Search Algorithms for rule 23/3/3
Posted: April 1st, 2021, 12:29 pm
A while ago I decided to explore the generations rule 23/3/3 to see if I could find the same kinds of interesting patterns as life. Specifically I was looking to see if I could construct a breeder.
I first discussed this in an earlier thread on the Other Cellular Automata forums, and the thread contains some interesting patterns from other users. There is also an old thread discussing this rule, and the rule is on Catalogue.
Futzing around with the rule, I found a 14c/28 puffer.
Asking around the forums it was confirmed to me that it was indeed new, and I set out to see if I could construct a rake, however because spaceships are rare in this rule I needed to search a broad scope of interactions between the puff from the 14c/28 puffer and the 2c/4 spaceships the forum calls parvoships to see if one of them would produce a spaceship.
parvoship:
In the end I ended up crudely engineering a bulky p28 rake as well as a p56 version:
My question is threefold: One, in the interest of finding a smaller version of these rakes I would like to ask the best way to search different parvoship configurations underneath the 14c/28 puffer for ones that produce spaceships and can be made into rakes.
Two, because rakes of longer periods may be useful in the construction of a breeder, c/2 spaceships of other periods would be useful when their periods are combined with the 14c/28 puffer, and I would like to ask the best way to search for spaceships of unusual periods.
Three, in the case that I do find a sufficiently small/long-period rake, I would then need to find a spaceship synthesis for a small infinite growth pattern, the best candidate for which I believe to be the 14c/28 puffer itself, although other puffers have been found, like this one by Schiaparelliorbust and RocknLol:
Therefore my third question is what is the best way to search for spaceship synthesis for a complex pattern.
These questions are specific to the rule 23/3/3 but I have been told that it wouldn't be out of the question to believe that any approach for solving these problems algorithmically doesn't have a wider application.
Thank you.
I first discussed this in an earlier thread on the Other Cellular Automata forums, and the thread contains some interesting patterns from other users. There is also an old thread discussing this rule, and the rule is on Catalogue.
Futzing around with the rule, I found a 14c/28 puffer.
Code: Select all
x = 24, y = 14, rule = 23/3/3
.3A9.3A$A2BA9.A2BA$AB2.BA5.AB2.BA$2.A2BA5.A2BA$2.A2BA5.A2BA2$6.2A.2A$
5.A.A.A.A$5.A.A.A.A$4.2A.A.A.2A8.A$5.B.A.A.B8.3A$4.2B.B.B.2B6.A2.2A$
4.3A3.3A5.4AB$19.2A!
parvoship:
Code: Select all
x = 6, y = 5, rule = 23/3/3
3.A$2.3A$.A2.2A$4AB$.2A!
Code: Select all
x = 70, y = 1188, rule = 23/3/3
9.A11.A$8.3A9.3A$7.A2.2A7.2A2.A$7.B4.B5.B4.B$8.AB2.2A3.2A2.BA$9.B2.B
5.B2.B$13.A3.A$13.2A.2A$12.A.A.A.A$12.A.A.A.A$.3A7.2A.A.A.2A$A2BA10.A
.A$AB2.BA5.2A.A.A.2A$2.A2BA5.2A.A.A.2A$2.A2BA8.B.B3$9.A.2A5.B$9.4B$7.
AB.3B$7.AB5AB.2B29.3A9.3A$8.A38.A2BA7.A2BA$46.BA.2A7.2A.AB$50.A7.A$
47.B3.2B3.2B3.B$52.A3.A$52.2A.2A$6.A44.ABA.ABA$5.3A43.A.A.A.A$4.2A2.A
42.A.A.A.A9.A$5.B4A40.2A.A.A.2A7.3A$7.2A42.A.A.A.A7.2A2.A$11.2A39.2B.
2B7.B4.B$11.B.A38.2B.2B6.2A2.BA$10.2A2.A38.A.A8.B2.B$11.3A8.3A27.B3.B
$21.A2BA$21.2A.AB$21.A$19.2B3.B2$24.A11.A$23.3A9.3A$22.2A2.A7.A2.2A
17.2A$16.2A5.B4A5.4AB18.2A$16.2A7.2A7.2A19.A$56.B.B$28.2A.2A24.AB3.3A
$27.ABA.ABA28.A2BA$27.A.A.A.A26.AB2.BA$26.2A.A.A.2A25.A2BA$27.A.A.A.A
8.3A15.A2BA$26.2A.A.A.2A6.A2BA$26.2A.B.B.2A6.2A.AB$41.A$39.2B3.B$29.B
.B$54.A$16.2A35.2AB$16.2A34.AB$53.2AB$54.A2$60.3A$60.A2BA$32.2A24.AB
2.BA$31.ABA24.A2BA$31.BA25.A2BA2$33.B3$16.2A$16.2A2$51.2A$49.2A.A$49.
2A$49.2A.A$32.2A17.2A5.3A$31.A.A24.A2BA$32.A23.AB2.BA$56.A2BA$56.A2BA
3$16.2A$16.2A4$49.A$48.ABA$32.2A14.B.2A$31.A.A12.ABA.B$32.A13.AB8.3A$
46.ABA.B5.A2BA$48.B.2A2.AB2.BA$48.ABA3.A2BA$49.A4.A2BA$16.2A$16.2A5$
38.3A$32.2A3.A2BA$31.A.A3.2A.AB$32.A4.A10.A$35.2B3.B6.A.A$48.2A4.3A$
54.A2BA$52.AB2.BA$16.2A4.A26.A2.A2BA$16.2A3.3A24.A.3A2BA$20.A2.2A22.A
2.A$20.B4.B22.2A$21.AB2.2A$22.B2.B$28.B$29.BA$28.ABA$27.A2.B$27.A2.BA
$28.A2BA$28.3A$46.A5.3A$16.2A27.A.A4.A2BA$16.2A28.2A2.AB2.BA$50.A2BA$
50.A2BA$47.AB$46.A2.A$45.A2.2A$46.4A$47.A6$16.2A$16.2A32.3A$50.A2BA$
44.B3.AB2.BA$26.2A3.2A10.A2.3A2BA$25.A2.A2.2A11.AB3A2BA$26.2A5.A10.3A
$30.B.B$30.BA$44.A$43.A.B$42.2A.A$43.2AB$44.A$16.2A$16.2A2$48.3A$26.
2A3.2A15.A2BA$25.A2.A2.A.A12.AB2.BA$26.2A4.A13.A2BA$42.A3.A2BA$41.BAB
$43.A$41.B.B$42.A2$40.A$16.2A21.2AB$16.2A20.AB$39.2AB$40.A$26.2A3.2A$
25.A2.A2.A.A12.3A$26.2A4.A13.A2BA$44.AB2.BA$44.A2BA$44.A2BA5$16.2A$
16.2A2$37.2A$26.2A3.2A2.2A.A$25.A2.A2.A.A.2A$26.2A4.A2.2A.A$37.2A7$
16.2A$16.2A3$26.2A6.A11.A$25.A2.A4.3A9.3A$26.2A4.A2.2A7.2A2.A$32.B4.B
5.B4.B$33.AB2.2A3.2A2.BA$34.B2.B5.B2.B$38.A3.A$38.2A.2A$37.A.A.A.A$
37.A.A.A.A$16.2A18.2A.A.A.2A7.3A$16.2A20.AB.BA9.A2BA$38.A3.A7.AB2.BA$
36.BAB3.BAB5.A2BA$26.2A9.A5.A6.A2BA$25.A2.A$26.2A8$16.2A$16.2A24.2A$
41.A.A$42.A6.A$26.2A20.3A$25.A2.A18.A2.2A$26.2A18.4AB$47.2A7$16.2A$
16.2A21.2A$38.A.A$37.2A$26.2A10.A.A$25.A2.A10.2A6.A$26.2A18.3A$45.A2.
2A$44.4AB$45.2A5$16.2A$16.2A3$26.2A8.3A$25.A2.A7.ABA$26.2A7.2A.A$34.
2A9.A$35.2A.A5.3A$36.ABA4.A2.2A$36.3A3.4AB$43.2A3$16.2A$16.2A3$26.2A$
25.A2.A$26.2A$36.A$35.A.A$36.2A5.A$42.3A$41.A2.2A$37.A2.4AB$36.ABA2.
2A$16.2A17.A.BA$16.2A18.2A3$26.2A$25.A2.A$26.2A5$34.A6.A$33.A.A4.3A$
34.2A3.A2.2A$16.2A20.4AB$16.2A21.2A$35.2A$34.A.B$26.2A5.A2.2A$25.A2.A
5.3A$26.2A8$16.2A$16.2A3$25.2A6.A11.A$24.A2.A4.3A9.3A$25.2A4.A2.2A7.
2A2.A$31.B4.B5.B4.B$32.AB2.2A3.2A2.BA$33.B2.B5.B2.B$37.A3.A$37.2A.2A$
36.A.A.A.A$36.A.A.A.A$16.2A17.2A.A.A.2A7.3A$16.2A19.AB.BA9.A2BA$37.A
3.A7.AB2.BA$35.BAB3.BAB5.A2BA$25.2A9.A5.A6.A2BA$24.A2.A$25.2A8$16.2A$
16.2A23.2A$40.A.A$41.A6.A$25.2A20.3A$24.A2.A18.A2.2A$25.2A18.4AB$46.
2A7$16.2A$16.2A20.2A$37.A.A$36.2A$25.2A10.A.A$24.A2.A10.2A6.A$25.2A
18.3A$44.A2.2A$43.4AB$44.2A5$16.2A$16.2A3$25.2A8.3A$24.A2.A7.ABA$25.
2A7.2A.A$33.2A9.A$34.2A.A5.3A$35.ABA4.A2.2A$35.3A3.4AB$42.2A3$16.2A$
16.2A3$25.2A$24.A2.A$25.2A$35.A$34.A.A$35.2A5.A$41.3A$40.A2.2A$36.A2.
4AB$35.ABA2.2A$16.2A16.A.BA$16.2A17.2A3$25.2A$24.A2.A$25.2A5$33.A6.A$
32.A.A4.3A$33.2A3.A2.2A$16.2A19.4AB$16.2A20.2A$34.2A$33.A.B$25.2A5.A
2.2A$24.A2.A5.3A$25.2A8$16.2A$16.2A3$24.2A6.A11.A$23.A2.A4.3A9.3A$24.
2A4.A2.2A7.2A2.A$30.B4.B5.B4.B$31.AB2.2A3.2A2.BA$32.B2.B5.B2.B$36.A3.
A$36.2A.2A$35.A.A.A.A$35.A.A.A.A$16.2A16.2A.A.A.2A7.3A$16.2A18.AB.BA
9.A2BA$36.A3.A7.AB2.BA$34.BAB3.BAB5.A2BA$24.2A9.A5.A6.A2BA$23.A2.A$
24.2A8$16.2A$16.2A22.2A$39.A.A$40.A6.A$24.2A20.3A$23.A2.A18.A2.2A$24.
2A18.4AB$45.2A7$16.2A$16.2A19.2A$36.A.A$35.2A$24.2A10.A.A$23.A2.A10.
2A6.A$24.2A18.3A$43.A2.2A$42.4AB$43.2A5$16.2A$16.2A3$24.2A8.3A$23.A2.
A7.ABA$24.2A7.2A.A$32.2A9.A$33.2A.A5.3A$34.ABA4.A2.2A$34.3A3.4AB$41.
2A3$16.2A$16.2A3$24.2A$23.A2.A$24.2A$34.A$33.A.A$34.2A5.A$40.3A$39.A
2.2A$35.A2.4AB$34.ABA2.2A$16.2A15.A.BA$16.2A16.2A3$24.2A$23.A2.A$24.
2A5$32.A6.A$31.A.A4.3A$32.2A3.A2.2A$16.2A18.4AB$16.2A19.2A$33.2A$32.A
.B$24.2A5.A2.2A$23.A2.A5.3A$24.2A8$16.2A$16.2A3$23.2A6.A11.A$22.A2.A
4.3A9.3A$23.2A4.A2.2A7.2A2.A$29.B4.B5.B4.B$30.AB2.2A3.2A2.BA$31.B2.B
5.B2.B$35.A3.A$35.2A.2A$34.A.A.A.A$34.A.A.A.A$16.2A15.2A.A.A.2A7.3A$
16.2A17.AB.BA9.A2BA$35.A3.A7.AB2.BA$33.BAB3.BAB5.A2BA$23.2A9.A5.A6.A
2BA$22.A2.A$23.2A8$16.2A$16.2A21.2A$38.A.A$39.A6.A$23.2A20.3A$22.A2.A
18.A2.2A$23.2A18.4AB$44.2A7$16.2A$16.2A18.2A$35.A.A$34.2A$23.2A10.A.A
$22.A2.A10.2A6.A$23.2A18.3A$42.A2.2A$41.4AB$42.2A5$16.2A$16.2A3$23.2A
8.3A$22.A2.A7.ABA$23.2A7.2A.A$31.2A9.A$32.2A.A5.3A$33.ABA4.A2.2A$33.
3A3.4AB$40.2A3$16.2A$16.2A3$23.2A$22.A2.A$23.2A$33.A$32.A.A$33.2A5.A$
39.3A$38.A2.2A$34.A2.4AB$33.ABA2.2A$16.2A14.A.BA$16.2A15.2A3$23.2A$
22.A2.A$23.2A5$31.A6.A$30.A.A4.3A$31.2A3.A2.2A$16.2A17.4AB$16.2A18.2A
$32.2A$31.A.B$23.2A5.A2.2A$22.A2.A5.3A$23.2A8$16.2A$16.2A3$22.2A6.A
11.A$21.A2.A4.3A9.3A$22.2A4.A2.2A7.2A2.A$28.B4.B5.B4.B$29.AB2.2A3.2A
2.BA$30.B2.B5.B2.B$34.A3.A$34.2A.2A$33.A.A.A.A$33.A.A.A.A$16.2A14.2A.
A.A.2A7.3A$16.2A16.AB.BA9.A2BA$34.A3.A7.AB2.BA$32.BAB3.BAB5.A2BA$22.
2A9.A5.A6.A2BA$21.A2.A$22.2A8$16.2A$16.2A20.2A$37.A.A$38.A6.A$22.2A
20.3A$21.A2.A18.A2.2A$22.2A18.4AB$43.2A7$16.2A$16.2A17.2A$34.A.A$33.
2A$22.2A10.A.A$21.A2.A10.2A6.A$22.2A18.3A$41.A2.2A$40.4AB$41.2A5$16.
2A$16.2A3$22.2A8.3A$21.A2.A7.ABA$22.2A7.2A.A$30.2A9.A$31.2A.A5.3A$32.
ABA4.A2.2A$32.3A3.4AB$39.2A3$16.2A$16.2A3$22.2A$21.A2.A$22.2A$32.A$
31.A.A$32.2A5.A$38.3A$37.A2.2A$33.A2.4AB$32.ABA2.2A$16.2A13.A.BA$16.
2A14.2A3$22.2A$21.A2.A$22.2A5$30.A6.A$29.A.A4.3A$30.2A3.A2.2A$16.2A
16.4AB$16.2A17.2A$31.2A$30.A.B$22.2A5.A2.2A$21.A2.A5.3A$22.2A8$16.2A$
16.2A3$21.2A6.A11.A$20.A2.A4.3A9.3A$21.2A4.A2.2A7.2A2.A$27.B4.B5.B4.B
$28.AB2.2A3.2A2.BA$29.B2.B5.B2.B$33.A3.A$33.2A.2A$32.A.A.A.A$32.A.A.A
.A$16.2A13.2A.A.A.2A7.3A$16.2A15.AB.BA9.A2BA$33.A3.A7.AB2.BA$31.BAB3.
BAB5.A2BA$21.2A9.A5.A6.A2BA$20.A2.A$21.2A8$16.2A$16.2A19.2A$36.A.A$
37.A6.A$21.2A20.3A$20.A2.A18.A2.2A$21.2A18.4AB$42.2A7$16.2A$16.2A16.
2A$33.A.A$32.2A$21.2A10.A.A$20.A2.A10.2A6.A$21.2A18.3A$40.A2.2A$39.4A
B$40.2A5$16.2A$16.2A3$21.2A8.3A$20.A2.A7.ABA$21.2A7.2A.A$29.2A9.A$30.
2A.A5.3A$31.ABA4.A2.2A$31.3A3.4AB$38.2A3$16.2A$16.2A3$21.2A$20.A2.A$
21.2A$31.A$30.A.A$31.2A5.A$37.3A$36.A2.2A$32.A2.4AB$31.ABA2.2A$16.2A
12.A.BA$16.2A13.2A3$21.2A$20.A2.A$21.2A5$29.A6.A$28.A.A4.3A$29.2A3.A
2.2A$16.2A15.4AB$16.2A16.2A$30.2A$29.A.B$21.2A5.A2.2A$20.A2.A5.3A$21.
2A8$16.2A$16.2A3$20.2A6.A11.A$19.A2.A4.3A9.3A$20.2A4.A2.2A7.2A2.A$26.
B4.B5.B4.B$27.AB2.2A3.2A2.BA$28.B2.B5.B2.B$32.A3.A$32.2A.2A$31.A.A.A.
A$31.A.A.A.A$16.2A12.2A.A.A.2A7.3A$16.2A14.AB.BA9.A2BA$32.A3.A7.AB2.B
A$30.BAB3.BAB5.A2BA$20.2A9.A5.A6.A2BA$19.A2.A$20.2A8$16.2A$16.2A18.2A
$35.A.A$36.A6.A$20.2A20.3A$19.A2.A18.A2.2A$20.2A18.4AB$41.2A7$16.2A$
16.2A15.2A$32.A.A$31.2A$20.2A10.A.A$19.A2.A10.2A6.A$20.2A18.3A$39.A2.
2A$38.4AB$39.2A5$16.2A$16.2A3$20.2A8.3A$19.A2.A7.ABA$20.2A7.2A.A$28.
2A9.A$29.2A.A5.3A$30.ABA4.A2.2A$30.3A3.4AB$37.2A3$16.2A$16.2A3$20.2A$
19.A2.A$20.2A$30.A$29.A.A$30.2A5.A$36.3A$35.A2.2A$31.A2.4AB$30.ABA2.
2A$16.2A11.A.BA$16.2A12.2A3$20.2A$19.A2.A$20.2A5$28.A6.A$27.A.A4.3A$
28.2A3.A2.2A$16.2A14.4AB$16.2A15.2A$29.2A$28.A.B$20.2A5.A2.2A$19.A2.A
5.3A$20.2A8$16.2A$16.2A3$19.2A6.A11.A$18.A2.A4.3A9.3A$19.2A4.A2.2A7.
2A2.A$25.B4.B5.B4.B$26.AB2.2A3.2A2.BA$27.B2.B5.B2.B$31.A3.A$31.2A.2A$
30.A.A.A.A$30.A.A.A.A$16.2A11.2A.A.A.2A7.3A$16.2A13.AB.BA9.A2BA$31.A
3.A7.AB2.BA$29.BAB3.BAB5.A2BA$19.2A9.A5.A6.A2BA$18.A2.A$19.2A8$16.2A$
16.2A17.2A$34.A.A$35.A6.A$19.2A20.3A$18.A2.A18.A2.2A$19.2A18.4AB$40.
2A7$16.2A$16.2A14.2A$31.A.A$30.2A$19.2A10.A.A$18.A2.A10.2A6.A$19.2A
18.3A$38.A2.2A$37.4AB$38.2A5$16.2A$16.2A3$19.2A8.3A$18.A2.A7.ABA$19.
2A7.2A.A$27.2A9.A$28.2A.A5.3A$29.ABA4.A2.2A$29.3A3.4AB$36.2A3$16.2A$
16.2A3$19.2A$18.A2.A$19.2A$29.A$28.A.A$29.2A5.A$35.3A$34.A2.2A$30.A2.
4AB$29.ABA2.2A$16.2A10.A.BA$16.2A11.2A3$19.2A$18.A2.A$19.2A5$27.A6.A$
26.A.A4.3A$27.2A3.A2.2A$16.2A13.4AB$16.2A14.2A$28.2A$27.A.B$19.2A5.A
2.2A$18.A2.A5.3A$19.2A8$16.2A$16.2A3$18.2A5.A11.A$17.A2.A3.3A9.3A$18.
2A3.A2.2A7.2A2.A$23.B4.B5.B4.B$24.AB2.2A3.2A2.BA$25.B2.B5.B2.B$29.A3.
A$29.2A.2A$28.A.A.A.A$28.A.A.A.A$16.2A9.2A.A.A.2A7.3A$16.2A12.A.A10.A
2BA$27.2B.A.A.2B5.AB2.BA$30.A.A8.A2BA$18.2A6.ABA.A.A.ABA4.A2BA$17.A2.
A5.ABA.A.A.AB2AB$18.2A6.A3.A.A3.A.A$26.B3.A.A3.B2AB$25.A3.2A.2A3.A$
25.B11.B5$16.2A$16.2A2$40.A$18.2A19.3A$17.A2.A17.A2.2A$18.2A14.A2.4AB
$33.ABA2.2A$32.A.BA$33.2A5$16.2A$16.2A3$18.2A$17.A2.A10.A6.A$18.2A10.
A.A4.3A$31.2A3.A2.2A$35.4AB$36.2A$32.2A$31.A.B$30.A2.2A$31.3A$16.2A$
16.2A3$18.2A$17.A2.A$18.2A$36.A$35.3A$29.A4.A2.2A$28.A.BA.4AB$29.3A2.
2A$30.A2$16.2A$16.2A11.A$28.A.A2.B$28.AB$18.2A8.3A$17.A2.A$18.2A3$34.
A$33.3A$32.A2.2A$31.4AB$32.2A$16.2A8.3A$16.2A8.2B$26.ABA$27.AB$18.2A$
17.A2.A$18.2A4.3A$24.AB$24.3A$26.B!
Code: Select all
x = 72, y = 1590, rule = 23/3/3
39.3A9.3A$38.A2BA9.A2BA$38.AB2.BA5.AB2.BA$40.A2BA5.A2BA$40.A2BA5.A2BA
2$44.2A.2A$43.A.A.A.A$43.A.A.A.A$33.A8.2A.A.A.2A$32.3A8.B.A.A.B$31.2A
2.A6.2A.A.A.2A$32.B4A8.A.A$34.2A6.2A.A.A.2A$39.A.3A.A.A.3A$38.BAB4.A.
A4.2B$38.A2.A3.A.A3.A$39.BAB2.2A.2A2.BAB$40.A11.A3$50.A11.A$49.3A9.3A
$48.2A2.A7.A2.2A$49.B4A5.4AB$51.2A7.2A2$54.2A.2A$53.ABA.ABA$53.A.A.A.
A$43.2A7.2A.A.A.2A$43.A.A7.A.A.A.A8.3A$44.A7.2A.A.A.2A6.A2BA$55.A.A9.
2A.AB$52.2A.B.B.2A6.A$52.3A3.3A4.2B3.B2$19.A11.A$18.3A9.3A$17.A2.2A7.
2A2.A$17.B4.B5.B4.B$18.AB2.2A3.2A2.BA27.2A$19.B2.B5.B2.B27.A3B.B$23.A
3.A31.A3BA$23.2A.2A15.2A15.3A$22.A.A.A.A14.A.A$22.A.A.A.A15.A$21.2A.A
.A.2A7.3A$24.A.A10.A2BA24.A$21.2A.A.A.2A5.AB2.BA23.3A$19.AB.A.A.A.A.B
A3.A2BA24.2A2.A$19.A2BA.A.A.A2BA3.A2BA23.B4.B$19.A2.B.A.A.B2.A29.2A2.
BA$19.2A3.A.A3.2A30.B2.B$20.B2.A3.A2.B28.B$22.B5.B29.2A.A$57.A2.2BA$
58.A2BA$43.2A13.2A$8.3A9.3A20.A.A$7.A2BA9.A2BA20.A$7.AB2.BA5.AB2.BA$
9.A2BA5.A2BA$9.A2BA5.A2BA$63.A$13.2A.2A44.3A$12.A.A.A.A8.2A32.2A2.A$
12.A.A.A.A7.A.A31.A4.B$2.A8.2A.A.A.2A7.A27.B.2A2B2.BA$.3A8.B.A.A.B36.
2A.2BA2.B$2A2.A6.2A.A.A.2A36.ABA$.B4A5.2A.A.A.2A37.A$3.2A8.BA.AB25.2A
$14.B.B26.A.A10.B$9.2B2.2B.2B26.A9.2A$9.A.A.2B.2BA.B33.AB.B$9.4A2B.2B
36.A2B$7.2A.3A.B.B38.2A$7.3A3.2A.2A2$27.2A32.A$26.A.A31.3A$27.A31.2A
2.A$58.B4.B$57.2A2.BA$54.B3.B2.B$5.3A35.2A9.A$5.A2BA34.A.A9.B$4.BA.2A
35.A$8.A45.B$5.B3.B.2A$9.B.A.A37.2A$10.2A2.A36.2A$12.2A36.A7.A$27.2A
22.2A4.3A$26.A.A22.2A3.A2.2A$27.A27.4AB$56.2A3$43.2A$43.A.A$7.3A34.A$
7.A2BA4.A21.A$6.BA.2A3.A.A19.3A$10.A2.3A19.A2.2A$7.B3.2B22.B4.B7.A$
36.AB2.2A5.A.A$27.2A8.B2.B6.A.A$12.B.BA10.A.A19.A$11.A2.A.A10.A$12.B
2.2A$14.2A2$46.2A$46.2A$48.A$46.2A$9.3A34.2A$9.A2BA$8.BA.2A35.A$12.AB
33.A.A$9.B5.B2A9.2A18.A.A$13.B3.2A7.A.A19.A$15.B.2A8.A$16.A3$18.2A$
19.2A$19.A$12.3A2.BA$11.A2BA$11.AB2.BA$13.A2BA$13.A2BA$27.2A$26.A.A
25.3A$27.A25.A2BA$53.2A.AB$53.A$33.3A15.2B3.B$23.A8.A2BA$22.A.A7.2A.A
B$22.A.A7.A15.AB.B$23.A6.2B3.B11.A.A2.A$47.2A2.B$48.2A4$25.2B2$52.3A$
23.B3.B23.A2BA$22.3ABA24.2A.AB$22.3AB25.A$22.2A25.2B3.B$22.2A$22.2A3.
A$23.2B3A$21.B.B2A$22.2A4$22.2A2.B$22.ABA$23.AB$50.3A$49.A2BA$49.2A.A
B$49.A$47.2B3.B$16.A$15.3A26.B$14.2A2.A$15.B4A$17.2A2$41.2A$40.ABA$
32.3A5.A$31.A2BA5.ABA$31.2A.AB5.2A$31.A16.3A$29.2B3.B12.A2BA$47.2A.AB
$47.A$45.2B3.B2$26.2A$26.2A$32.A$31.3A$30.A2.2A13.A11.A$30.B4.B11.3A
9.3A$31.AB2.2A9.A2.2A7.2A2.A$32.B2.B10.B4.B5.B4.B$47.AB2.2A3.2A2.BA$
48.B2.B5.B2.B$52.A3.A$52.2A.2A$51.A.A.A.A$51.A.A.A.A$50.2A.A.A.2A7.3A
$53.A.A10.A2BA$50.2A.A.A.2A5.AB2.BA$48.AB.A.A.A.A.BA3.A2BA$48.A2BA.A.
A.A2BA3.A2BA$48.A2.B.A.A.B2.A$48.2A3.A.A3.2A$49.B2.A3.A2.B$51.B5.B6$
26.2A$26.2A2$63.A$62.3A$36.3A.2A14.2A3.A2.2A$36.A2B2.A13.A.A2.4AB$38.
3BA14.A4.2A$38.ABA$39.A8$54.A$53.A.A$54.2A5.A$60.3A$59.A2.2A$55.A2.4A
B$54.ABA2.2A$53.A.BA$54.2A3$26.2A$26.2A3$36.2A3.2A$35.A2.A2.A.A$36.2A
4.A$52.A6.A$51.A.A4.3A$52.2A3.A2.2A$56.4AB$57.2A$53.2A$52.A.B$51.A2.
2A$52.3A8$57.A$56.3A$50.A4.A2.2A$49.A.BA.4AB$50.3A2.2A$26.2A23.A$26.
2A2$50.A$36.2A3.2A6.A.A2.B$35.A2.A2.A.A5.AB$36.2A4.A6.3A7$54.3A$54.A
2BA$48.B3.AB2.BA$47.A2.3A2BA$48.AB3A2BA$48.3A3$48.A$47.A.B$46.2A.A$
47.2AB$48.A$52.A$51.3A$26.2A22.2A2.A$26.2A21.B4.B$48.2A2.BA$49.B2.B$
36.2A$35.A2.A$36.2A3$50.3A$50.A2BA$48.AB2.BA$48.A2BA$48.A2BA8$44.A11.
A$43.3A9.3A$42.2A2.A7.A2.2A$43.B4A5.4AB$45.2A7.2A2$48.2A.2A$26.2A19.A
BA.ABA$26.2A19.A.A.A.A$46.2A.A.A.2A$47.A.A.A.A8.3A$36.2A8.2A.A.A.2A6.
A2BA$35.A2.A7.2A.A.A.2A6.2A.AB$36.2A9.2A3.2A7.A$47.2A3.2A5.2B3.B$47.B
5.B8$53.2A$52.2A2.B$53.A$54.A.B$55.A3.A$58.3A$57.2A2.A$56.B4.B$55.2A
2.BA$56.B2.B3$26.2A$26.2A24.B$50.2A$50.AB.B$36.2A12.A2B$35.A2.A12.2A$
36.2A2$57.A$56.3A$55.2A2.A$54.B4.B$53.2A2.BA$50.B3.B2.B$50.A$51.B2$
50.B2$47.2A$47.2A$46.A$47.2A$47.2A$55.A$54.3A$53.2A2.A$52.B4.B$26.2A
23.2A2.BA$26.2A24.B2.B3$36.2A$35.A2.A$36.2A3$44.3A$43.AB.A$42.A2B$43.
AB.A6.A$44.3A5.3A$51.2A2.A$50.B4.B$49.2A2.BA$50.B2.B8$43.A$42.B.2A$
41.A2.2A$26.2A12.B.B8.A$26.2A11.2A9.3A$40.B.B6.2A2.A$41.A2.2A2.B4.B$
36.2A4.B.2A.2A2.BA$35.A2.A4.A4.B2.B$36.2A9$42.A$41.A.A$42.2A$48.3A$
47.A2BA$47.2A.AB$42.3A2.A$41.A.2A2B3.B$42.A5$26.2A$26.2A2$46.A$35.2A
8.3A$34.A2.A6.A2.2A$35.2A6.4AB$44.2A7$44.3A$43.A2BA$43.2A.AB$43.A$41.
2B3.B6$42.3A9.3A$42.A2BA7.A2BA$41.BA.2A7.2A.AB$45.A7.A$26.2A14.B3.2B
3.2B3.B$26.2A19.A3.A$47.2A.2A$46.ABA.ABA$35.2A9.A.A.A.A$34.A2.A8.A.A.
A.A9.A$35.2A8.2A.A.A.2A7.3A$48.A.A9.2A2.A$45.2A.A.A.2A5.B4.B$45.2A.B.
B.2A4.2A2.BA$59.B2.B3$52.2B.B2$57.B$51.B4A.A$52.5A6$57.3A$57.A2BA$55.
AB2.BA$55.A2BA$55.A2BA$26.2A24.AB$26.2A23.A2.A$50.A2.2A$51.4A$35.2A
15.A$34.A2.A$35.2A5$55.3A$55.A2BA$49.B3.AB2.BA$48.A2.3A2BA$49.AB3A2BA
$49.3A3$49.A$48.A.B$47.2A.A$48.2AB$49.A4$53.3A$26.2A25.A2BA$26.2A23.A
B2.BA$51.A2BA$47.A3.A2BA$35.2A9.BAB$34.A2.A10.A$35.2A9.B.B$47.A2$45.A
$44.2AB$43.AB$44.2AB$45.A2$51.3A$51.A2BA$49.AB2.BA$49.A2BA$49.A2BA8$
42.2A$26.2A12.2A.A$26.2A12.2A$40.2A.A$42.2A5.3A$35.2A12.A2BA$34.A2.A
9.AB2.BA$35.2A10.A2BA$47.A2BA8$40.A$39.ABA$39.B.2A$37.ABA.B$37.AB$37.
ABA.B6.A$39.B.2A4.3A$39.ABA4.2A2.A$40.A4.B4.B$44.2A2.BA$45.B2.B3$26.
2A$26.2A3$34.2A$33.A2.A$34.2A8.3A$43.A2BA$43.2A.AB$43.A$41.2B3.B6$44.
A$43.3A$42.2A2.A$41.B4.B$40.2A2.BA$36.ABA2.B2.B$36.A2BA$35.2A2.A$35.
2A2.A$36.B.B$42.A11.A$41.3A9.3A$26.2A12.A2.2A7.2A2.A$26.2A12.B4.B5.B
4.B$41.AB2.2A3.2A2.BA$42.B2.B5.B2.B$34.2A10.A3.A$33.A2.A9.2A.2A$34.2A
9.A.A.A.A$45.A.A.A.A$44.2A.A.A.2A7.3A$47.A.A10.A2BA$44.2B.A.A.2B5.AB
2.BA$47.A.A8.A2BA$43.ABA.A.A.ABA4.A2BA$43.ABA.A.A.AB2AB$43.A3.A.A3.A.
A$43.B3.A.A3.B2AB$42.A3.2A.2A3.A$42.B11.B8$57.A$56.3A$55.A2.2A$26.2A
23.A2.4AB$26.2A22.ABA2.2A$49.A.BA$50.2A$34.2A$33.A2.A$34.2A7$48.A6.A$
47.A.A4.3A$48.2A3.A2.2A$52.4AB$53.2A$49.2A$48.A.B$47.A2.2A$48.3A7$26.
2A$26.2A25.A$52.3A$46.A4.A2.2A$34.2A9.A.BA.4AB$33.A2.A9.3A2.2A$34.2A
11.A3$46.A$45.A.A2.B$45.AB$45.3A5$51.A$50.3A$49.A2.2A$48.4AB$49.2A$
43.3A$43.2B$43.ABA$44.AB3$26.2A13.3A$26.2A13.AB$41.3A$43.B$34.2A$33.A
2.A12.A$34.2A12.3A$47.A2.2A$46.4AB$47.2A8$39.2A$38.A.A$37.2A$38.A.A$
39.2A2$46.3A$46.A2BA$44.AB2.BA$44.A2BA$44.A2BA$26.2A$26.2A3$33.2A$32.
A2.A$33.2A2$44.A$43.3A$42.2A2.A$41.B4.B$40.2A2.BA$41.B2.B6$42.3A$42.A
2BA$40.AB2.BA$35.2A3.A2BA$36.2A2.A2BA$33.B2.A$34.2A3$26.2A$26.2A12.3A
9.3A$39.A2BA9.A2BA$39.AB2.BA5.AB2.BA$33.2A6.A2BA5.A2BA$32.A2.A5.A2BA
5.A2BA$33.2A$45.2A.2A$44.A.A.A.A$44.A.A.A.A$43.2A.A.A.2A8.A$44.B.A.A.
B8.3A$43.2A.A.A.2A6.A2.2A$42.A.A.A.A.A.A4.4AB$41.3A2.A.A2.3A4.2A$41.A
2.A.A.A.A2.A$42.A2B.A.A.2BA$42.A2BA3.A2BA$44.A5.A10$26.2A27.3A$26.2A
21.2A3.A2BA$48.A.A3.2A.AB$49.A4.A$33.2A17.2B3.B$32.A2.A$33.2A7$46.BA$
46.ABA$44.B2.2A$53.3A$42.2B8.A2BA$52.2A.AB$44.B2.3A2.A$46.AB2A2B3.B$
46.BA7$26.2A$26.2A2$45.A$33.2A9.A.A4.3A$32.A2.A9.2A3.A2BA$33.2A15.2A.
AB$50.A$46.2A.B3.B$45.A.A.B$44.A2.2A$45.2A9$49.3A$43.A4.A2BA$42.A.A3.
2A.AB$43.3A2.A$46.2B3.B3$43.AB.B$26.2A14.A.A2.A$26.2A14.2A2.B$43.2A2$
33.2A$32.A2.A$33.2A2$47.3A$46.A2BA$46.2A.AB$45.BA$41.2AB5.B$40.2A3.B$
40.2A.B$42.A3$39.2A$38.2A$39.A$40.AB4$46.A$45.3A$44.A2.2A$26.2A15.4AB
$26.2A16.2A3$32.2A$31.A2.A$32.2A5$42.3A$42.A2BA$40.AB2.BA$40.A2BA$40.
A2BA5$33.2A$32.B3A6.A$30.B5.B4.3A$29.2A.B7.A2.2A$30.B.A.AB3.4AB$32.B
2A5.2A3$26.2A$26.2A2$40.A11.A$32.2A5.3A9.3A$31.A2.A3.2A2.A7.A2.2A$32.
2A5.B4A5.4AB$41.2A7.2A2$44.2A.2A$43.ABA.ABA$43.A.A.A.A$42.2A.A.A.2A$
43.A.A.A.A8.3A$42.2A.A.A.2A6.A2BA$42.A.BA.AB.A6.2A.AB$43.2A3.2A7.A$
43.2A3.2A5.2B3.B11$26.2A$26.2A20.2A$47.A.A5.A$48.A5.3A$32.2A19.2A2.A$
31.A2.A17.B4.B$32.2A17.2A2.BA$52.B2.B8$44.3A$43.AB.A$42.A2B$43.AB.A6.
A$44.3A5.3A$51.2A2.A$50.B4.B$49.2A2.BA$50.B2.B5$26.2A$26.2A2$43.A$32.
2A8.B.2A$31.A2.A6.A2.2A$32.2A6.B.B8.A$39.2A9.3A$40.B.B6.2A2.A$41.A2.
2A2.B4.B$42.B.2A.2A2.BA$43.A4.B2.B10$42.A$41.A.A5.A$42.2A4.3A$47.2A2.
A$46.B4.B$43.2A.A2.BA$42.A.ABA2.B$26.2A13.A2.A$26.2A14.2A3$32.2A$31.A
2.A$32.2A4$47.A$40.A5.3A$39.A.A3.2A2.A$40.2A2.B4.B$43.2A2.BA$44.B2.B$
41.B$40.2A.A$39.A2.2BA$40.A2BA$40.2A8$26.2A16.3A$26.2A15.A2BA$43.2A.A
B$43.A$31.2A8.2B3.B$30.A2.A$31.2A7$42.A$41.3A$40.A2.2A$39.4AB$40.2A4$
32.3A$31.2A.A$30.AB$31.2AB6.3A$32.A6.A2BA$39.2A.AB$39.A$26.2A9.2B3.B$
26.2A3$31.2A$30.A2.A$31.2A5.3A9.3A$38.A2BA7.A2BA$37.BA.2A7.2A.AB$41.A
7.A$38.B3.2B3.2B3.B$43.A3.A$43.2A.2A$42.ABA.ABA$42.A.A.A.A$42.A.A.A.A
9.A$41.2A.A.A.2A7.3A$42.A.A.A.A7.2A2.A$43.2B.2B7.B4.B$43.2B.2B6.2A2.B
A$44.A.A8.B2.B$43.B3.B7$26.2A$26.2A19.2A$47.2A$46.A$31.2A14.B.B$30.A
2.A14.AB3.3A$31.2A20.A2BA$51.AB2.BA$51.A2BA$51.A2BA6$45.A$44.2AB$43.A
B$44.2AB$45.A2$51.3A$51.A2BA$49.AB2.BA$49.A2BA$49.A2BA3$26.2A$26.2A3$
31.2A$30.A2.A8.2A$31.2A7.2A.A$40.2A$40.2A.A$42.2A5.3A$49.A2BA$47.AB2.
BA$47.A2BA$47.A2BA8$40.A$39.ABA$39.B.2A$37.ABA.B$37.AB8.3A$37.ABA.B5.
A2BA$39.B.2A2.AB2.BA$26.2A11.ABA3.A2BA$26.2A12.A4.A2BA3$31.2A$30.A2.A
$31.2A5$39.A$38.A.A$39.2A4.3A$45.A2BA$43.AB2.BA$40.A2.A2BA$39.A.3A2BA
$38.A2.A$39.2A9$26.2A$26.2A$44.A$43.3A$30.2A10.2A2.A$29.A2.A8.B4.B$
30.2A8.2A2.BA$41.B2.B9$40.3A$39.A2BA$39.2A.AB$39.A$37.2B3.B$32.2A$30.
B2.A$30.A.A$31.A2$40.A$39.3A$26.2A10.2A2.A$26.2A9.B4.B$36.2A2.BA$37.B
2.B$30.2A$29.A2.A$30.2A2$38.A11.A$37.3A9.3A$36.A2.2A7.2A2.A$36.B4.B5.
B4.B$37.AB2.2A3.2A2.BA$38.B2.B5.B2.B$42.A3.A$42.2A.2A$41.A.A.A.A$41.A
.A.A.A$40.2A.A.A.2A7.3A$43.A.A10.A2BA$40.2BAB.BA2B5.AB2.BA$40.2A5.2A
5.A2BA$40.B7.B5.A2BA$40.A.B3.B.A$41.A5.A4$26.2A$26.2A20.B$47.2A$47.A.
A$30.2A16.3A$29.A2.A15.3A$30.2A$53.A$52.3A$51.A2.2A$50.4AB$51.2A4$46.
A$45.A.A2.B$45.AB$45.3A5$51.A$50.3A$49.A2.2A$48.4AB$49.2A$26.2A15.3A$
26.2A15.2B$43.ABA$44.AB$30.2A$29.A2.A$30.2A9.3A$41.AB$41.3A$43.B2$49.
A$48.3A$47.A2.2A$46.4AB$47.2A8$39.2A$38.A.A$37.2A$38.A.A$39.2A6.A$26.
2A18.3A$26.2A17.A2.2A$44.4AB$45.2A$30.2A$29.A2.A$30.2A6$36.3A$36.ABA$
35.2A.A$34.2A9.A$35.2A.A5.3A$36.ABA4.A2.2A$36.3A3.4AB$43.2A9$26.2A$
26.2A3$29.2A$28.A2.A10.3A$29.2A11.A2BA$40.AB2.BA$40.A2BA$40.A2BA9$40.
A$34.B4.3A$32.3A3.2A2.A$32.3A2.B4.B$31.A2.2A.A2.BA$30.3A.3AB2.B$31.A
2.2A$32.2A$32.B2$26.2A$26.2A10.3A$38.A2BA$36.AB2.BA$29.2A5.A2BA$28.A
2.A4.A2BA$29.2A5$36.3A9.3A$35.A2BA9.A2BA$35.AB2.BA5.AB2.BA$37.A2BA5.A
2BA$37.A2BA5.A2BA2$41.2A.2A$40.A.A.A.A$40.A.A.A.A$39.2A.A.A.2A8.A$40.
B.A.A.B8.3A$39.2A.A.A.2A6.A2.2A$39.2A.A.A.2A5.4AB$41.BA.AB8.2A$42.B.B
$41.2B.2B2.2B$38.B.A2B.2B.A.A$26.2A13.2B.2B4A$26.2A14.B.B.3A.2A$41.2A
.2A3.3A2$29.2A$28.A2.A$29.2A4$51.3A$50.A2BA$50.2A.AB$50.A$46.2A.B3.B$
45.A.A.B$44.A2.2A$45.2A9$49.3A$43.A4.A2BA$26.2A14.A.A3.2A.AB$26.2A15.
3A2.A$46.2B3.B2$29.2A$28.A2.A11.AB.B$29.2A11.A.A2.A$42.2A2.B$43.2A6$
47.3A$46.A2BA$46.2A.AB$45.BA$41.2AB5.B$40.2A3.B$40.2A.B$42.A3$39.2A$
38.2A$39.A$40.AB$26.2A$26.2A$45.3A$44.A2BA$29.2A13.2A.AB$28.A2.A12.A$
29.2A11.2B3.B2$39.B5$36.2A$35.ABA$35.A$35.ABA$36.2A$43.3A$42.A2BA$42.
2A.AB$42.A$40.2B3.B6$26.2A$26.2A$34.A$29.A2B.A.A$29.A3BA.B$28.A$29.A
3BA.B$29.A2B.A.A6.A$34.A6.3A$40.A2.2A$39.4AB$40.2A9$31.3A$31.ABA4.3A$
30.2A.A4.A2BA$29.2A2.2A.AB2.BA$30.2A.B3A2BA$31.A3B2A2BA$31.A2BA2$26.
2A$26.2A2$38.A$28.2A7.3A$27.A2.A5.A2.2A$28.2A5.4AB$36.2A7$34.3A9.3A$
34.A2BA7.A2BA$33.BA.2A7.2A.AB$37.A7.A$34.B3.2B3.2B3.B$39.A3.A$39.2A.
2A$38.ABA.ABA$38.A.A.A.A$38.A.A.A.A9.A$37.2A.A.A.2A7.3A$38.A.A.A.A7.
2A2.A$39.A3.A7.B4.B$37.BA5.AB4.2A2.BA$26.2A10.A5.A6.B2.B$26.2A9.B7.B$
38.B5.B2$28.2A$27.A2.A$28.2A2$44.2A$44.A.BA$44.A3B$45.ABA$46.A$49.3A$
49.A2BA$47.AB2.BA$47.A2BA$47.A2BA4$43.A$42.A.B$41.2A.A$42.2AB$43.A3$
26.2A$26.2A19.3A$47.A2BA$45.AB2.BA$28.2A15.A2BA$27.A2.A10.A3.A2BA$28.
2A10.BAB$42.A$40.B.B$41.A2$39.A$38.2AB$37.AB$38.2AB$39.A2$45.3A$45.A
2BA$43.AB2.BA$43.A2BA$43.A2BA7$26.2A$26.2A8.2A$34.2A.A$34.2A$28.2A4.
2A.A$27.A2.A5.2A5.3A$28.2A13.A2BA$41.AB2.BA$41.A2BA$41.A2BA8$34.A$33.
ABA$33.B.2A$31.ABA.B$31.AB$31.ABA.B$33.B.2A$33.ABA$34.A4$39.BA$38.A2.
A$37.2B2.2A$40.2A$40.A$37.BAB$38.A8$42.A$41.3A$35.A4.A2.2A$34.A.BA.4A
B$35.3A2.2A$28.A7.A$27.3A$26.A2.2A$26.B4.B3.A$27.AB2.2A.A.A2.B$28.B2.
B2.AB$34.3A!
Two, because rakes of longer periods may be useful in the construction of a breeder, c/2 spaceships of other periods would be useful when their periods are combined with the 14c/28 puffer, and I would like to ask the best way to search for spaceships of unusual periods.
Three, in the case that I do find a sufficiently small/long-period rake, I would then need to find a spaceship synthesis for a small infinite growth pattern, the best candidate for which I believe to be the 14c/28 puffer itself, although other puffers have been found, like this one by Schiaparelliorbust and RocknLol:
Code: Select all
x = 57, y = 73, rule = 23/3/3
22$15.A7.A$14.3A5.3A$14.A2.B3.B2.A$15.A7.A$10.2A3.3A3.3A3.2A$9.2A.B2A
2.BA.AB2.2AB.2A$9.A4.2A.2A.2A.2A4.A$10.3A.2A7.2A.3A$10.AB4.3A.3A4.BA$
11.2A5.A.A5.2A$12.B13.B$14.BAB5.BAB$13.3A7.3A$12.2A11.2A$11.B.A11.A.B
$13.A11.A$11.B2A11.2AB$13.3A7.3A$12.A3.A5.A3.A$12.2A.A.A3.A.A.2A$11.A
.A.A.2A.2A.A.A.A$10.2A.A2.A.A.A.A2.A.2A$10.A2.B.AB.A.A.BA.B2.A$9.2A4B
2.AB.BA2.4B2A$9.B2.2BA9.A2B2.B$11.AB3.B5AB3.BA$12.2A3.A.A.A3.2A$9.2A
2.A11.A2.2A$8.B3AB2A9.2AB3AB$13.2A9.2A$8.B.A4.A7.A4.A.B$9.2B.4AB2A.2A
B4A.2B$10.2B3A2.BA.AB2.3A2B$10.A2.A4.A.A4.A2.A$11.AB4.2A.2A4.BA$18.A.
A$16.B2A.2AB$9.3A4.A5.A4.3A$8.AB.BA4.2B.2B4.AB.BA!These questions are specific to the rule 23/3/3 but I have been told that it wouldn't be out of the question to believe that any approach for solving these problems algorithmically doesn't have a wider application.
Thank you.