Rule table: Branches

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

Rule table: Branches

Post by ebcube » April 9th, 2010, 2:17 am

This rule table expands quickly into colorful, unpredictable branches from simple and/or random patterns. Oscillators appear naturally in the branches. It's my first rule table, so please tell me what you think!

Code: Select all

n_states:5
neighborhood:Moore
symmetries:rotate8reflect

var z={0,1,2,3,4}
var x={1,2,3,4}
var y={1,2,3,4}
var w={1,2,3,4}

# transform (& kill) (2)

1,3,3,z,z,z,z,z,z,0
2,4,4,z,z,z,z,z,z,0
3,1,1,z,z,z,z,z,z,0
4,2,2,z,z,z,z,z,z,0

1,1,1,z,z,z,z,z,z,3
2,2,2,z,z,z,z,z,z,4
3,3,3,z,z,z,z,z,z,1
4,4,4,z,z,z,z,z,z,2

4,3,3,z,z,z,z,z,z,3
4,1,1,z,z,z,z,z,z,1
1,4,4,z,z,z,z,z,z,4
1,2,2,z,z,z,z,z,z,2
2,1,1,z,z,z,z,z,z,1
2,3,3,z,z,z,z,z,z,3
3,2,2,z,z,z,z,z,z,2
3,4,4,z,z,z,z,z,z,4

# transform (3)

1,2,3,2,z,z,z,z,z,4
2,3,4,3,z,z,z,z,z,1
3,4,1,4,z,z,z,z,z,2
4,1,2,1,z,z,z,z,z,3

# born (1)

# 0,1,z,z,z,z,z,z,z,1
# 0,2,z,z,z,z,z,z,z,2
# 0,3,z,z,z,z,z,z,z,3
# 0,4,z,z,z,z,z,z,z,4

# born (3)

0,x,x,x,z,z,z,z,z,x
0,x,x,z,1,z,z,z,z,2
0,x,x,z,2,z,z,z,z,3
0,x,x,z,3,z,z,z,z,4
0,x,x,z,4,z,z,z,z,1

# born (4)

0,x,y,w,z,z,z,z,z,y
0,x,z,w,w,z,y,z,z,w
0,w,z,x,y,z,w,z,z,w
EDIT: silly bug on state 4 fixed ^^

User avatar
calcyman
Posts: 2096
Joined: June 1st, 2009, 4:32 pm

Re: Rule table: Branches

Post by calcyman » April 9th, 2010, 12:18 pm

It produces some intricate, dendritic, coral-like structures. There are several types of infinite growth pattern, the most interesting comprising two halves with a blank diagonal between them. This type of puffer has a relatively high period, as compared with the others.

The rule is more interesting for its aesthetics than the actual behaviour, contrary to most cellular automata. You can easily make undersea images by taking a screenshot of Golly and adding a few sea creatures in Microsoft Paint. Please excuse my terrible drawing skills; you could probably do this six orders of magnitude better than me. :)
Attachments
Picture generated using a Golly rule table
Picture generated using a Golly rule table
branches.PNG (17.83 KiB) Viewed 6045 times
What do you do with ill crystallographers? Take them to the mono-clinic!

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

Re: Rule table: Branches

Post by ebcube » April 9th, 2010, 3:37 pm

Wow! It does look cool :P

An interesting thing to note about the rule is that, while all states behave in the same way on their own, they move differently when combined.

State 1 and 3 interact on a different way with each other than with state 2 and 4; the same kind of relation happens between 2 and 4. They seem to "stop" each other. This is most commonly observed on simple patterns, which develop in completely different ways:

Code: Select all

# States 2 & 1
x = 5, y = 5, rule = Branches
$.A$.2B$.2BA!

# States 2 & 4
x = 5, y = 5, rule = Branches
$.D$.2B$.2BD!
But two patterns with the colors in the same order are exactly the same. For example, 2 & 3 versus 3 & 4.

EDIT: Also, how many different infinite growth patterns have you found? I've only found three:

The blank diagonal, a puffer with period near 200 (here, a double blank diagonal with slightly asynchronous sides):

Code: Select all

x = 7, y = 4, rule = Branches
$.2AB.D$.B.D2C!
The "tree"? (again, a double tree):

Code: Select all

x = 3, y = 3, rule = Branches
.A$.A$3A!
The helix:

Code: Select all

x = 3, y = 8, rule = Branches
.C$.D$3A$.B$.B$.B$.B$.B!
Sometimes, a "branch" gets stuck on a tree, bouncing on and off it constantly at a slightly lower velocity than the tree's.

EDIT2: This is what I mean by "branch stuck on a tree":

Code: Select all

x = 46, y = 6, rule = Branches
.A$.A$3A$44.C$44.C$43.3C!

Axaj
Posts: 232
Joined: September 26th, 2009, 12:23 am

Re: Rule table: Branches

Post by Axaj » April 9th, 2010, 4:18 pm

Neat rule, and looks turing complete as well. Here are some "trains" I found:

Code: Select all

x = 308, y = 291, rule = Branches
283.B2.2C3B.BD.D2B3.2B2.3B$283.2B2.2C4BD3B4.7B$283.C2B2.2C3BCB.D.2B2.
2B2DB$283.4B2.2C2B3C2.2BCB.4BC$283.D4B2.2C2B2D.3BD2B.2B$283.D.BD2B2.
2C2B.A.6B$283.2A2BD2B2.2C3B.BD.D2B$286.5B2.2C4BD3B$283.B.3BAC2B2.2C3B
CB.D$283.B.BD2C4B2.2C2B3C$283.2C3BCD4B2.2C2B2D$285.2B.CD.BD2B2.2C2B.A
$283.B2.C3.A2BD2B2.2C3B$283.3B.D4.5B2.2C4B$283.BD3B.C4BAC2B2.2C3B$
283.2BD3B.B2D2C4B2.2C2B$283.D4B2.4BCD4B2.2C$283.D.BD3B.2B.CD.B.2B$
284.A2BD2B2.C3.A4B$283.B2.6B6.2B$283.5BCBD2B$283.2B2D2C2BD2B$284.4BCD
3B$284.3B.CD.B$284.3B97$175.B3D.4D$175.2B4DB2D$176.2B3DAD$177.2B2D3A$
175.B2.2B2D2B$175.2B2.2B2D$175.D2B2.2B2D$175.4B2.2B$175.5B$175.2C4B$
175.BCD2B$176.CD99$47.A$45.CB2A$44.2A.2A$43.5A$44.2A.2A.2CA6C$45.3ABC
.2CA4C$45.2ACB2C.4CA2D$47.C.A2C.4C2A$49.CA2C.4C$49.5C.4C$49.6C.3C$49.
ACA4C$49.2CDA3C$49.C.DA.2C39$4.A$2.2CAD$2.3CA$6C$6C$3CA2C$.CAD2C$4.C!
Image

User avatar
calcyman
Posts: 2096
Joined: June 1st, 2009, 4:32 pm

Re: Rule table: Branches

Post by calcyman » April 10th, 2010, 7:31 am

There's another impressive infinite growth pattern:

Code: Select all

x = 153, y = 142, rule = branches
23$95.D$94.3D4.D$56.D36.2DBD2.B3D$54.B3D36.4DA.DB2D$49.2D.BA.DB2D2.2D
30.2D.2D.4D$41.D6.4DBA2D.D2.4DA.2D24.8DB3D$33.3D3.B4D4.2DB2D2A2B2D.2D
.D.4D20.D3.D2.3DB4D$33.3D.BA.DB2D4.3DB7D.6DB2D18.4DB2.C2DB3D.2D$33.4D
BA3DB2D5.3D2BD2.C3.3DB3D8.2D.D.A4.2DBD.AB.DB2D.2C$32.A.4DADB3D6.C.5DB
.2C2DB3D9.6DABD.2DB3DAB4D2BC2.B4.B$32.4DB3DBD.C7.2B2DBD.AB.DB2D.B9.2D
.3DA2D2.3DBDA3DC3A.C4B.3BC.B$31.2DB3DB.B2DB3.2D3.3AD.2DAB4D.A10.10D.C
.DB3DB2DAD.B.B.2BCBDB.3B$32.3D.3DBD2A.A4D3.D.D2B2A2DB4D.3D9.3D2BD3.B
2DB.B3DB3D.4B.5BD2B$33.D2.C.6D.DB2D2.9DB3DB5D9.C.5DA.2ADB3D.DB.2DA3B
3.3BD2B$37.B2D2BD.ADBD3.2DB2.D2B3D.DB.2B2D10.2B2DBD.6D.C.4D.3B2.D2BD
3B$37.2AD2B4DB2D5.A5D.C.6D11.3ADBDA.D2B2DB.3D3.4BC.BD2B2.C$36.13D4.D.
DB2D2B.3DA3D10.B.DCDB4D2BD2A2.2D.3BD2B.4B.C2B$37.2DBD2.D7.C4D.D3A.3DA
B2D10.13DC2D4.8BD7B$36.2DB3DC2.D.D.AB.DB.2BDAD2.2D.AB11.4DA4.D2.4D5.
2B2.3BD7B$37.3DBD.BA4DAB2DB4DB2D17.2DB2.D.D2.C2DB3D6.A2BD3B.2B2.2C$
37.A.DB3DAC3DA5D.4D.A19.A4DAB.DB3D2.2B.CD.BD2B.D3.CBD$38.2DBDB2DADB3D
.D.A.2D2.2A18.D.3D2A3D.D3A.3BCD4B.C2.5B$39.4DB4DB.2B2D3.6A7.2D.A.D2.B
4DB5D2B2DB2.BD2C2BD4B.2BDB.C$38.2A2.3D2.DB4D.ABC.AC2AC7.ADBA3DA.3DB3D
2B7D.3B.BD3BD4BD2B$39.BDA3.C4D3.2AB3ACA2B2A.2A.D.2D.3D.2DB3D.4D4.C3.
6B.BD.2DBCB$39.4D.B.DCA2D6ACAC4AB.BA4DA.2DA.DB2D.B.C4.B.B2.A2BD2B.A.
4BDB3C$41.3DBA2D2C.5AC3AC2A.3D2A2BD.3D.4D.A2.DBDC4BCD.BD2B2D.2B.C4BDC
$39.AB4D2ADBC3A2.3A.3A.B8D.5DB4D.C.2BC3B.C3B.B3C2.2BCD3B$39.3ADB4D.2A
2D.D2.C2.2A3.2DAB2D3.3DB3DB2DC5BD5B2D3B.D.2B.D.2B$15.2A.D.2D18.3D2B.B
D.BA4DAB.2DB2A.2B2DBD2.B2DB3D.DB2D.2BD.D3B2D3B2D3B$15.BA4DA.2D14.2DB
4DB3DADB2DA5DB3.2AD.2DA.DB2D.B.3D3.BD3B.B2DBC4BD2B$13.3D2A2BD.3D15.2D
BD.3D.4DB3DBD.AD2.2DAD2BD.4D.A.C3D.5B.A.4BCD.BD2B$13.8D.5D13.4D.B.3D
2B5DB2D4.9DB4D3.D2.B2D2BD.3B.B2.A4B$14.2D2B2D3.4D15.D3.A2.D2BD2.C3D3.
D3.D2.3DB6D4.2B2DB2C2.2BC.C3.B$13.2B2DBD2.B2DB3D16.D.2D.5DB2.2D.4DB2.
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DC2B2.D2BD3B.5BD2BD$13.9DB3D5.2D.A.D2.B4DB5DA2DBDA2D2.3DBDA3D4A.C4B.
3BC.BD3B.CB.C2BDB3C$13.3D2.3DB3D6.ADBA3DA.3DB3DB2D.2DB5D.C.DB3DB2DAD.
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.B3DB3D.BD2B.5BD3B.D2B.CD.B2D2B.D2B$9.2D.D.AB.DB2D3.2D.BA4DA.2DA.DB2D
.B2.A.A2.C.5DA.2ADB3D.D2B2DA3B3.3BD3B2.3BD2.A2B.B.C.5B$6.2D.A4DAB4D2.
B.C3D2A2BD.3D.4D.A2.4D3.2B2DBD.6D.C.4D.3B2.D2BD3B.D2.2B3.B2.BD3B.BD3B
$6.3D.D2B2A2DBD2.3B.8D.5DB4D.2DB3D2.3ADBDA.D2B2DB.3D3.4BC.BD2B2.C7.5B
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7.3BD5BD3B$4.4D3.2DB.B3D2.3B.2B2DBD2.B2DB3D.DB.BDAD.B2.13DA2D4.8BD7B
8.2BDBC2BDB.C$3.3DB2DB2.DB3D.B.2D2B2.2AD.2DA.DB2D.B.3DBD3A2.4DA4.D2.
4D5.2B2.3BD7B9.4BCD4B2.2B$4.3DBD.A2D.D3A2.B2DBA2DAD2BD.4D.A4.DB2DB3.
2DB2.D.D2.C2DB3D6.A2BD3B.2B2.2C10.B.CD.2B2.4B$4.A.4D.D2B2DBAC.2A2D.9D
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B7DB.A9.D.3D.A3D.D3A.3BCD4B.C2.6B5.2C.B.2B.3B.2BD3B$6.3DB3D2.C.2D.A4D
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$6.B.3DB2DB2.3D.2DBD.AB.DB2D.B2.A2.2A.ADBA3DA.3DB3D2B7D.3BABD3BD4BD2B
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.B.C4.B.B2.A2BD2B.A.4B.B3C6.2B2D2B3.3BD7B$6.7DB6D.7DB3DB3DA3D2A2BD.3D
.4D.A2.DBDC4BCD.BD2B2D.2BAC4BDC5.2D2BDB2.D2BD3B.BD3B$7.7DB3D3.C2.D2B
3D.DB.BD.8D.5DB4D.C.2BC3BAC3B.B3C2.2BCD3B7.3CB.2BC.BD2B.D.5B$6.2A2.2D
.3DB2D2C.B5D.C.5D2.3DB2D3.3DB3DB2DC5BD5B2D3B.D.2B.D.2BDC6.BCB2DB.4B.C
.A2B$7.BDA3.B.2DBD.BA.DB2D2B.2D.A2D.2B2DBD2.B2DB3D.DB2D.2BD.D3B2D3B2D
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BC4BD2B3.C2.2CDAC3.3B2.3BD7B$6.DA.DB2D.4DB2D2A2BDAD2.2D.A3.2D.D2BD.4D
.A.C3D.5B.A.4BCD.BD2B2.BD5CA4C4.A2BD3B.BD3B$8.2DB4DB3DB9D8.9DB4D3.D2.
B2D2BD.3B.B2.A4B2.CBD2CA5C.B.CD.BD2B.A.4B$9.DAD2B.BD.3D2BD2.B2D6.D3.D
2.3DB3D.2D4.2B2DB2C2.2BC.C3.B3.B.2B.2C3AC.3BCD4B2DA5.CB$8.3A6D.C.5DA
7.4DB2.C2DB3DA3D5.5BC2B.5B.B3.6B2.5C.BD2C2BDB3C.A2B.3B$8.AB4D2A2D.2B
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7B$10.3DBA3D.3AD.4DABD.2DB3DAB4D2BC2.B.DC2B2.D2BD3B.5BD2BD2.4BD.CA2CA
.3BD.D3BD3B.BD.D3B$10.2D.BA.2D2.3D2B.B2A2D2.3DBDA3D.3A.C4B.3BC.BD3B.C
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.B.4B.C.3BCD5B.D.5B.4C.C2B.B.C.5BDBCB.D$20.2DBD.3D2BD3.B2DB.B3DB3D.4B
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.2DA3B3.3BD3B2.3BD2.A9BD2B3C.7B2.3BCD4B2D.3B$22.3D.2B2DBD.6D.C.4D.3B
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2DB.3D3.4BC.BD2B2.C7.B4.2C.B2DB4C.B.BD2B2D2.2C4.A2BD3B.BD3B$25.B.D.DB
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2D4.8BD7B3.C.3B.5B2.3B2.DACB2D3B2.2B.BD2B.5BD4B$24.4DA4.D2.4D5.2B2.3B
D7B2.BDC2BDBCB.BDCB.7BA3BD3B.5BDB.3B.4B.C$24.2DB2.D.D2.C2DB3D6.A2BD3B
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3BCD4B.C2.6B.B3DB2.D2BD3B3.BD2B2D.3B2C2.2BC.C3.B2.C.6B$16.2D.A.D2.B4D
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2B$16.ADBA3DA.3DB3D2B7D.3BCBD3BD4BD2B5.B2DB.4B.C.2BD6B.2BDB.A.4BCD.BD
2B$12.2A.D.2D.3D.2DB3D.4D4.C3.6B.BD.2DBCB.2CDB.6BD3B3.2BDBC3BC.5B.B2D
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2BC.BD2B.D3.CBD21.2BCB2D2C2BD4B.B$3D5.D3.D2.3DB3DB2D4.2B2DB2C2.2BC.C
3.B5.BCB2DB.4B.C2.6B21.2CB.2BCD4B.C$2.B3.4DB2.C2DB3DA3D5.5B.2B.5B.B6.
9BD4B.2BDB.CB20.2D2BDB.CD.BD2B.D$.A4.2DBD.AB.DB2D.2CD.C2.2B.A2.4B2.B
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.BD2B.5BD3B.D2B.CD.B2D2B.DBAC2BDB3C2.2BCD3B4.C4B13.3BDC2BDB3.3B$5DA.
2ADB3D.D2B2DA3B3.3BD3B2.3BD2.A2B.B.C.5BDBCB.D.2B.D.3BC.B.4B16.DC.3B$B
2DBD.6D.C.4D.3B2.D2BD3B.D2.2B3.B2.BD3B.BD.D3BD3B2.C4.AB.4BD4B18.B$2AD
BDA.D2B2DB.3D3.4BC.BD2B2.C7.5BD.D3BD3B.BD.D3B5D3.3BD5B$DCDB4D2BD2A2.
2D.6B.4B.C2B7.3BD5BDBCB.D.8B2DB2D.2BD3B.2B$11DC2D4.8BD7B8.2BDBC2BDB3C
.A2B.3BC2B3D2.BD2B.D3.CB$DA4.D2.4D5.2B2.3BD7B9.4BCD4B2DA5.CBCDB4.4B.C
2.4B$2.D.D2.C2DB3D6.A2BD3B.2B2.2C10.B.CD.BD2B.A.4B6.B.2BD4B.2BDB$A4DA
B.DB3D2.2B.CD.BD2B.D3.CBD15.A2BD3B.BD3BDA.D4BD3BD4BD2B$.3D2A3D.D3A.3B
CD4B.C2.6B11.3B2.3BD7B.2C.B2D3B.BD.2DBCB$2DB5D2B2DB2.BD2C2BD4B.2BDB.C
B11.9BD4B3.DC5B.A.4BCB3C$DB3D2B7D.3B.BD3BD4BD2B14.BAB2DB.4B.C.A2BCBD
2B2D.2BAC4BDC$3D.4D4.C3.6B.BD.2DBCB14.3CB.2BC.BD2B.D.4B.B3C.3BCD3B$D.
B.C4.B.B2.A2BD2B.A.4B.B3C13.2D2BDB2.D2BD3B.BD.2DBCB2.2B.CD.2B$.A2.DBD
C4BCD.BD2B2D.2B.C4BDC14.2B2D2B3.3BD3BD4BD2B$2D.C.2BC3B.C3B.B3C2.2BCD
3B15.8B.5BD4B.2BDB$B2DC5BD5B2D3B.D.2B.D.2B15.3B2C2DB.3B.4B.C2.4B$B2D.
2BD.D3B2D3B2D3B25.DC4BC.2BC.BD2B.D3.CB$2D3.BD3B.B2DBC4BD2B24.2C.B.2B.
3B.2BD3B.2B$2D.5B.A.4BCD.BD2B29.CBDC3BC.3BD5B$D2.B2D2BD.3B.B2.A4B29.
2B.C.B2.D4BD4B$2.2B2DB2C2.2BC.C3.B41.B.4B$2.5BA2B.5B.B44.C4B$B.A2.4B
2.B3D5B3.B40.B$B2.D2BD3B.5BD2BD.D4B$2BC.BD3B.CB.C2BDB3C.B2DB!

This runs incrementally faster than the blank-diagonal puffer, so it out-competes it when they are in close proximity.
What do you do with ill crystallographers? Take them to the mono-clinic!

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

Re: Rule table: Branches

Post by ebcube » April 10th, 2010, 9:00 am

A variation of the helix. In this one, the branches are connected.

Code: Select all

x = 10, y = 8, rule = branches
$2.D4.B$.3D2.3B$.DBD2.BDB$.3D2.3B$2.2D2.2B$3.D2.B!

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

Re: Rule table: Branches

Post by ebcube » April 10th, 2010, 11:09 am

calcyman wrote:There's another impressive infinite growth pattern:

This runs incrementally faster than the blank-diagonal puffer, so it out-competes it when they are in close proximity.
Impressive, indeed. :o

It does run faster than the blank diagonal, but the difference is almost zero: It took 30000 generations to destroy the blank diagonal.

Also, it needs a name :P Ideas?

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Extrementhusiast
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Location: USA

Re: Rule table: Branches

Post by Extrementhusiast » April 11th, 2010, 2:31 am

And how do you view this?
I Like My Heisenburps! (and others)

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

Re: Rule table: Branches

Post by ebcube » April 11th, 2010, 6:44 am

Extrementhusiast wrote:And how do you view this?
What? :D You copy the code from the first post to a file, save it on the Rules folder as Branches.table, and then set the rule in Golly.

knightlife
Posts: 566
Joined: May 31st, 2009, 12:08 am

Re: Rule table: Branches

Post by knightlife » April 11th, 2010, 5:08 pm

Unidimensional starting patterns produce weave patterns with fewer dendrite structures:

Code: Select all

x = 163, y = 1, rule = Branches
46C34D3A34D46C!
The vertical centerline looks like a 2c signal but it is of course an optical illusion.

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

Re: Rule table: Branches

Post by ebcube » April 13th, 2010, 4:24 pm

knightlife, I've been playing with unidimensional seeds. The "weave pattern" of a seed of width 177 seems to be non-periodical:

Code: Select all

x = 10177, y = 1, rule = Branches
5000D177A5000D!
Other weave patterns (like 34, the one you showed, or 43, which has a surprisingly long period when compared with 34) are also interesting.

EDIT: I'm testing some other patterns, I'll write here the results. (I'm only posting the relevant ones)

width 59 -> period 440
width 63 -> period 380
width 67 -> period 1062
width 71 -> period 1826
width 75 -> period 1864
Last edited by ebcube on April 14th, 2010, 10:10 am, edited 2 times in total.

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Extrementhusiast
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Location: USA

Re: Rule table: Branches

Post by Extrementhusiast » April 13th, 2010, 6:23 pm

And how do you view this?
What? :D You copy the code from the first post to a file, save it on the Rules folder as Branches.table, and then set the rule in Golly.
It doesn't work. (At least I have my posted rules...)
I Like My Heisenburps! (and others)

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

Re: Rule table: Branches

Post by ebcube » April 13th, 2010, 6:42 pm

Extrementhusiast wrote:
And how do you view this?
What? :D You copy the code from the first post to a file, save it on the Rules folder as Branches.table, and then set the rule in Golly.
It doesn't work. (At least I have my posted rules...)
Weird...

Here, I uploaded it for you. Just copy it inside Golly/Rules/.

http://kttns.org/zezmj

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