## 2456/3457/4

For discussion of other cellular automata.
ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### 2456/3457/4

This rule has (as far as I know) two different spaceships with 4 variations (kind of like tagalongs) each:

Code: Select all

``````x = 78, y = 44, rule = 2456/3457/4
2\$4.2A19.2A24.2A19.2A\$3.4A17.4A22.4A17.4A\$3.C2AC17.C2AC22.C2AC17.C2AC
\$4.2B18.2AB23.3A19.2B\$24.BC24.CB20.2A\$51.B19.4A\$71.C2AC\$72.2B23\$4.2A
20.2A23.2A19.2A\$3.5A17.5A20.5A16.5A\$3.CABAB17.CABAB20.CABAB16.CABAB\$
3.2A.A18.2A.A21.2A.A17.2A.A\$2.4AB17.4ACA19.4AB17.BCAB\$2.CABC18.C2A.BC
19.CABCA18.2A\$3.C20.2A.2A21.C21.2A\$24.A.2AB\$25.2AC\$25.2A!
``````
I've also found 3 oscillators:

Code: Select all

``````x = 23, y = 25, rule = 2456/3457/4
2\$2.2A12.BC\$3.2A12.3A\$2.CB2A10.3A\$2.BC.A12.CB12\$3.2A\$2.A2.A\$.A4.A\$.A
4.A\$2.A2.A\$3.2A!
``````
EDIT: I managed to stabilize a third kind of spaceship:
EDIT2: Here you can see all the different spaceships, sorted by the width of its main "block":

Code: Select all

``````x = 97, y = 161, rule = 2456/3457/4
2\$5.2A4.2A\$5.2A4.2A2\$5.2A4.2A\$5.2A4.2A\$22.2A19.2A24.2A19.2A\$5.2A.2A.
2A8.4A17.4A22.4A17.4A\$5.2A.2A.2A8.C2AC17.C2AC22.C2AC17.C2AC\$22.2B18.
2AB23.3A19.2B\$11.2A29.BC24.CB20.2A\$11.2A56.B19.4A\$89.C2AC\$11.2A77.2B\$
11.2A19\$5.2A.2A.2A\$5.2A.2A.2A2\$5.2A15.2A20.2A23.2A19.2A\$5.2A14.5A17.
5A20.5A16.5A\$21.CABAB17.CABAB20.CABAB16.CABAB\$5.2A.2A.2A8.2A.A18.2A.A
21.2A.A17.2A.A\$5.2A.2A.2A7.4AB17.4ACA19.4AB17.BCAB\$20.CABC18.C2A.BC
19.CABCA18.2A\$11.2A8.C20.2A.2A21.C21.2A\$11.2A29.A.2AB\$43.2AC\$5.2A.2A.
2A30.2A\$5.2A.2A.2A26\$5.2A.2A.2A\$5.2A.2A.2A2\$11.2A\$11.2A8.4A18.4A22.2A
17.4A\$19.7A15.7A19.6A13.7A\$11.2A6.BABACAC15.BABACAC18.4ABAB13.BABACAC
\$11.2A7.A.B3A16.A.B3A18.CACA.A15.A.B3A\$19.A2B.2CB15.A2B.2CB18.2A.2BC
15.BA.2CB\$11.2A6.C21.CA22.4A19.AB\$11.2A52.C2AC18.BA\$66.2B20.BA\$11.2A
76.C\$11.2A8\$23.2A18.4A21.4A17.2A\$21.6A14.7A18.7A14.6A\$20.4ABAB14.BABA
CAC18.BABACAC13.4ABAB\$20.CACA.A16.A.2AB20.A.2AB14.CACA.A\$20.2A.2BC14.
4A2C19.4A2C15.3AC2BA\$19.4A17.B4A20.B4A15.3AB3.C\$19.C5A16.BC3A20.BC3A
14.C2A\$20.C.BAB16.C3AC20.C3AC15.C2A\$21.3A18.B.B22.CAB15.C2AB\$20.B2AC
17.C2A24.B16.ABC\$20.A2C19.B2A\$42.2C9\$22.2A\$20.6A\$19.4ABAB\$19.CACA.A\$
20.2AC2BA\$20.C2A2.C\$21.CB22\$5.2A.2A.2A\$5.2A.2A.2A\$22.4A18.2A22.4A\$5.
2A4.2A7.7A15.6A18.7A\$5.2A4.2A6.3ABACAC13.5ABAB17.3ABACAC\$19.C2A.B3A
13.B2ACA.A18.C2A.B3A\$5.2A.2A.2A6.2A.A.2CB14.3AC2BA17.2A.A.2CB\$5.2A.2A
.2A6.C2AB17.BCAB3.C16.4AB\$20.BA19.C22.CACA\$5.2A4.2A8.CB42.ACAB\$5.2A4.
2A8.C44.2A\$66.CBA\$5.2A.2A.2A55.C\$5.2A.2A.2A!
``````

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: 2456/3457/4

An unstable width 9 spaceship is synthesized from a width 8 and a width 5:

Code: Select all

``````x = 23, y = 14, rule = 2456/3457/4
17.AB\$17.3AB\$16.2AB.AC\$16.5AB\$17.AC3AC\$20.AC2\$4.2A\$2.6A\$5ABAB\$B2ACA.A
\$.3AC2BA\$BCAB3.C\$.C!
``````
I can't stabilize it... help?

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: 2456/3457/4

A lot of new stuff!

You can use this to make oscillators of almost any period (here, 60 and 120)

Code: Select all

``````x = 35, y = 58, rule = 2456/3457/4
.4A25.4A\$6A23.6A\$6A23.6A\$6A23.6A\$6A23.6A\$.4A25.4A5\$13.CA\$12.B3A\$12.B
3A\$13.CA5\$.4A25.4A\$6A23.6A\$6A23.6A\$6A23.6A\$6A23.6A\$.4A25.4A11\$.4A10.
4A\$6A8.6A\$6A8.6A\$6A8.6A\$6A8.6A\$.4A10.4A5\$5.AC\$4.3AB\$4.3AB\$5.AC5\$.4A
10.4A\$6A8.6A\$6A8.6A\$6A8.6A\$6A8.6A\$.4A10.4A!
``````
Also, this incredibly simple pattern (i don't know how i missed this before) sends a stream of width 4 spaceships:

Code: Select all

``````x = 8, y = 8, rule = 2456/3457/4
3.2A\$2.A2.A\$.A4.A\$A6.A\$A6.A\$.A4.A\$2.A2.A\$3.2A!
``````
I found more spaceships, this is the updated list:

Code: Select all

``````x = 96, y = 235, rule = 2456/3457/4
3\$3.2A4.2A\$3.2A4.2A2\$3.2A4.2A\$3.2A4.2A\$20.2A19.2A24.2A19.2A\$3.2A.2A.
2A8.4A17.4A22.4A17.4A\$3.2A.2A.2A8.C2AC17.C2AC22.C2AC17.C2AC\$20.2B18.
2AB23.3A19.2B\$9.2A29.BC24.CB20.2A\$9.2A56.B19.4A\$87.C2AC\$9.2A77.2B\$9.
2A11\$20.2A\$19.4A\$19.C2AC\$19.4A\$18.2A2.2A\$18.C4AC\$19.B2AB\$20.2A\$20.2C
22\$3.2A.2A.2A\$3.2A.2A.2A2\$3.2A15.2A20.2A23.2A19.2A\$3.2A14.5A17.5A20.
5A16.5A\$19.CABAB17.CABAB20.CABAB16.CABAB\$3.2A.2A.2A8.2A.A18.2A.A21.2A
.A17.2A.A\$3.2A.2A.2A7.4AB17.4ACA19.4AB17.BCAB\$18.CABC18.C2A.BC19.CABC
A18.2A\$9.2A8.C20.2A.2A21.C21.2A\$9.2A29.A.2AB\$41.2AC\$3.2A.2A.2A30.2A\$
3.2A.2A.2A24\$3.2A.2A.2A\$3.2A.2A.2A\$19.4A17.4A22.4A19.2A\$3.2A12.5AB15.
5AB20.5AB17.5A\$3.2A12.B2ACA16.B2ACA21.B2ACA17.3ABAC\$18.ACABA16.2A.3A
20.3ABA16.C2A.2A\$3.2A.2A.2A7.B2A.C16.CB.4A18.B3A.C17.A.BCB\$3.2A.2A.2A
7.ABAB18.3ACAC18.CBA19.2C.2A\$18.B2A19.B4A20.BC.C18.C.CA\$3.2A4.2A8.BC
19.2ACBC20.2A20.B.CB\$3.2A4.2A7.C21.B3.B43.B\$40.C2.2B\$3.2A.2A.2A32.A\$
3.2A.2A.2A31.CAB\$42.ABC9\$19.4A\$17.5AB\$17.B2ACA\$18.2A.3A\$18.CB.4A\$19.
3ACAC\$19.4AB\$20.BCA2C\$19.C.B2AB\$19.CAC.A\$19.BC24\$3.2A.2A.2A\$3.2A.2A.
2A2\$9.2A\$9.2A8.4A18.4A22.2A17.4A\$17.7A15.7A19.6A13.7A\$9.2A6.BABACAC
15.BABACAC18.4ABAB13.BABACAC\$9.2A7.A.B3A16.A.B3A18.CACA.A15.A.B3A\$17.
A2B.2CB15.A2B.2CB18.2A.2BC15.BA.2CB\$9.2A6.C21.CA22.4A19.AB\$9.2A52.C2A
C18.BA\$64.2B20.BA\$9.2A76.C\$9.2A8\$21.2A18.4A21.4A17.2A\$19.6A14.7A18.7A
14.6A\$18.4ABAB14.BABACAC18.BABACAC13.4ABAB\$18.CACA.A16.A.2AB20.A.2AB
14.CACA.A\$18.2A.2BC14.4A2C19.4A2C15.3AC2BA\$17.4A17.B4A20.B4A15.3AB3.C
\$17.C5A16.BC3A20.BC3A14.C2A\$18.C.BAB16.C3AC20.C3AC15.C2A\$19.3A18.B.B
22.CAB15.C2AB\$18.B2AC17.C2A24.B16.ABC\$18.A2C19.B2A\$40.2C37\$3.2A.2A.2A
\$3.2A.2A.2A\$20.4A18.2A22.4A17.2A\$3.2A4.2A7.7A15.6A18.7A14.6A\$3.2A4.2A
6.3ABACAC13.5ABAB17.3ABACAC12.5ABAB\$17.C2A.B3A13.B2ACA.A18.C2A.B3A12.
B2ACA.A\$3.2A.2A.2A6.2A.A.2CB14.3AC2BA17.2A.A.2CB13.ACAC2BA\$3.2A.2A.2A
6.C2AB17.BCAB3.C16.4AB16.A3B3.C\$18.BA19.C22.CACA17.CAC\$3.2A4.2A8.CB
42.ACAB\$3.2A4.2A8.C44.2A\$64.CBA\$3.2A.2A.2A55.C\$3.2A.2A.2A!
``````
I'm still trying to stabilize the width 9 spaceship. It lasts around 100 generations:

Code: Select all

``````x = 67, y = 42, rule = 2456/3457/4
3\$5.BA\$3.B3A\$2.CA.B2A\$2.B5A\$.C3ACA\$2.CA8\$13.2ACA\$11.2A.4ACA\$11.3A.6A\$
12.C2A.A.B2A\$13.BABC3A\$15.CA.BA2\$26.BA\$24.B3A\$23.CA.B2A30.AB\$23.B5A
30.3AB\$22.C3ACA30.2AB.AC\$23.CA33.5AB\$59.AC3AC\$62.AC2\$46.2A\$44.6A\$42.
5ABAB\$42.B2ACA.A\$43.3AC2BA\$42.BCAB3.C\$43.C!
``````

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: 2456/3457/4

Two width 7 spaceships can be "tied" together to create a wickstretcher:

Code: Select all

``````x = 9, y = 12, rule = 2456/3457/4
4.4A\$2.7A\$2.BABACAC\$3.A.B3A\$3.BA.2CB\$4.AB\$3.BA\$B2C.AB\$3AB.A\$CACABAB\$
7A\$.4A!``````