## Search Algorithms for rule 23/3/3

For scripts to aid with computation or simulation in cellular automata.
Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Search Algorithms for rule 23/3/3

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.

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!
``````
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:

Code: Select all

``````x = 6, y = 5, rule = 23/3/3
3.A\$2.3A\$.A2.2A\$4AB\$.2A!
``````
In the end I ended up crudely engineering a bulky p28 rake as well as a p56 version:

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
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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
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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
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21.2A\$31.A\$30.A.A\$31.2A5.A\$37.3A\$36.A2.2A\$32.A2.4AB\$31.ABA2.2A\$16.2A
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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.
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2A\$16.2A11.A.BA\$16.2A12.2A3\$20.2A\$19.A2.A\$20.2A5\$28.A6.A\$27.A.A4.3A\$
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26.A.A4.3A\$27.2A3.A2.2A\$16.2A13.4AB\$16.2A14.2A\$28.2A\$27.A.B\$19.2A5.A
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17.A2.A\$18.2A4.3A\$24.AB\$24.3A\$26.B!
``````

Code: Select all

``````x = 72, y = 1590, rule = 23/3/3
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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!
``````
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:

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!``````
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.

silversmith
Posts: 119
Joined: June 15th, 2020, 6:20 pm

### Re: Search Algorithms for rule 23/3/3

As per your second question, rlifesrc could work well for finding medium period ships(eg. 3c/6, 4c/8).

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

Thank you,

Does anyone have suggestions for parameters or a method for using rlifesrc?

silversmith
Posts: 119
Joined: June 15th, 2020, 6:20 pm

### Re: Search Algorithms for rule 23/3/3

With rlifesrc the main settings are:

Rule - this is the rule the ship is run in
Width - the maximum width of the ship
Height - the maximum height of the ship
Period - the period of the ship
dx - The amount the ship moves horizontally each period
dy - The amount the ship moves vertically each period
Symmetry:
C1 - Asymmetric
D2 - Reflected along a line(the line next to it shows the orientation of the reflection)

For an example, this is for a 3c/6 ship
Rule- 23/3/3
Width- 19
Height- 21
Period- 6
dx- 0
dy- 3
Symmetry- D2|

After about 7 minutes I found this ship, along with a tagalong:

Code: Select all

``````x = 19, y = 16, rule = 23/3/3
9.A\$7.2AB2A\$3.A3.AB.BA3.A\$.2AB2A.A.A.A.2AB2A\$A2B.BA.A3.A.AB.2BA\$2B.A.
A.BABAB.A.A.2B\$2B2.ABA5.ABA2.2B\$.B15.B\$.AB2A9.2ABA\$3.3A7.3A\$3.A.BA5.A
B.A\$4.B.A5.A.B2\$6.2A\$6.2BA\$6.2A!``````

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

A little update on what I've been doing.

I have figured out how to sufficiently lower the period of the puffer, and am working on a search algorithm to enumerate parvoship configurations under a boat to make a smaller rake.

I still have yet to make headway on finding a synthesis for an infinite growth pattern, however I suspect if I can find a way to synthesize this still life and a way of synthesizing parvoships from the side so that they do not perturb the still life before forming I may be onto something:

Code: Select all

``````x = 46, y = 17, rule = 23/3/3
21.BA15.AB\$21.3A13.3A\$20.3A.A11.A.3A\$21.A.A13.A.A\$21.A3.2A7.2A3.A\$24.
2A9.2A\$23.A.A9.A.A\$2.2A.2A21.2A.2A\$.A.A.A.A19.A.A.A.A\$.A.A.A.A19.A.A.
A.A\$2A.A.A.2A17.2A.A.A.2A\$4.A25.A\$43.A\$42.3A\$41.A2.2A\$40.4AB\$41.2A!``````
I searched for syntheses on catalogue however none of them were very helpful.

If anyone has any suggestion on how to search for a synthesis for any of this or some simpler infinite growth pattern I would appreciate it.

wwei47
Posts: 1012
Joined: February 18th, 2021, 11:18 am

### Re: Search Algorithms for rule 23/3/3

Francisco wrote:
April 30th, 2021, 12:26 pm
I searched for syntheses on catalogue however none of them were very helpful.

If anyone has any suggestion on how to search for a synthesis for any of this or some simpler infinite growth pattern I would appreciate it.
Is this in any way, shape, or form, helpful?

Code: Select all

``````x = 25, y = 29, rule = 23/3/3
22.3A\$22.3B\$20.2A.2B\$20.AB.2A\$3.2A.2A12.A2B\$2.A.A.A.A.A10.2A\$2.A.A.A2.
2A\$.2A.A.A\$5.A12.2A\$9.2A7.2A\$8.A2.A\$9.2A2\$7.A\$6.A.A\$7.A.A\$8.A5.3A\$5.A
7.A2BA\$4.A.A6.AB2.BA\$4.A2.A7.A2BA\$5.2A8.A2BA3\$2.A\$.3A\$A2.2A\$B4.B\$.AB2.
2A\$2.B2.B!
``````
EDIT: And this?

Code: Select all

``````x = 22, y = 46, rule = 23/3/3
4.B2.B\$3.AB2.2A\$2.B4.B\$2.A2.2A\$3.3A\$4.A3\$7.2A8.A2BA\$6.A2.A7.A2BA\$6.A.
A6.AB2.BA\$7.A7.A2BA\$10.A5.3A\$9.A.A\$8.A.A\$9.A2\$11.2A\$10.A2.A\$11.2A7.2A
\$20.2A\$3.2A.2A.A\$A.A.A.A.2A\$2A2.A.A\$4.A.A13.2A\$5.A5.2A7.2A\$10.A2.A\$11.
2A2\$9.A\$8.A.A\$9.A.A\$10.A\$7.A9.A\$6.A.A7.3A\$6.A2.A5.A2.2A\$7.2A6.B4.B\$16.
AB2.2A\$17.B2.B3\$3.3A\$3.A2BA\$2.BA.2A\$6.A\$3.B3.2B!
``````
Edit 2: And this?

Code: Select all

``````x = 18, y = 24, rule = 23/3/3
4.B2.B\$3.2A2.BA\$4.B4.B\$5.2A2.A\$6.3A\$7.A5\$2A7.2A\$.A7.A\$.A.2A.2A.A2.2A\$
2.A.A.A.A3.A.A\$4.A.A6.2A\$4.A.A\$5.A2\$13.A\$12.3A\$11.A2.2A\$11.B4.B\$12.AB
2.2A\$13.B2.B!
``````
Edit 3: And this?

Code: Select all

``````x = 47, y = 34, rule = 23/3/3
10.2A7.2A\$11.A7.A\$11.A.2A.2A.A\$12.A.A.A.A\$13.A2.A\$16.A.A\$13.A3.A.A\$12.
A.A3.2A24.A\$11.A.A29.2AB\$12.A29.2A.A\$15.A27.A.2A\$14.A.A27.3A\$13.A.A29.
A\$14.A\$17.A\$16.A.A\$15.A2.A\$16.2A\$35.2A\$34.A2B\$34.AB.2A\$34.2A.2B\$36.3B
\$36.3A3\$.A\$A.A\$.2A5.A\$7.3A\$6.2A2.A\$5.B4.B\$4.2A2.BA\$5.B2.B!
``````
Edit 4: And this?

Code: Select all

``````x = 22, y = 19, rule = 23/3/3
.2A7.2A\$2.A7.A\$2.A.2A.2A.A\$3.A.A.A.A\$5.A.A\$2A3.A2.A\$2A4.2A\$10.A\$9.A.A
\$8.A.A3.A\$9.A3.A.A\$12.A2.A\$13.2A2\$2.3A12.3A\$2.A2BA10.A2BA\$AB2.BA10.AB
2.BA\$A2BA14.A2BA\$A2BA14.A2BA!
``````
Edit 5: And this?

Code: Select all

``````x = 93, y = 63, rule = 23/3/3
92.B\$92.B\$26.A62.3A\$25.B2A60.ABA\$25.A.2A11.A47.AB\$24.2A.A11.A.A46.3A.
B\$24.3A13.A49.B\$25.A21.2A\$46.A2.A\$47.A.A\$48.A\$45.A\$44.A.A\$45.A.A\$46.A
\$31.2A9.2A\$32.A8.A2.A\$32.A.2A.2A2.A2.A\$33.A.A.A4.2A3.2A\$34.A2.A9.A.A\$
37.A.A8.A\$38.A.A2.2A\$39.A2.A.A\$43.A2\$2.2A\$2.2BA\$2A.BA\$2B.2A\$3B\$3A28\$52.
3A\$51.A2BA\$51.AB2.BA\$53.A2BA\$53.A2BA!
``````
Edit 6: And this?

Code: Select all

``````x = 24, y = 24, rule = 23/3/3
2A\$.A\$.A.2A.2A\$2.A.A.A\$3.A2.A\$6.A.A\$7.A.A10.A\$8.A10.A.A\$20.A11\$21.A\$20.
3A\$19.A2.2A\$18.4AB\$19.2A!
``````
Edit 7: And this?

Code: Select all

``````x = 31, y = 20, rule = 23/3/3
10.2A\$10.2A8.3A\$2A18.3B\$.A16.2A.2B\$.A.2A.2A10.AB.2A\$2.A.A.A11.A2B\$3.A
2.A12.2A\$6.A.A\$7.2A3.A\$11.A.A\$11.A.A3.A\$12.A3.A.A\$15.A.A3.A\$16.A3.A.A
6.A\$19.A2.A5.BAB\$20.2A5.A\$26.2A\$25.2A2.2B\$26.A2.A\$27.AB!
``````
Edit 8: And this?

Code: Select all

``````x = 20, y = 18, rule = 23/3/3
2A\$.A\$.A.2A.2A\$2.A.A.A\$6.A\$6.A.2A\$2.2A3.A2.A\$2.2A4.2A\$12.A\$11.A.A\$10.
A2.A\$11.2A\$16.2A\$4.3A8.A2B\$4.A2BA7.AB.2A\$2.AB2.BA7.2A.2B\$2.A2BA11.3B\$
2.A2BA11.3A!
``````
Edit 9: And this?

Code: Select all

``````x = 13, y = 18, rule = 23/3/3
3.2A\$4.A\$4.A.2A.2A\$5.A.A.A\$9.A\$9.A.A\$10.A.A\$11.A5\$2.2A\$2.2BA\$2A.BA3.2A
\$2B.2A2.A.A\$3B5.A\$3A!
``````
Edit 10: And this?

Code: Select all

``````x = 34, y = 20, rule = 23/3/3
2.BA\$.A2.A\$2B2.2A9.2A\$3.2A11.A\$3.A5.2A5.A.2A.2A\$BAB5.A2.A5.A.A.A\$.A6.
A.A3.A6.A\$9.A3.A.A5.2A\$12.A.A3.A\$13.A3.A.A5.A\$17.A.A4.A.A\$18.A5.2A2\$10.
2A18.A\$10.2BA16.3A\$8.2A.BA15.2A2.A\$8.2B.2A16.B4A\$8.3B20.2A\$8.3A8.2A\$19.
2A!
``````
Edit 11: And this?

Code: Select all

``````x = 20, y = 27, rule = 23/3/3
2.2A\$3.A\$3.A.2A.2A\$4.A.A.A.A.2A\$9.2A.A.A\$13.A\$18.2A\$9.2A7.2A\$8.A2.A\$9.
2A2\$7.A\$6.A.A\$7.A.A\$8.A5.3A\$5.A7.A2BA\$4.A.A6.AB2.BA\$4.A2.A7.A2BA\$5.2A
8.A2BA3\$2.A\$.3A\$A2.2A\$B4.B\$.AB2.2A\$2.B2.B!
``````
Edit 12: And this?

Code: Select all

``````x = 25, y = 20, rule = 23/3/3
4.2A\$4.2A8.3A\$14.3B\$2A10.2A.2B\$.A10.AB.2A\$.A.A8.A2B\$2.2A9.2A2\$6.A\$.2A
2.A.A\$.2A2.A.A3.A\$6.A3.A.A\$9.A.A3.A\$10.A3.A.A6.A\$13.A2.A5.BAB\$14.2A5.
A\$20.2A\$19.2A2.2B\$20.A2.A\$21.AB!
``````
Self-proclaimed synthesis "expert"

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

Thank you for that synthesis, I am a little curious as to how you found it.

Finding a way to synthesize parvoships from the side without damaging the modified twin hat is proving difficult. I am experimenting with pairing one-time turner patterns with still lifes that have a similar leading edge as the modified twin hat. This one, for example comes pretty close:

Code: Select all

``````x = 33, y = 14, rule = 23/3/3
10.2A9.2A\$10.A.A7.A.A\$11.A9.A\$8.A15.A\$7.A.A13.A.A\$7.A.A4.2A.2A4.A.A\$
8.A4.A.A.A.A4.A\$2.BA10.A3.A10.AB\$.A2.A23.A2.A\$2B2.2A21.2A2.2B\$3.2A23.
2A\$3.A25.A\$BAB27.BAB\$.A29.A!
``````
I am also curious if you also have the intervening steps in the synthesis between the ones you posted where the sacrificial ash is synthesized, as the ash is very tightly packed and I'm not entirely sure it's trivial how to put them together.

wwei47
Posts: 1012
Joined: February 18th, 2021, 11:18 am

### Re: Search Algorithms for rule 23/3/3

Francisco wrote:
May 6th, 2021, 12:02 pm
Thank you for that synthesis, I am a little curious as to how you found it.

I am also curious if you also have the intervening steps in the synthesis between the ones you posted where the sacrificial ash is synthesized, as the ash is very tightly packed and I'm not entirely sure it's trivial how to put them together.
1. I just messed around, figuring out what sparks I needed and generally trying to reduce it to a simple still life. I just got lucky that I got back to the beginning.
2. No. I was hoping for a smaller rake than these:

Code: Select all

``````x = 59, y = 170, rule = 23/3/3
37.3A9.3A\$36.A2BA9.A2BA\$36.AB2.BA5.AB2.BA\$38.A2BA5.A2BA\$38.A2BA5.A2BA
2\$42.2A.2A\$41.A.A.A.A\$41.A.A.A.A\$40.2A.A.A.2A6.3A\$41.B.A.A.B7.A2BA\$19.
3A9.3A6.2A.A.A.2A4.AB2.BA\$19.A2BA7.A2BA6.A2.A.A2.A4.A2BA\$18.BA.2A7.2A
.AB5.A2BA.A2BA4.A2BA\$22.A7.A10.2A3.2A\$19.B3.2B3.2B3.B\$24.A3.A\$24.2A.2A
\$23.ABA.ABA\$23.A.A.A.A\$13.3A7.A.A.A.A\$13.A2BA5.2A.A.A.2A\$12.BA.2A6.A.
A.A.A19.2A\$16.A7.A3.A19.A.A\$13.B3.2B3.BA5.AB18.A\$23.A5.A\$22.B7.B24.3A
\$23.B5.B18.2A5.A2BA\$20.A27.2A3.AB2.BA\$19.B2A31.A2BA\$19.A2.A30.A2BA\$19.
B.2A\$20.2A19.3A\$18.A.2A19.A2BA\$17.A3BA18.BA.2A\$17.A3BA22.A\$19.A21.B3.
2B6.2A\$13.3A36.2A.A\$13.A2BA34.A3.A\$12.BA.2A34.2A.A\$16.A35.2A\$13.B3.B.
2A\$17.B.A.A22.ABA.ABA\$18.2A2.A4.3A14.ABA.ABA\$20.2A5.A2BA15.2A.A\$21.A3.
AB2.BA\$22.A2.A2BA\$21.A.3A2BA8.3A\$21.A.A13.A2BA\$22.A13.BA.2A\$40.A\$37.B
3.2B3\$35.3A\$34.A2BA\$34.AB2.BA4.2A7.3A\$36.A2BA2.2ABA6.A2BA\$36.A2B3A3.A
6.2A.AB\$41.A.2A7.A\$42.3A5.2B3.B2\$23.3A\$23.2BA6.3A\$21.4B2.B3.A2BA\$23.B
.A.2A2.2A.AB12.B\$20.B2.B.AB2A2.A17.B\$23.2A.A2.2B3.B\$21.BAB25.A6.A\$22.
A24.B3A4.3A\$50.A3.2A2.A\$47.2A.A2.B4.B\$46.A2BA2.2A2.BA\$46.A2BA3.B2.B\$42.
2A3.A\$36.A5.2A\$35.3A\$34.A2.2A\$34.B4.B\$35.AB2.2A\$9.A11.A5.2A7.B2.B\$8.3A
9.3A3.A2.A\$7.A2.2A7.2A2.A3.2A\$7.B4.B5.B4.B\$8.AB2.2A3.2A2.BA\$9.B2.B5.B
2.B\$13.A3.A21.3A\$13.2A.2A22.BA5.B\$12.A.A.A.A20.2A5.A2.B\$12.A.A.A.A19.
BA2.B3.A2BA\$.3A7.2A.A.A.2A18.A7.ABA\$A2BA10.A.A22.B.B\$AB2.BA5.2B.A.A.2B
\$2.A2BA8.A.A\$2.A2BA4.ABA.A.A.ABA6.2A\$8.B2ABA.A.A.ABA5.A2.A16.3A\$8.A.A
3.A.A3.A6.2A17.A2BA\$7.B2AB3.A.A3.B23.AB2.BA\$9.A3.2A.2A3.A13.3A6.A2BA\$
9.B11.B12.AB.BA5.A2BA\$34.AB.2BA\$35.2A2.A\$37.2A5\$6.A31.2A5.A\$5.3A19.2A
9.2A4.3A\$4.2A2.A17.A2.A13.A2.2A\$5.B4A2.A14.2A13.4AB\$7.2A2.ABA29.2A\$11.
AB.A\$12.2A4\$35.A\$34.A.A\$34.A.A\$35.A2.3A\$37.A3BA\$27.2A7.A2B.BA6.3A\$8.A
6.A10.A2.A6.A2B2.BA4.A2BA\$7.3A4.A.A10.2A6.2A.2ABA5.2A.AB\$6.2A2.A3.2A20.
A3.BA5.A\$7.B4A25.3A5.2B3.B\$9.2A26.3A\$13.2A\$13.B.A\$12.2A2.A\$13.3A32.3A
\$47.A2BA\$47.2A.AB\$47.A\$45.2B3.B\$27.2A\$26.A2.A\$27.2A\$10.A\$9.3A26.A\$8.2A
2.A4.A14.AB3.BAB\$9.B4A.AB.A12.A2BAB\$11.2A2.3A13.A3.A6.B\$16.A14.4A4.2A
.A.A\$32.A2.A.A2.2A.2A5.3A\$33.A.A.2BA.3A5.A2BA\$17.A16.2A.BA10.2A.AB\$13.
B2.A.A16.3A11.A\$17.BA28.2B3.B\$16.3A8.2A\$26.A2.A\$27.2A3\$12.A\$11.3A\$10.
2A2.A\$11.B4A\$13.2A\$18.3A8.2A\$19.2B8.2A\$18.ABA\$18.BA\$27.2A\$26.A2.A\$20.
3A4.2A\$21.BA\$20.3A\$20.B!``````

Code: Select all

``````x = 59, y = 414, rule = 23/3/3
27.A11.A\$26.3A9.3A\$25.2A2.A7.A2.2A\$26.B4A5.4AB\$28.2A7.2A2\$31.2A.2A\$
30.ABA.ABA\$30.A.A.A.A\$29.2A.A.A.2A\$30.A.A.A.A8.3A\$29.2A.A.A.2A6.A2BA\$
29.A.BA.AB.A6.2A.AB\$30.2A3.2A7.A\$30.2A3.2A5.2B3.B8\$16.3A9.3A\$16.A2BA
7.A2BA\$15.BA.2A7.2A.AB\$19.A7.A\$16.B3.2B3.2B3.B4.2A\$21.A3.A8.A.A\$21.2A
.2A9.A\$20.ABA.ABA\$20.A.A.A.A\$10.A9.A.A.A.A\$9.3A7.2A.A.A.2A\$8.A2.2A9.A
.A\$8.B4.B5.2A.A.A.2A\$9.AB2.2A2.B2.A.A.A.A2.B\$10.B2.B2.2A2.B.A.A.B2.2A
\$16.2A4.A.A4.2A\$17.2A2.2A.2A2.2A\$21.B3.B\$35.2A\$34.A.A\$35.A7\$13.3A\$12.
A2BA\$12.AB2.BA2.2A\$14.A2BA2.A.A\$14.A2BA3.A\$35.2A\$34.A.A\$35.A7\$23.A\$
22.A.A\$15.3A4.2A\$14.A2BA\$14.AB2.BA\$16.A2BA2.A12.2A\$16.A2B3A.A10.A.A\$
21.A2.A10.A\$22.2A10\$17.3A5.A\$16.A2BA4.A.A8.2A\$16.AB2.BA2.2A8.A.A\$18.A
2BA13.A\$18.A2BA\$23.BA\$22.A2.A\$22.2A2.A\$22.4A\$24.A4\$20.3A\$20.A2BA\$19.B
A.2A11.2A\$23.A10.A.A\$20.B3.2B9.A4\$31.A\$30.A.A\$30.A.A8.3A\$31.A9.A2BA\$
39.AB2.BA\$39.A2BA\$39.A2BA\$36.AB\$35.A2.A\$34.A2.2A\$35.4A\$36.A2\$31.A\$30.
3A\$29.A.A.B\$28.A\$29.AB2.AB\$31.AB.2A\$31.2A2.A\$31.5A\$31.A2.2A\$30.2A2.A\$
31.3A\$32.A11\$24.A\$23.3A\$22.A2.2A\$22.B4.B\$23.AB2.2A\$24.B2.B3\$40.3A\$40.
A2BA\$38.AB2.BA\$38.A2BA\$38.A2BA\$7.3A9.3A\$6.A2BA9.A2BA11.2A\$6.AB2.BA5.A
B2.BA10.B2AB\$8.A2BA5.A2BA\$8.A2BA5.A2BA\$34.ABA\$12.2A.2A16.A2BA\$11.A.A.
A.A15.AB\$11.A.A.A.A15.A.A4.3A\$.3A6.2A.A.A.2A14.A.A3.A2BA\$A2BA7.B.A.A.
B16.A4.2A.AB\$AB2.BA4.2A.A.A.2A9.A10.A\$2.A2BA4.A2.A.A2.A8.3A7.2B3.B\$2.
A2BA4.A2BA.A2BA7.2A2.A\$11.2A3.2A9.B4A\$29.2A2\$43.3A\$43.A2BA\$41.AB2.BA\$
41.A2BA\$41.A2BA\$8.2A\$8.A.A\$9.A20.2A\$29.A2.A\$.3A26.2A\$A2BA5.2A\$AB2.BA
3.2A25.B\$2.A2BA33.2A\$2.A2BA32.A.2A\$37.2A.A\$15.3A20.2A\$14.A2BA\$14.2A.A
B\$14.A\$4.2A6.2B3.B\$3.A.2A\$3.A3.A\$4.A.2A\$5.2A2\$8.ABA.ABA\$8.ABA.ABA\$9.A
.2A3\$19.3A\$18.A2BA\$18.2A.AB\$18.A\$16.2B3.B\$30.2A\$29.A2.A\$21.3A6.2A\$21.
A2BA\$3.3A7.2A4.AB2.BA\$3.A2BA6.AB2A2.A2BA\$2.BA.2A6.A3.3A2BA\$6.A7.2A.A\$
3.B3.2B5.3A5\$10.B\$9.B2\$2.A6.A\$.3A4.3AB\$A2.2A3.A\$B4.B2.A.2A\$.AB2.2A2.A
2BA\$2.B2.B3.A2BA\$11.A3.2A\$15.2A5.A\$21.3A\$20.2A2.A\$19.B4.B\$18.2A2.BA\$
19.B2.B7.2A5.A11.A\$29.A2.A3.3A9.3A\$30.2A3.A2.2A7.2A2.A\$35.B4.B5.B4.B\$
36.AB2.2A3.2A2.BA\$37.B2.B5.B2.B\$17.3A21.A3.A\$11.B5.AB22.2A.2A\$9.B2.A
5.2A20.A.A.A.A\$9.A2BA3.B2.AB19.A.A.A.A\$10.ABA7.A18.2A.A.A.2A7.3A\$17.B
.B22.A.A10.A2BA\$39.2B.A.A.2B5.AB2.BA\$42.A.A8.A2BA\$38.ABA.A.A.ABA4.A2B
A\$10.3A25.ABA.A.A.AB2AB\$9.A2BA25.A3.A.A3.A.A\$9.AB2.BA23.B3.A.A3.B2AB\$
11.A2BA6.3A13.A3.2A.2A3.A\$11.A2BA5.AB.BA12.B11.B\$19.A2B.BA\$19.A2.2A\$
20.2A5\$13.A5.2A31.A\$12.3A4.2A9.2A19.3A\$11.2A2.A13.A2.A17.A2.2A\$12.B4A
13.2A14.A2.4AB\$14.2A29.ABA2.2A\$44.A.BA\$45.2A4\$23.A\$22.A.A\$22.A.A\$18.
3A2.A\$17.A3BA\$8.3A6.AB.2BA\$8.A2BA4.AB2.2BA20.A6.A\$7.BA.2A5.AB2A.2A18.
A.A4.3A\$11.A5.AB3.A20.2A3.A2.2A\$8.B3.2B5.3A25.4AB\$19.3A26.2A\$44.2A\$
43.A.B\$42.A2.2A\$8.3A32.3A\$8.A2BA\$7.BA.2A\$11.A\$8.B3.2B\$30.2A\$29.A2.A\$
30.2A\$48.A\$20.A26.3A\$19.BAB3.BA14.A4.A2.2A\$23.BA2BA12.A.BA.4AB\$16.B6.
A3.A13.3A2.2A\$14.A.A.2A4.4A14.A\$6.3A5.2A.2A2.A.A2.A\$6.A2BA5.3A.A2B.A.
A\$5.BA.2A10.AB.2A16.A\$9.A11.3A16.A.A2.B\$6.B3.2B28.AB\$40.3A5\$46.A\$45.
3A\$44.A2.2A\$43.4AB\$44.2A\$28.2A8.3A\$28.2A8.2B\$38.ABA\$39.AB\$30.2A\$29.A
2.A\$30.2A4.3A\$36.AB\$36.3A\$38.B5\$28.2A\$28.2A2\$37.A\$36.A.A\$37.2A4\$37.2A
\$36.A.A\$37.A4\$51.2A\$51.2BA\$49.2A.BA\$49.2B.2A\$49.3B\$49.3A\$43.3A\$43.A2B
A\$41.AB2.BA\$41.A2BA\$41.A2BA3\$28.2A\$28.2A6\$35.A\$34.A.A\$35.2A4.3A\$41.A
2BA\$39.AB2.BA\$36.A2.A2BA\$35.A.3A2BA\$34.A2.A\$35.2A10\$39.3A\$39.A2BA\$37.
AB2.BA\$28.2A7.A2BA\$28.2A7.A2BA12\$37.3A\$37.A2BA\$31.B3.AB2.BA\$30.A2.3A
2BA\$31.AB3A2BA\$31.3A3\$21.A9.A\$20.3A7.A.B\$19.2A2.A5.2A.A\$20.B4A5.2AB\$
22.2A7.A3\$28.2A\$28.2A5.3A\$34.A2BA\$34.2A.AB\$34.A\$32.2B3.B!``````
Self-proclaimed synthesis "expert"

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

I am unbelievably close.

Code: Select all

``````x = 86, y = 20, rule = 23/3/3
60.A6.2A3.2A6.A\$30.A.A3.A5.A3.A.A12.A.A13.A.A\$2.A11.A17.A2.2A5.2A2.A
15.2A3.A.3A.A3.2A\$2.A11.A15.3A2.4A.4A2.3A12.2A3.3A3.3A3.2A\$2A13.2A19.
A5.A\$3.2A7.2A\$2.2A9.2A18.2A9.2A18.2A9.2A\$2.2A9.2A18.2A9.2A18.2A9.2A\$
6.2A.2A26.2A.2A26.2A.2A\$5.A.A.A.A24.A.A.A.A24.A.A.A.A\$5.A.A.A.A24.A.A
.A.A24.A.A.A.A\$4.2A.A.A.2A22.2A.A.A.2A22.2A.A.A.2A\$8.A30.A30.A\$21.A\$
20.3A29.A\$19.A2.2A27.3A28.3A\$18.4AB27.2A2.A27.A2BA\$19.2A28.B4.B25.AB
2.BA\$48.2A2.BA26.A2BA\$49.B2.B27.A2BA!
``````

wwei47
Posts: 1012
Joined: February 18th, 2021, 11:18 am

### Re: Search Algorithms for rule 23/3/3

Francisco wrote:
May 13th, 2021, 1:51 pm
I am unbelievably close.

Code: Select all

``````x = 33, y = 25, rule = 23/3/3
2.2A25.2A\$2.2BA23.A2B\$2A.BA23.AB.2A\$2B.2A23.2A.2B\$3B5.2A13.2A5.3B\$3A4.
A2.A11.A2.A4.3A\$7.A.A13.A.A\$8.A15.A\$11.2A7.2A\$11.A9.A\$9.A.A9.A.A\$.3A4.
A.A3.2A.2A3.A.A4.3A\$.3B5.A3.A.A.A.A3.A5.3B\$.2B.2A7.A.A.A.A7.2A.2B\$.2A
.BA6.2A.A.A.2A6.AB.2A\$3.2BA10.A10.A2B\$3.2A23.2A4\$29.A\$28.3A\$27.A2.2A\$
26.4AB\$27.2A!
``````
Self-proclaimed synthesis "expert"

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

Very crude, but a good proof of concept.

I will post more when I finish my search algorithm and find smaller rakes.

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

I have finished my search algorithm and have found interactions that allow me to significantly downscale the rakes:

Code: Select all

``````x = 640, y = 532, rule = 23/3/3
588.3A9.3A\$587.A2BA9.A2BA\$587.AB2.BA5.AB2.BA\$589.A2BA5.A2BA\$589.A2BA
5.A2BA2\$593.2A.2A\$592.A.A.A.A\$592.A.A.A.A\$591.2A.A.A.2A8.A\$592.B.A.A.
B8.3A\$591.2A.A.A.2A6.A2.2A\$591.2A.A.A.2A5.4AB\$593.BA.AB8.2A\$594.B.B\$
593.2B.2B2.2B\$590.B.A2B.2B.A.A\$593.2B.2B4A\$594.B.B.3A.2A\$593.2A.2A3.
3A2\$579.A11.A\$578.3A9.3A\$577.2A2.A7.A2.2A\$578.B4A5.4AB\$580.2A7.2A2\$
583.2A.2A\$582.ABA.ABA\$582.A.A.A.A\$581.2A.A.A.2A\$571.3A8.A.A.A.A\$571.A
2BA6.2A.A.A.2A7.2A\$570.BA.2A6.2A.A.A.2A6.A.A\$574.A7.2A3.2A8.A\$571.B3.
2B5.2A3.2A\$582.B5.B8\$581.2A\$579.B2.2A\$582.A14.2A\$579.B.A14.A.A\$576.A
3.A16.A\$575.3A\$574.A2.2A\$574.B4.B\$575.AB2.2A\$576.B2.B4\$583.B\$584.2A\$
582.B.BA\$583.2BA11.2A\$583.2A11.A.A\$597.A2\$578.A\$577.3A\$576.A2.2A\$576.
B4.B\$577.AB2.2A\$578.B2.B3.B\$585.A\$584.B2\$585.B\$597.2A\$587.2A7.A.A\$
587.2A8.A\$589.A\$587.2A\$587.2A\$580.A\$579.3A\$578.A2.2A\$578.B4.B\$579.AB
2.2A\$580.B2.B3\$597.2A\$596.A.A\$597.A\$219.A11.A\$218.3A9.3A\$217.2A2.A7.A
2.2A349.A5.3A\$218.B4A5.4AB349.3A4.A.BA\$220.2A7.2A350.2A2.A5.2BA\$582.B
4A.2A.BA\$223.2A.2A356.2A2.4A\$222.ABA.ABA360.A\$222.A.A.A.A\$221.2A.A.A.
2A\$211.3A8.A.A.A.A\$211.A2BA6.2A.A.A.2A367.2A\$210.BA.2A9.A.A369.A.A5.A
\$214.A6.2A.A.A.2A367.A5.3A\$211.B3.2B4.2A.A.A.2A372.2A2.A\$217.3A4.A.A
4.2A368.B4.B\$218.2B4.A.A4.2B367.2A2.BA\$218.3A2.2A.2A2.3A360.A7.B2.B\$
592.A.A\$592.A.A\$593.A2\$228.3A9.3A\$228.A2BA7.A2BA\$227.BA.2A7.2A.AB\$
231.A7.A353.3A\$228.B3.2B3.2B3.B349.AB.A\$233.A3.A354.2B\$233.2A.2A355.B
\$232.ABA.ABA353.2A.2A\$222.2A8.A.A.A.A352.2A2.2A\$222.A.A7.A.A.A.A9.A
342.2A2.A\$223.A7.2A.A.A.2A7.3A341.2A.2A\$234.A.A9.2A2.A341.A.2A\$231.2A
.A.A.2A5.B4.B342.A\$231.2A.B.B.2A4.2A2.BA\$245.B2.B3\$238.2B.B2\$243.B\$
237.B4A.A\$238.5A\$222.2A\$222.A.A\$223.A361.3A\$585.A2BA\$584.BA.2A\$243.3A
342.A\$243.A2BA338.B3.2B\$241.AB2.BA\$241.A2BA362.3A\$241.A2BA361.2A.2A\$
238.AB361.3A2.A.A.A2.3A\$237.A2.A359.2A.2A.A.B.A.2A.2A\$236.A2.2A353.2A
4.A3.A.A.A.A.A3.A\$237.4A354.2A4.AB.A2.B.B2.A.BA\$222.2A14.A356.A5.2A.
2A5.2A.2A\$222.A.A368.BA7.B.2A5.2A.B\$223.A377.2A.2A5.2A.2A\$602.B.2B5.
2B.B\$603.3A5.3A3\$241.3A\$241.A2BA\$235.B3.AB2.BA\$234.A2.3A2BA\$235.AB3A
2BA362.A\$235.3A366.3A\$603.2A2.A\$222.2A378.B4.B\$222.A.A10.A365.2A2.BA\$
223.A10.A.B365.B2.B\$233.2A.A\$234.2AB\$235.A\$600.3A\$600.A2BA\$598.AB2.BA
\$239.3A356.A2BA\$239.A2BA355.A2BA\$237.AB2.BA\$237.A2BA\$233.A3.A2BA\$222.
2A8.BAB349.A\$222.A.A9.A348.3A\$223.A8.B.B347.2A2.A5.A\$233.A349.B4A3.2A
B\$585.2A3.AB\$231.A359.2AB\$230.2AB359.A\$229.AB\$230.2AB3.3A\$231.A3.A2BA
\$235.2A.AB\$235.A376.A11.A\$233.2B3.B372.3A9.3A\$610.2A2.A7.A2.2A\$222.2A
387.B4A5.4AB\$222.A.A388.2A7.2A\$223.A\$529.A11.A39.3A32.2A.2A\$215.3A
310.3A9.3A38.A2BA30.ABA.ABA\$214.A2BA309.2A2.A7.A2.2A36.BA.2A30.A.A.A.
A\$214.AB2.BA7.A300.B4A5.4AB41.A29.2A.A.A.2A\$216.A2BA6.A.A301.2A7.2A
40.B3.2B28.A.A.A.A8.3A\$216.A2BA6.A.A385.2A.A.A.2A6.A2BA\$227.A305.2A.
2A76.A.BA.AB.A6.2A.AB\$532.ABA.ABA76.2A3.2A7.A\$532.A.A.A.A76.2A3.2A5.
2B3.B\$531.2A.A.A.2A\$532.A.A.A.A8.3A48.3A\$225.A305.2A.A.A.2A6.A2BA47.A
2BA\$224.B2A303.A3.A.A3.A5.2A.AB46.2A.AB\$226.BA302.2AB.A.A.B2A5.A50.A\$
224.B2A302.AB.A.A.A.A.BA2.2B3.B45.2B3.B\$225.A304.3A.A.A.3A\$531.3A3.3A
61.3A9.3A\$227.A373.A2BA7.A2BA\$226.A.A371.BA.2A7.2A.AB\$226.A.A375.A7.A
\$227.A373.B3.2B3.2B3.B4.2A\$606.A3.A8.A.A\$518.3A9.3A73.2A.2A9.A\$518.A
2BA7.A2BA72.ABA.ABA\$517.BA.2A7.2A.AB71.A.A.A.A\$521.A7.A65.A9.A.A.A.A\$
518.B3.2B3.2B3.B61.3A7.2A.A.A.2A\$523.A3.A65.A2.2A9.A.A\$523.2A.2A9.2A
54.B4.B5.2A.A.A.2A\$522.ABA.ABA7.A.A55.AB2.2A2.B2.A.A.A.A2.B\$522.A.A.A
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339.3A7.2A.A.A.2A72.2A2.2A.2A2.2A\$158.3A9.3A337.A2.2A9.A.A79.B3.B\$
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7.A.A.A.A8.3A37.2A105.ABA63.2A65.3A7.3A31.ABA133.3A7.3A41.ABA\$6.2A.A.
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2A2.BA42.2A126.A.A.2A2.BA52.2A\$12.A3.B2.B28.2A8.3A46.A3.B2.B52.A.A
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57.3A29.AB2.BA135.3A43.AB2.BA125.3A46.AB2.BA135.3A\$2.A2BA56.A2.2A30.A
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121.2A65.2A\$46.2A8.3A115.3A42.2A8.3A119.3A42.2A8.3A132.3A42.2A8.3A\$
46.2A8.2B115.A2BA42.2A8.2B119.A2BA42.2A8.2B132.A2BA42.2A8.2B\$56.ABA
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3.B44.2A\$3.3A41.A2.A47.3A59.3A57.A2.A61.3A49.3A5.A51.A2.A64.3A59.3A5.
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64.B55.2B3.B60.A2BA64.B!
``````

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

Here is an improved version of the Breeder:

Code: Select all

``````x = 1443, y = 1705, rule = 23/3/3
1078.2A\$1078.2BA\$1076.2A.BA\$1076.2B.2A\$1061.A14.3B\$1060.B2A13.3A\$
1045.A14.A.2A\$1044.B2A12.2A.A24.BA\$1029.A14.A.2A11.3A24.A2.A\$1028.B2A
12.2A.A13.A24.2B2.2A\$1028.A.2A11.3A42.2A\$1015.BA10.2A.A13.A18.2A.B13.
A7.A\$931.BA81.A2.A9.3A34.B.2A7.B4.3A2.BAB\$920.A9.A2.A79.2B2.2A9.A35.A
BA8.A.2A4.2A.A\$919.3A7.2B2.2A37.2A42.2A31.BA.A12.A10.8A\$919.2A.A9.2A
38.2BA41.A33.ABA\$920.A.2A8.A37.2A.BA38.ABA34.3A23.8A\$920.B2A6.BAB38.
2B.2A37.A2B16.2A.2A39.A.2A4.2A.A22.B\$921.A8.A39.3B39.A.2B15.A3.A39.B
4.3A2.BAB19.B.3A\$970.3A39.B2.AB2A13.3A45.A7.A21.BA\$928.3A57.B28.BA14.
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2A3.2A8.2A12.3A69.A2.A8.2A.4A2.B\$985.2A2.3A2.2A3.A2.A12.A71.BA15.B2AB
\$961.B.B21.A3.3A2.BA4.2A96.B7A\$960.2A.2A21.A3.2A.3A\$961.ABA23.B2.B16.
A13.A13.A13.A13.A13.A20.B7A\$938.B23.A43.A.A11.A.A11.A.A11.A.A11.A.A
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2.B\$939.3A21.2A125.2A2.B3.2A.A6.3A\$940.ABA18.5A124.2A17.ABA\$941.BA18.
AB2.2A38.A84.2A2.B15.BA\$938.B.3A5.A11.2A.BA.A37.3A83.A16.B.3A\$940.B6.
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960.B3.4A131.BA290.B2A13.3A\$958.2A416.A14.A.2A\$956.2B.A2.B3A409.B2A
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963.2A279.2A.BA13.BA81.A2.A9.3A25.A2.A11.A2BA3.2A.3A2.BAB\$1244.2B.2A
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98.3A49.3A67.2A5.A13.ABA\$1297.2A.B115.2B2.2A8.A.A6.3A\$1296.2A2.A20.2A
12.2A80.A2.A7.B2A.4A2.B\$1221.A75.A.A20.A2.A10.A2.A80.BA5.BA8.B2AB\$
1220.B2A75.A22.2A3.3A6.2A89.11A\$1220.A.2A102.ABA\$956.A262.2A.A11.3A
88.BA.A13.A13.A13.A13.A13.A13.A13.11A\$955.BAB245.B15.3A12.3B32.B71.A.
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2A30.B72.2A12.2A12.2A12.2A12.2A12.2A14.B2A.4A2.B\$953.B.B.B.B227.B16.B
A28.2A.BA31.3A22.B134.A.A6.3A\$921.A30.A7.A224.B.3A13.ABA24.2A4.2BA32.
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22.2A38.A89.3AB11.BA\$923.A13.A15.2A3.2A209.B.3A13.ABA11.B26.2A.BA36.B
.3A5.A9.AB2A.BA.A37.3A89.2A9.B.3A\$923.2A11.BAB233.BA12.3A12.B26.2B.2A
38.B6.3A9.2B2A2.2A37.2A.A101.B\$920.2B2.2A13.A13.A204.2A11.ABA11.B33.
3A.A4.3B47.2A.A8.3A.3A39.A.2A89.A\$921.A2.A14.2A11.BAB203.2BA9.3A12.B
19.2A11.AB.AB3A2.3A48.A.2A5.BA3.B42.B2A89.BAB\$922.BA12.2B2.2A13.A13.A
186.2A.BA8.B34.A.A11.AB6.A52.B2A13.4A38.A93.A\$937.A2.A14.2A11.BAB144.
A40.2B.2A8.B35.A13.8A53.A13.B3.2A131.2A\$938.BA12.2B2.2A13.A13.A128.B
2A39.3B10.2A17.2A.2A102.ABA.A128.2B2.2A\$953.A2.A14.2A11.BAB127.A.2A
38.3A10.2A3.2A11.2A3.2A25.8A67.B3.2A129.A2.A\$954.BA12.2B2.2A13.A13.A
66.A44.2A.A51.ABA3.ABA11.A3.A25.AB6.A24.BA42.4A131.BA\$969.A2.A14.2A
11.BAB64.BAB43.3A52.BA5.AB12.A.A26.AB.AB3A2.3A19.A2.A34.BA3.B\$970.BA
12.2B2.2A13.A13.A48.A3.A43.A75.A28.3A.A4.3B18.2B2.2A35.3A.3A\$985.A2.A
14.2A11.BAB46.B.B.B.B98.B3.B53.2B.2A19.2A36.2B2A2.2A\$986.BA12.2B2.2A
13.A13.A30.A7.A99.B55.2A.BA11.A7.A36.AB2A.BA.A\$1001.A2.A14.2A11.BAB
30.2A3.2A67.2A12.2A17.B57.2BA6.B4.3A2.BAB44.2A\$1002.BA12.2B2.2A13.A
13.A15.2A3.2A62.3A.A2.A10.A2.A74.2A7.A.2A4.2A.A40.B4.A\$1017.A2.A14.2A
11.BAB52.2A28.A.BA2.2A12.2A85.8A47.B\$1018.BA12.2B2.2A13.A13.A33.2A.A
2BA27.A.2A\$1033.A2.A14.2A11.BAB32.2A2.2A29.A11.A13.A13.A13.A13.A13.A
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2A10.B.2A7.B4.3A2.BAB\$1050.BA12.2B2.2A13.A21.2BA38.2A79.2A.B13.A7.A\$
1065.A2.A14.2A18.A4BA37.B105.2A\$1066.BA12.2B2.2A3.B13.B3.BA37.B102.2B
2.2A\$1081.A2.A4.B11.3A2.A.BA37.3A100.A2.A\$1082.BA6.3A7.B.2A.A.BA39.AB
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2B13.2B3.B240.A2.BA131.2BA\$844.A17.A243.B4A48.2A81.2A\$840.BA.2A17.2A.
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.2A.A.BA48.2B.2A\$1101.3A2.A.BA32.A14.3B\$1103.B3.BA32.B2A13.3A\$1103.A
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1109.B2A12.2A.A7.B5.A4.2A18.2B2.2A\$996.2A111.A.2A11.3A19.3A20.2A\$996.
2BA97.BA10.2A.A13.A20.2A.AB5.ABAB.A7.A\$994.2A.BA13.BA81.A2.A9.3A22.A.
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A\$994.3B13.2B2.2A37.2A42.2A21.BA.A9.3A23.B5A\$994.3A16.2A38.2BA41.A22.
A2BA\$858.A105.2A47.A37.2A.BA38.BAB17.BA.A3.ABA35.B5A\$857.B2A100.A3.2A
44.BAB38.2B.2A39.A19.ABA38.B2.A4.2A.A22.B\$857.A.2A98.A.A49.A39.3B61.
3A37.A2.AB.3A2.BAB19.B.3A\$856.2A.A99.A.A89.3A16.A25.2A.2A55.ABAB.A7.A
4.B2.A13.BA\$856.3A101.A108.B.B24.A3.A68.2A5.BAB11.ABA\$857.A30.A178.2A
28.3A66.2B2.2A4.A5.A6.3A\$887.A.A170.2A3.2AB2A2B11.2A13.A68.A2.A6.2B3.
4A2.B\$886.A3.A85.2A81.A.A3.2B.2A12.A2.A82.BA4.A5.A4.B2AB\$857.A5.A21.
2A3.2A84.2BA49.2B30.A3.A.2A15.2A89.13A\$855.2A.A3.A.A21.2A.2A14.3A66.
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2A.BA6.B.A2B43.2BA89.B191.B2A\$676.B37.A.2A11.3A34.B.2A7.B4.3A2.BAB51.
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4.3A10.B.A.A.BA36.3B83.A18.B2A\$676.ABA35.A37.ABA44.BA33.A.2A16.B.2A.B
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A\$674.B58.2A.2A39.A.2A4.2A.A8.2B2.2A30.3A147.A2BA5.2A.A.A4.3A\$674.B
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2A\$669.2A.BA82.A.A65.B42.A38.B18.A3.A43.5A2.B22.B2A\$671.2BA83.A3.2A
61.B42.2A37.A18.2A.2A15.A23.B.2B4.B2AB23.A\$671.2A88.2A45.A16.3A36.2B
2.2A37.B.B34.ABA23.A2B6A\$807.BAB16.ABA36.A2.A40.3A31.2A.2A\$810.A16.BA
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2AB\$807.2B2.2A13.B81.B.3A8.3B33.A2.2A11.5A2.B\$808.A2.A98.B10.2B.2A11.
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923.2A12.2A.BA11.3B24.B.3A\$939.2BA11.2B.2A24.B\$939.2A12.2A.BA13.A\$
955.2BA12.BAB\$955.2A16.A\$973.2A\$970.2B2.2A\$971.A2.A\$972.BA!
``````

wwei47
Posts: 1012
Joined: February 18th, 2021, 11:18 am

### Re: Search Algorithms for rule 23/3/3

Francisco wrote:
June 27th, 2021, 9:27 am
Here is an improved version of the Breeder:
Very nice! That absolutely DESTROYS my synthesis!
Self-proclaimed synthesis "expert"

Francisco
Posts: 23
Joined: March 9th, 2021, 4:53 pm

### Re: Search Algorithms for rule 23/3/3

A slightly smaller p168 rake:

Code: Select all

``````x = 42, y = 143, rule = 23/3/3
19.3A9.3A\$18.A2BA9.A2BA\$18.AB2.BA5.AB2.BA\$20.A2BA5.A2BA\$20.A2BA5.A2BA
2\$24.2A.2A\$23.A.A.A.A\$23.A.A.A.A\$22.2A.A.A.2A8.A\$23.B.A.A.B8.3A\$22.2A
.A.A.2A6.A2.2A\$22.2A.A.A.2A5.4AB\$24.BA.AB8.2A\$25.B.B\$24.2B.2B2.2B\$21.
B.A2B.2B.A.A\$24.2B.2B4A\$25.B.B.3A.2A\$24.2A.2A3.3A8\$34.3A\$33.A2BA\$33.
2A.AB\$33.A\$29.2A.B3.B\$28.A.A.B\$27.A2.2A\$18.A9.2A\$17.3A\$16.A2.2A\$16.B
4.B\$17.AB2.2A\$18.B2.B10.3A\$32.A2BA\$30.AB2.BA\$30.A2BA\$24.BA4.A2BA\$26.
2A\$25.A2B\$22.2A2.2BA\$21.2A4.A\$22.B.B.2A\$23.AB.B\$35.A\$24.B9.3A\$33.A2.
2A\$32.4AB\$33.2A3\$25.2A\$25.2A\$21.2A8.3A\$20.A2.A7.A2BA\$21.2A6.AB2.BA\$
29.A2BA\$29.A2BA5\$12.3A\$12.A2BA\$11.BA.2A\$15.A\$12.B3.2B4\$11.3A\$11.A2BA\$
10.BA.2A\$14.A\$11.B3.2B4\$16.A\$15.3A\$14.AB2.A11.A\$15.2A.A10.3A\$16.2A10.
2A2.A\$23.2A2.B4.B\$22.A.A.2A2.BA\$23.A3.B2.B\$8.A\$6.2AB2A\$2.A3.AB.BA3.A\$
2AB2A.A.A.A.2AB2A\$AB.BA.A3.A.AB.BA\$A.A.A.BABAB.A.A.A\$2A2.A7.A2.2A\$.2A
.2B5.2B.2A\$4.2BA3.A2B\$.2B3A5.3A2B2\$3.BAB5.BAB\$4.A7.A6\$10.3A\$9.A2BA\$9.
AB2.BA\$11.A2BA\$11.A2BA4\$15.A\$14.3A\$13.2A2.A\$14.B4A\$16.2A5\$31.3A\$30.A
2BA\$30.2A.AB\$30.A\$28.2B3.B7\$29.3A\$28.A2BA\$28.AB2.BA\$30.A2BA\$30.A2BA!
``````