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Snake (Generations 03467/25/6)

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Snake (Generations 03467/25/6)

Postby dvgrn » June 5th, 2017, 8:17 pm

Moving this discussion of the 03467/25/6 rule to a new thread, since it certainly didn't belong where it was.

It seemed better to start a new thread than to continue the Snake Rule Extension thread. Here's the Snake.zip archive from that thread, reworked to use "rule = 03467/25/6" instead:

Snake(Generations03467_25_6).zip
Snake.zip with rule changed to 03467/25/6 in all RLE header lines
(205.7 KiB) Downloaded 40 times

There are some wonderfully artistic spaceships and other patterns in there, and LifeViewer and Golly can run them perfectly well:

Ships 09 and 14:
Code: Select all
x = 515, y = 209, rule = 03467/25/6:T800,240
16$423.B.D$421.3ACBED3.ABCDE$421.3ACBED2.ABCDE$423.B.DA.CAECAEC.E$75.B.D
348.ABCDE2.AC2DE$73.3ACBED3.ABCDE327.CBA3.E5.ABDAE2.D2B$73.3ACBED2.AB
CDE325.A.2CD2A2.2E2.ABCDE5.2A2.2E$75.B.DA.CAECAEC.E321.6ABEBE5.ABCDE
9.2D$78.ABCDE2.AC2DE320.4AB2CE21.2C$67.CBA3.E5.ABDAE2.D2B323.A.CBC2.E
19.2B$64.A.2CD2A2.2E2.ABCDE5.2A2.2E321.AB.CBCD18.2A2.2E$62.6ABEBE5.AB
CDE9.2D323.C2BD23.2D$62.4AB2CE21.2C323.3CD3.A7.A7.A3.2C36.A.C.E$64.A.
CAC22.2B323.C2BD23.2B35.2ABADC.E2.ABCDE$67.2A2D20.2A2.2E317.AB.CBCD
22.2A35.2ABADC.E.ABCDE$66.2A.2C23.DC316.A.CBC2.E36.ED23.A.C.EBADB.DB.
D$66.A.B2.A7.A7.A6.CD314.4AB2CE26.A6.A4.EDBC25.ABCDE.AB2CD$66.2A.2C
339.6ABEBE23.ACA12.CB13.BA3.ED5.2ACADE.C2A2.2E$67.2A2D28.2E311.A.2CD
2A2.2E20.CEC24.A.2BCA3.2D3.ABCDE8.2D$64.A.CAC32.DCBA310.CBA3.E21.E.E
23.6ADADE.E3.ABCDE8.2C$62.4AB2CE29.AEDCBA2.A328.A32.4A2BDE20.2B$62.6A
BEBE27.E.E333.ACA32.A.BAB2.E19.2A2.2E$64.A.2CD2A2.2E17.A342.CEC35.2A
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24.2D$36.A.A.2DE2B38.ACA341.E.E40.A.BAB2.E27.2C$35.4ABABC.C38.CEC334.
A48.4A2BDE28.2B$35.4ABC2D40.E.E333.ACA47.6ADADE.E24.2A$36.A.A.DCD33.A
342.CEC48.A.2BCA3.2D$39.2AC.DCDE28.ACA341.E.E51.BA3.ED$42.D2CE29.CEC
334.A$42.3DE3.A7.A7.C2.A6.ECE333.ACA99.2E$42.D2CE19.B3AB341.CEC98.DC$
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C18.BA3.ED5.2ACADE.C2A2.2E$43.2E108.BA3.ED29.2C164.ACA19.EDCBA11.E39.
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2CE2.E20.2D$154.B2AC23.2A188.CEC12.EDB12.E40.2ED9.A.2B2.2E19.CB$51.2D
101.3BCE2.A7.A7.A3.2B188.ACA11.EDBA7.A2.2ED2.A7.A7.A7.A7.A4.E.D11.A2.
A7.A7.A6.BC$51.2E101.B2AC23.2C189.A26.2DC52.A.2B2.2E24.2E$50.D2BD99.A
.BABC22.2D196.E.E17.2CB52.2A2CE2.E24.2D$51.2C97.A.BAB2.D19.2A2.2E196.
CEC17.2BA49.A.BAB2.E27.2C$50.B2AB95.4A2BDE20.2B200.ACA17.2A49.4A2BDE
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3.2D3.ABCDE8.2D208.E.E61.A.2BCA3.2D$153.BA3.ED5.2ACADE.C2A2.2E208.CEC
19.E44.BA3.ED$59.2D104.ABCDE.AB2CD211.ACA17.2ED$59.2E100.A.C.EBADB.DB
.D213.A18.2DC84.2E$58.D2BD98.2ABADC.E.ABCDE221.E.E9.2CB84.2D$59.2C99.
2ABADC.E2.ABCDE220.CEC9.2BA84.2C$58.B2AB99.A.C.E229.ACA9.2A85.2B$59.
2A335.A97.2A$41.DCB15.2A342.E.E$36.A.A.2DE2B358.CEC11.E$35.4ABABC.C
22.2D334.ACA8.A2ED4.A7.A7.A7.A7.A7.A7.A7.A7.A7.A$35.4ABC2D24.2E335.A
9.3DC$36.A.A.DCD23.D2BD341.E.E2.CA7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A6.
CD$39.2AC.DCDE18.2ABC342.CEC98.DC$42.D2CE19.B3AB341.ACA99.2E$42.3DE3.
A7.A7.C2.A6.ECE334.A$42.D2CE29.CEC341.E.E51.BA3.ED$39.2AC.DCDE28.ACA
341.CEC48.A.2BCA3.2D$36.A.A.DCD33.A342.ACA47.6ADADE.E24.2A$35.4ABC2D
40.E.E334.A48.4A2BDE28.2B$35.4ABABC.C38.CEC341.E.E40.A.BAB2.E27.2C$
36.A.A.2DE2B38.ACA341.CEC43.2A2CE2.E24.2D$41.DCB40.A342.ACA43.A.2B2.
2E24.2E$91.E.E334.A45.A2.A7.A7.A6.BC$91.CEC341.E.E35.A.2B2.2E19.CB$
67.CBA3.E17.ACA341.CEC35.2A2CE2.E20.2D$64.A.2CD2A2.2E17.A342.ACA32.A.
BAB2.E19.2A2.2E$62.6ABEBE27.E.E334.A32.4A2BDE20.2B$62.4AB2CE29.AEDCBA
2.A307.CBA3.E21.E.E23.6ADADE.E3.ABCDE8.2C$64.A.CAC32.DCBA307.A.2CD2A
2.2E20.CEC24.A.2BCA3.2D3.ABCDE8.2D$67.2A2D28.2E309.6ABEBE23.ACA12.CB
13.BA3.ED5.2ACADE.C2A2.2E$66.2A.2C339.4AB2CE26.A6.A4.EDBC25.ABCDE.AB
2CD$66.A.B2.A7.A7.A6.CD316.A.CBC2.E36.ED23.A.C.EBADB.DB.D$66.2A.2C23.
DC318.AB.CBCD22.2A35.2ABADC.E.ABCDE$67.2A2D20.2A2.2E319.C2BD23.2B35.
2ABADC.E2.ABCDE$64.A.CAC22.2B323.3CD3.A7.A7.A3.2C36.A.C.E$62.4AB2CE
21.2C323.C2BD23.2D$62.6ABEBE5.ABCDE9.2D321.AB.CBCD18.2A2.2E$64.A.2CD
2A2.2E2.ABCDE5.2A2.2E319.A.CBC2.E19.2B$67.CBA3.E5.ABDAE2.D2B321.4AB2C
E21.2C$78.ABCDE2.AC2DE320.6ABEBE5.ABCDE9.2D$75.B.DA.CAECAEC.E323.A.2C
D2A2.2E2.ABCDE5.2A2.2E$73.3ACBED2.ABCDE328.CBA3.E5.ABDAE2.D2B$73.3ACB
ED3.ABCDE338.ABCDE2.AC2DE$75.B.D345.B.DA.CAECAEC.E$421.3ACBED2.ABCDE$
421.3ACBED3.ABCDE$423.B.D!
[[ AUTOSTART HEIGHT 240 THUMBNAIL THUMBSIZE 2 ZOOM -1 ]]

(The "Snakes" rule is something completely different, by the way.)

The reason this came up was a question about the period of one of the patterns:
dvgrn wrote:
bprentice wrote:...is the following pattern an oscillator and if so what is its period?


EDIT3: No matches up to the next order of magnitude, past 20 billion -- takes about a week. It's possible to set up a distributed search using multiple cores, that might get to the next order of magnitude in a few more weeks or a month.

Well, the repeat point finally showed up. It turned out to be not very far past the 20 billion mark, at 21,858,777,744.

Here's the updated list of periods from samples of different sizes. No doubt many other oscillator periods are possible at those sizes, even with the same symmetry in effect, so this is just a likely list of maybe-about-average periods for each size:

Sample sizes and periods
3x3            60
5x5           274
7x7          3948
9x9         27276
11x11      511248
13x13    17615268
15x15 21858777744

At this rate, it seems as if finding the period of a 17x17 version is out of reach of even a reasonable distributed search, unless someone can figure out a simpler way to model what these oscillators are "really" doing.

In the pattern below, the original start pattern is to the left -- from Snakes.zip Oscillators/Oscillator 03.rle. It's not actually an oscillator, but it's a 430-tick predecessor of one. To the right is the same pattern after 21,858,777,744 ticks.

Run both patterns for 13 ticks and you'll see the two squares, in the NE and SW corners of the original pattern, that are out of phase with everything else -- they're one tick ahead. It takes until T=430 for the rest of the pattern to catch up, ending with the NW and SE corner blocks.

x = 123, y = 59, rule = 03467/25/6
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5.BCB5.BCB5.BCB5.BCB$ACD5.DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.DCA5.ABCE4.CB
A5.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA$66.E.E13.E.E13.E.E13.E.E$4.DCA5.AC
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CA5.ABC4.ECBA5.ABC4.ECBA5.ABC4.ECBA5.ABC4.ECBA$CDC5.CDC5.CDC5.CDC5.CD
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5.ABCE4.CBA5.ABCE4.CBA$66.E.E13.E.E13.E.E13.E.E$4.DCA5.ACD5.DCA5.ACD
5.DCA5.ACD5.DCA12.ECBA5.ABC4.ECBA5.ABC4.ECBA5.ABC4.ECBA$4.CDC5.CDC5.C
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5.ACD5.DCA5.ACD5.DCA5.ACD13.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABCE$70.
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BA5.ABC4.ECBA5.ABC4.ECBA5.ABC4.ECBA$CDC5.CDC5.CDC5.CDC5.CDC5.CDC5.CDC
5.CDC5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB$DCA5.ACD5.DCA5.ACD5.DCA
5.ACD5.DCA5.ACD5.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABC$74.E.E13.E
.E13.E.E$4.ACD5.DCA5.ACD5.DCA5.ACD5.DCA5.ACD13.ABC4.ECBA5.ABC4.ECBA5.
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CB5.BCB5.BCB5.BCB$4.DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.DCA13.CBA5.ABCE4.CB
A5.ABCE4.CBA5.ABCE4.CBA$78.E.E13.E.E13.E.E$DCA5.ACD5.DCA5.ACD5.DCA5.A
CD5.DCA5.ACD5.CBA5.ABC4.ECBA5.ABC4.ECBA5.ABC4.ECBA5.ABC$CDC5.CDC5.CDC
5.CDC5.CDC5.CDC5.CDC5.CDC5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB$ACD
5.DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.DCA5.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA
5.ABCE4.CBA$66.E.E13.E.E13.E.E13.E.E$4.DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.
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5.CDC5.CDC13.BCB5.BCB5.BCB5.BCB5.BCB5.BCB5.BCB$4.ACD5.DCA5.ACD5.DCA5.
ACD5.DCA5.ACD13.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABCE$70.E.E13.E.E13.
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ACD5.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABC$74.E.E13.E.E13.E.E$4.A
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5.ABCE4.CBA$78.E.E13.E.E13.E.E$DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.DCA5.ACD
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ACD13.ABCE4.CBA5.ABCE4.CBA5.ABCE4.CBA5.ABCE$70.E.E13.E.E13.E.E13.E.E$
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BA5.ABC4.ECBA$CDC5.CDC5.CDC5.CDC5.CDC5.CDC5.CDC5.CDC5.BCB5.BCB5.BCB5.
BCB5.BCB5.BCB5.BCB5.BCB$DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.DCA5.ACD5.CBA5.
ABC5.CBA5.ABC5.CBA5.ABC5.CBA5.ABC!
[[ STOP 429 ]]

What seems to be happening is that blocks often spend several ticks in a "rest" state, either completely empty or with just a single cell turned on. That ordinarily lasts the full cycle of 6 ticks, but if neighboring blocks are one step ahead, the "rest" time can just as easily be only 5 ticks long -- so the +1 phase spreads inevitably through the whole area.

Signal Circuitry

It seems as if it ought to be straightforward to build logic circuitry out of these 3x3 block structures, maybe taking advantage of this "self-synchronizing" feature somehow -- but I'm not too sure. Haven't really tried to figure out the details yet.

On first glance Oscillators/Shuttle 3.rle looks like maybe the most promising option for a stable signal track, but the track actually shifts by two cells as the 3x3 block follows it, so it seems like the return trip is necessary to avoid permanent damage.

Shuttle 3.rle:
Code: Select all
x = 75, y = 5, rule = 03467/25/6
A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.ACD$72.CDC$72.D
CA2$2.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A!
#C [[ THUMBNAIL THUMBSIZE 2 HEIGHT 240 AUTOSTART ]]

There are some other similar possibilities in the Snake.zip Oscillators folder, numbers 18 and up. Maybe some of the other structures supported by this rule could also make logic gates --

x = 136, y = 63, rule = 03467/25/6
88.A31.A6$.A6.A6.A6.A6.A6.A6.A6.A$3AE2.E3A4.3AE2.E3A4.3AE2.E3A4.3AE2.
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6.A.D2.D.A6.A.D2.D.A36.E2CE28.2B$ABC4.CBA4.ABC4.CBA4.ABC4.CBA4.ABC4.C
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6.A6.A6.A6.A6.A6.A6.A2$95.E.C.A10.E.C.A$93.E.CDAB2A7.E.CDAB2A$73.A19.
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D2.D.A$ABC4.CBA4.ABC4.CBA4.ABC4.CBA4.ABC4.CBA3$ABC4.CBA4.ABC4.CBA4.AB
C4.CBA4.ABC4.CBA$.A.D2.D.A6.A.D2.D.A6.A.D2.D.A6.A.D2.D.A$3AE2.E3A4.3A
E2.E3A4.3AE2.E3A4.3AE2.E3A$.A6.A6.A6.A6.A6.A6.A6.A5$88.A31.A!
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