,0,0,0,2
1,1,1,1,0,0,0,0,0,0
1,1,1,1,1,0,0,0,0,0
1,1,1,1,1,1,0,0,0,0
1,1,1,1,1,1,1,0,0,0
1,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1,1,0

#B358S3
0,2,2,2,0,0,0,0,0,1
0,2,2,2,2,2,0,0,0,1
0,2,2,2,2,2,2,2,2,1
2,0,0,0,0,0,0,0,0,0
2,2,0,0,0,0,0,0,0,0
2,2,2,0,0,0,0,0,0,0
2,2,2,2,0,0,0,0,0,1
2,2,2,2,2,0,0,0,0,0
2,2,2,2,2,2,0,0,0,0
2,2,2,2,2,2,2,0,0,0
2,2,2,2,2,2,2,2,0,0
2,2,2,2,2,2,2,2,2,0

And here's the ship itself:

Code: Select all

x = 3, y = 3, rule = B26S2B358S3
A.A$A$.2A!

[wildmyron]

There was some discussion about the fastest possible diagonal spaceship speeds in 2-state rules on the Moore nighbourhood, both with and without B0, some time ago but I can't remember which thread it was in. For non-totalistic rules, the limit is c:

Code: Select all

x = 1, y = 1, rule = MAPQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

For isotropic rules with B0, the limit is 3c/4. Here's a small one which moves at that speed

Code: Select all

x = 3, y = 2, rule = B02akn3n4ak5ak6a/S01e2k4r5a6e7e
2bo$2o!

There's a nice collection of low period diagonal ships in rules with B0 here, many of which are faster than c/4.

In isotropic rules without B0, the limit is c/2:

Code: Select all

x = 3, y = 4, rule = B2ac/S1
2bo2$b2o$o!

There are example c/2 ships with many different periods in the 5S diagonal collection. You'll also find example ships for all speeds k/P c for P/4 < k <= P/2, where P < 20 as well as many more for P > 20.

In my collections of small spaceships I have over a hundred such ships which have a minimum population of 3 cells, and there would be far more if I hadn't filtered low period ships out of most of those searches.

Now, if you restrict the rulespace to isotropic rules in which the CGoL glider works, then I suspect the speed limit is c/3, but that's just a guess on my part. Here's a 2c/7 ship racing a glider.

Code: Select all

x = 9, y = 7, rule = B3-r4k5jy6e7c/S02-ci3ajnqr4arw5ak6e
7b2o$6b2o$6bo2$2bo$obo$b2o!

If you'd like to find more ships like this, then logic life search is your friend.

Code: Select all

./lls -r pB2-ace3aijn4-r5-n678/S02ae3jnr4-k5678 -b 7 -p 7 -x 2 -y 2 -i -s 'D2\'

is the command I used to find the 2c/7 above.

==========

Here are a few of the ships from the 5S collection:

c/2, period 4

Code: Select all

x = 3, y = 3, rule = B2-ei3aq4ik5ceq/S02aei3acjn4aijny5ejkn6ein7e
o$b2o$bo!

2c/5, period 2

Code: Select all

x = 3, y = 3, rule = B2aci3a4ny5a/S03i4ajw5a7c
2bo2$obo!

c/2, period 6

Code: Select all

x = 3, y = 3, rule = B2ac3a/S02-ik3a
o$b2o$bo!

c/3, period 6

Code: Select all

x = 3, y = 3, rule = B2cik3a4qt5kny6n/S01e2k3ejkn4ktw5ek6n
2bo2$obo!

3c/7, period 7

Code: Select all

x = 3, y = 3, rule = B2-en3ak4iw5acr/S02ek3aiy5ck
2bo2$obo!

c/2, period 8

Code: Select all

x = 3, y = 4, rule = B2acn3y4e/S12-ei3c4ey
2bo2$b2o$o!

3c/8, period 8

Code: Select all

x = 3, y = 3, rule = B2-ek3ae4r5a/S01e3j4e5ack
2bo2$obo!

[77topaz]

Now, if you restrict the rulespace to isotropic rules in which the CGoL glider works, then I suspect the speed limit is c/3, but that's just a guess on my part. Here's a 2c/7 ship racing a glider.

Code: Select all

x = 9, y = 7, rule = B3-r4k5jy6e7c/S02-ci3ajnqr4arw5ak6e
7b2o$6b2o$6bo2$2bo$obo$b2o!

Surprisingly, this rule also has a third tiny diagonal spaceship - but this one has a speed of c/19:

Code: Select all

x = 3, y = 3, rule = B3-r4k5jy6e7c/S02-ci3ajnqr4arw5ak6e
obo$2bo$3o!

EDIT: And there's a small 3c/17 diagonal too!

Code: Select all

x = 5, y = 5, rule = B3-r4k5jy6e7c/S02-ci3ajnqr4arw5ak6e
o$3bo$2b2o$b2obo$3b2o!

[cvojan]

Wow... that's a lot of spaceships

[Βεν Γ. Κυθισ]

I have these two hexagonal generations spaceships:

Code: Select all

x = 134, y = 132, rule = 0/2/256H
5.2A$4.AB2C$5.BD2E$2A4.DF2G$A2C4.FH2I$.C2E4.HJ2K$2.E2G4.JL2M$3.G2I4.L
N2O$4.I2K4.NP2Q$5.K2M4.PR2S$6.M2O4.RT2U$7.O2Q4.TV2W$8.Q2S4.VX2pA$9.S
2U4.XpB2pC$10.U2W4.pBpD2pE$11.W2pA4.pDpF2pG$12.pA2pC4.pFpH2pI$13.pC2pE
4.pHpJ2pK$14.pE2pG4.pJpL2pM$15.pG2pI4.pLpN2pO$16.pI2pK4.pNpP2pQ$17.pK
2pM4.pPpR2pS$18.pM2pO4.pRpT2pU$19.pO2pQ4.pTpV2pW$20.pQ2pS4.pVpX2qA$
21.pS2pU4.pXqB2qC$22.pU2pW4.qBqD2qE$23.pW2qA4.qDqF2qG$24.qA2qC4.qFqH
2qI$25.qC2qE4.qHqJ2qK$26.qE2qG4.qJqL2qM$27.qG2qI4.qLqN2qO$28.qI2qK4.qN
qP2qQ$29.qK2qM4.qPqR2qS$30.qM2qO4.qRqT2qU$31.qO2qQ4.qTqV2qW$32.qQ2qS
4.qVqX2rA$33.qS2qU4.qXrB2rC$34.qU2qW4.rBrD2rE$35.qW2rA4.rDrF2rG$36.rA
2rC4.rFrH2rI$37.rC2rE4.rHrJ2rK$38.rE2rG4.rJrL2rM$39.rG2rI4.rLrN2rO$
40.rI2rK4.rNrP2rQ$41.rK2rM4.rPrR2rS$42.rM2rO4.rRrT2rU$43.rO2rQ4.rTrV
2rW$44.rQ2rS4.rVrX2sA$45.rS2rU4.rXsB2sC$46.rU2rW4.sBsD2sE$47.rW2sA4.sD
sF2sG$48.sA2sC4.sFsH2sI$49.sC2sE4.sHsJ2sK$50.sE2sG4.sJsL2sM$51.sG2sI
4.sLsN2sO$52.sI2sK4.sNsP2sQ$53.sK2sM4.sPsR2sS$54.sM2sO4.sRsT2sU$55.sO
2sQ4.sTsV2sW$56.sQ2sS4.sVsX2tA$57.sS2sU4.sXtB2tC$58.sU2sW4.tBtD2tE$
59.sW2tA4.tDtF2tG$60.tA2tC4.tFtH2tI$61.tC2tE4.tHtJ2tK$62.tE2tG4.tJtL
2tM$63.tG2tI4.tLtN2tO$64.tI2tK4.tNtP2tQ$65.tK2tM4.tPtR2tS$66.tM2tO4.tR
tT2tU$67.tO2tQ4.tTtV2tW$68.tQ2tS4.tVtX2uA$69.tS2tU4.tXuB2uC$70.tU2tW
4.uBuD2uE$71.tW2uA4.uDuF2uG$72.uA2uC4.uFuH2uI$73.uC2uE4.uHuJ2uK$74.uE
2uG4.uJuL2uM$75.uG2uI4.uLuN2uO$76.uI2uK4.uNuP2uQ$77.uK2uM4.uPuR2uS$
78.uM2uO4.uRuT2uU$79.uO2uQ4.uTuV2uW$80.uQ2uS4.uVuX2vA$81.uS2uU4.uXvB
2vC$82.uU2uW4.vBvD2vE$83.uW2vA4.vDvF2vG$84.vA2vC4.vFvH2vI$85.vC2vE4.vH
vJ2vK$86.vE2vG4.vJvL2vM$87.vG2vI4.vLvN2vO$88.vI2vK4.vNvP2vQ$89.vK2vM
4.vPvR2vS$90.vM2vO4.vRvT2vU$91.vO2vQ4.vTvV2vW$92.vQ2vS4.vVvX2wA$93.vS
2vU4.vXwB2wC$94.vU2vW4.wBwD2wE$95.vW2wA4.wDwF2wG$96.wA2wC4.wFwH2wI$
97.wC2wE4.wHwJ2wK$98.wE2wG4.wJwL2wM$99.wG2wI4.wLwN2wO$100.wIwKwJ4.wNwP
2wQ$101.wK2wL4.wPwR2wS$102.wL2wN4.wRwT2wU$103.wN2wP4.wTwV2wW$104.wP2wR
4.wVwX2xA$105.wR2wT4.wXxB2xC$106.wT2wV4.xBxD2xE$107.wV2wX4.xDxF2xG$
108.wX2xB4.xFxH2xI$109.xB2xD4.xHxJ2xK$110.xD2xF4.xJxL2xM$111.xF2xH4.xL
xN2xO$112.xH2xJ4.xNxP2xQ$113.xJ2xL4.xPxR2xS$114.xL2xN4.xRxT2xU$115.xN
2xP4.xTxV2xW$116.xP2xR4.xVxX2yA$117.xR2xT4.xXyB2yC$118.xT2xV4.yByD2yE
$119.xV2xX4.yDyF2yG$120.xX2yB4.yFyH2yI$121.yB2yD4.yHyJ2yK$122.yD2yF4.
yJyL2yM$123.yF2yH4.yLyN2yO$124.yH2yJ4.yN$125.yJ2yL$126.yL2yN$127.yN!

[AlephAlpha]

A glider that outruns the glider (2c/7):

Code: Select all

x = 3, y = 3, rule = B2ce3aijkn4w5i7e/S1c2cei3aj4ainq5ry6c
bo$2bo$3o!

[Hunting]

Hello, AlephAlpha!

I will probably try to search some fast diagonal ship in RSS(Really Small Spaceship) project, or #76 at GitHub [s]Also known as "Manual LLS"[/s].

[AlephAlpha]

Restricting to the rules that the original glider works:

4c/15:

Code: Select all

x = 13, y = 13, rule = B2in3-eqy4ijkqw5cikq6aik/S02-ck3-aeky4inqtwy5nqry6an7e8
11bo$12bo$10b3o8$b2o$obo$3o!

3c/11:

Code: Select all

x = 13, y = 13, rule = B2ik3aijn4iqw5cky6c7c/S02-ci3-ciqy4ir5acq6k7c
11bo$12bo$10b3o8$2bo$b2o$3o!

2c/7:

Code: Select all

x = 13, y = 13, rule = B3-ckqy4k/S02ae3ijknr4iw5any6n7
11bo$12bo$10b3o8$b2o$obo$3o!

3c/10:

Code: Select all

x = 13, y = 13, rule = B3-ekqy4aqy5i6e7c8/S02ae3ajnr4cqrw5cknq6cn
11bo$12bo$10b3o8$obo$2bo$3o!

4c/13:

Code: Select all

x = 13, y = 13, rule = B2kn3-ekqy4jt5c/S02ae3-ckqy4jqw5aik7e
11bo$12bo$10b3o8$b2o$3o$3o!

c/3:

Code: Select all

x = 13, y = 13, rule = B3aijnr4k7c/S2ae3jnr4i5a7c
11bo$12bo$10b3o8$b2o$obo$3o!

[Hunting]

2c/7:

Code: Select all

x = 13, y = 13, rule = B3-ckqy4k/S02ae3ijknr4iw5any6n7
11bo$12bo$10b3o8$2bo$b2o$3o!

Hey, I think you posted the wrong pattern. The "2c/7d" is an oscillator.

[wildmyron]

Restricting to the rules that the original glider works:

Nice work. There's a 2c/7 in a glider compatible rule in my post above ^. Here are some other speeds:

5c/16d

Code: Select all

x = 13, y = 13, rule = B2k3aijn4qt5acjk6-ae7c/S23ajnqr4acijrt5-cenr6-a7e
12bo$10bobo$11b2o8$2bo$2bo$3o!

5c/17d

Code: Select all

x = 13, y = 13, rule = B2i3aijnr4eknqy5aceq6-k78/S02ae3-ceq4inrtwy5-enqy6-kn7e
12bo$10bobo$11b2o8$2bo$b2o$3o!

5c/18d

Code: Select all

x = 13, y = 13, rule = B2kn3-cekr4eijnqt5-ckn6ci7c/S2-k3-eky4nrwyz5aei6cen78
12bo$10bobo$11b2o8$2bo$b2o$3o!

5c/19d

Code: Select all

x = 13, y = 13, rule = B2i3-kq4ckntyz5cejk6ck7c/S02aen3jnry4cinqwz5-ey6an78
12bo$10bobo$11b2o8$b2o$obo$3o!

6c/19d

Code: Select all

x = 13, y = 13, rule = B2k3-cery4ikyz5ikqry6cek7c8/S02aek3-ci4ceinwz5iknr8
12bo$10bobo$11b2o8$b2o$3o$3o!

[AlephAlpha]

2c/7:

Code: Select all

x = 13, y = 13, rule = B3-ckqy4k/S02ae3ijknr4iw5any6n7
11bo$12bo$10b3o8$2bo$b2o$3o!

Hey, I think you posted the wrong pattern. The "2c/7d" is an oscillator.

Sorry. Edited.

[wildmyron]

Some more:

c/3d, p18

Code: Select all

x = 13, y = 13, rule = B2n3-kqr4-eijry5aciky6-ai7e8/S2-c3-eky4ejryz5aceir6kn7c8
12bo$10bobo$11b2o8$obo$b2o$3o!

3c/10, p20

Code: Select all

x = 13, y = 13, rule = B3aijn4-aeirt5eqry6ace7e8/S2aek3-cky4eirwyz5-ckry6cn7c
12bo$10bobo$11b2o8$2bo$b2o$3o!

2c/7d, p21

Code: Select all

x = 13, y = 13, rule = B2in3-eqy4cejwz5-jnr6-en7c8/S02-cn3-aey4cirtyz5aijky6-k8
12bo$10bobo$11b2o8$b2o$obo$3o!

3c/11d, p22

Code: Select all

x = 13, y = 13, rule = B2ikn3-q4aejtyz5acer67e/S02-ik3-aeiy4ejnqtz5aejqy6-k8
12bo$10bobo$11b2o8$obo$2bo$3o!

7c/22d

Code: Select all

x = 13, y = 13, rule = B2kn3-e4ceknqy5-ekny6-ac7c/S02-c3cjnr4einyz5-eikn6eik78
12bo$10bobo$11b2o8$b2o$obo$3o!

6c/23d

Code: Select all

x = 13, y = 13, rule = B3-qr4-aqryz5cry6-cn8/S02-n3-ai4ceijntz5-cejn6-en7e8
12bo$10bobo$11b2o8$obo$2bo$3o!

7c/23d

Code: Select all

x = 13, y = 13, rule = B2i3-ceqr4-krwy5ciqr6-i7c8/S2-c3-ekqy4iqrtw5aikq6kn7c8
12bo$10bobo$11b2o8$b2o$3o$3o!

These were all found with LLS. The shapes are mostly a function of the boundary conditions set up by the search. You can improve the search behaviour by using the make_lls_grid.py script. I used it for the 7c/22 and 7c/23 ships. As a bonus this reduces the search space and therefore improves the search speed considerably. Here's the command I used to find the 7c/23:

Code: Select all

./make_lls_grid.py -p 23 -x 7 -y 7 -f 3 3 5 5 | ./lls -r pB2-ace3aijn4-r5-n678/S0
2ae3jnr4-k5678 -i -s 'D2\'

This took about 15 seconds to run, most of which was in preprocessing.

[Hdjensofjfnen]

Can we either prove or disprove wildmyron's conjecture that rules with CGOL gliders have a maximum diagonal speed of c/3?

[AforAmpere]

Can we either prove or disprove wildmyron's conjecture that rules with CGOL gliders have a maximum diagonal speed of c/3?

It kind of already is known. In a non-B2a or B1e rule, the max diagonal speed is C/3. Therefore, there is no faster one in a rule with the glider.

[Hdjensofjfnen]

Can we either prove or disprove wildmyron's conjecture that rules with CGOL gliders have a maximum diagonal speed of c/3?

It kind of already is known. In a non-B2a or B1e rule, the max diagonal speed is C/3. Therefore, there is no faster one in a rule with the glider.

Oh. In that case, time to find every single possible speed between c/3 and c/4 with the CGOL glider.

[Moosey]

Can we either prove or disprove wildmyron's conjecture that rules with CGOL gliders have a maximum diagonal speed of c/3?

It kind of already is known. In a non-B2a or B1e rule, the max diagonal speed is C/3. Therefore, there is no faster one in a rule with the glider.

Oh. In that case, time to find every single possible speed between c/3 and c/4 with the CGOL glider.

That's also impossible (at least for small ships) because there are infinite rational numbers between any two different rational numbers.

[AforAmpere]

That's also impossible (at least for small ships) because there are infinite rational numbers between any two different rational numbers.

However, there are a finite number of rules with the glider, and if there aren't fast diagonal adjustable ships with the glider, there may only be finitely many speeds.

[Gamedziner]

That's also impossible (at least for small ships) because there are infinite rational numbers between any two different rational numbers.

However, there are a finite number of rules with the glider, and if there aren't fast diagonal adjustable ships with the glider, there may only be finitely many speeds.

If you limit the bounding box, the max period is less than or equal to 2^(number of cells in the bounding box).

[Entity Valkyrie 2]

This is Entity Valkyrie 2.

c/3:

Code: Select all

x = 5, y = 5, rule = B2e3-cjnr/S2aei3
b2o$obo$3o$4bo$3bo!

[Βεν Γ. Κυθισ]

This is Entity Valkyrie 2.

c/3:

Code: Select all

x = 5, y = 5, rule = B2e3-cnr/S2aei3
b2o$obo$3o$4bo$3bo!

No, it becomes ash instantly,

[Entity Valkyrie 2]

This is Entity Valkyrie 2.

c/3:

Code: Select all

x = 5, y = 5, rule = B2e3-cnr/S2aei3
b2o$obo$3o$4bo$3bo!

No, it becomes ash instantly,

I forgot the "j" in B2e3-cjnr/S2aei3! Fixed.

Code: Select all

x = 5, y = 5, rule = B2e3-cjnr/S2aei3
b2o$obo$3o$4bo$3bo!

[77topaz]

3c/11:

Code: Select all

x = 13, y = 13, rule = B2ik3aijn4iqw5cky6c7c/S02-ci3-ciqy4ir5acq6k7c
11bo$12bo$10b3o8$2bo$b2o$3o!

This rule also has a small 2c/8 orthogonal:

Code: Select all

x = 2, y = 6, rule = B2ik3aijn4iqw5cky6c7c/S02-ci3-ciqy4ir5acq6k7c
2o$2o2$bo2$bo!

Unfortunately, it is explosive.

[Redstoneboi]

Code: Select all

x = 4, y = 5, rule = B3ai4a/S2e34aeiwz5iqr6a
bo$3o$2bo$2b2o$3bo!

rule that's golfed to have a small explosive seed, modified a bit giving this c/3d with population going 8-9-10