Snake Rule Extension

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bprentice
Posts: 920
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Snake Rule Extension

Post by bprentice » February 20th, 2015, 4:55 am

The Snake rule (Generations 03467/25/6) was named after this shuttle ship:

Code: Select all

x = 1063, y = 136, rule = 03467/25/6
5.CBA3.E$2.A.2CD2A2.2E$6ABEBE$4AB2CE$2.A.CBC2.E$4.AB.CBCD$6.C2BD$6.
3CD3.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.
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A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A6.AD7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.
A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A6.AD7.A7.A7.
A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A
7.A7.A7.A7.A6.AD7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A
$6.C2BD193.AD2.B235.AD2.B235.AD2.B235.AD2.B$4.AB.CBCD193.B2AC236.B2A
C236.B2AC236.B2AC$2.A.CBC2.E194.E2AE236.E2AE236.E2AE236.E2AE133.2A$
4AB2CE205.2E238.2E238.2E238.2E90.A3.EDC29.2B$6ABEBE195.2E238.2E238.
2E238.2E97.2AB.2E.2C28.2C$2.A.2CD2A2.2E184.2A13.E2CE221.2A13.E2CE221.
2A13.E2CE221.2A13.E2CE86.5ACACD.D28.2D$5.CBA3.E184.4A13.2D221.4A13.
2D221.4A13.2D221.4A13.2D87.5ACD2E30.2E$197.2B13.C2AC221.2B13.C2AC221.
2B13.C2AC221.2B13.C2AC88.3A.ECE$196.C2AC13.2B221.C2AC13.2B221.C2AC13.
2B221.C2AC13.2B90.A.3AB$197.2D13.4A221.2D13.4A221.2D13.4A221.2D13.4A
90.3AB.2E$196.E2CE13.2A221.E2CE13.2A221.E2CE13.2A221.E2CE13.2A91.3A
BD2.A7.A7.A3.2A.E$221.2E238.2E238.2E238.2E83.3AB.2E20.2B2.E$197.2E238.
2E238.2E238.2E106.A.3AB22.2C$189.2A29.E2CE205.2A29.E2CE205.2A29.E2C
E205.2A29.E2CE80.3A.ECE22.2D$188.4A29.2D205.4A29.2D205.4A29.2D205.4A
29.2D79.5ACD2E18.2A2.2E$189.2B29.C2AC205.2B29.C2AC205.2B29.C2AC205.
2B29.C2AC78.5ACACD.D4.ABCDE7.2B$188.C2AC29.2B205.C2AC29.2B205.C2AC29.
2B205.C2AC29.2B81.2AB.2E.2C4.ABCDE7.2C$189.2D29.4A205.2D29.4A205.2D
29.4A205.2D29.4A81.A3.EDC7.BACD.B.A2.2D$188.E2CE29.2A205.E2CE29.2A205.
E2CE29.2A205.E2CE29.2A95.ABCDE.A2BCE$49.B.D177.2E238.2E238.2E238.2E
84.B.DA.CAECAEC.E$47.3ACBED3.ABCDE127.2E238.2E238.2E238.2E122.3ACBE
D2.ABCDE$47.3ACBED2.ABCDE120.2A45.E2CE189.2A45.E2CE189.2A45.E2CE189.
2A45.E2CE81.3ACBED3.ABCDE$49.B.DA.CAECAEC.E117.4A45.2D189.4A45.2D189.
4A45.2D189.4A45.2D84.B.D$52.ABCDE.A2BCE118.2B45.C2AC189.2B45.C2AC189.
2B45.C2AC189.2B45.C2AC$39.A3.EDC7.BACD.B.A2.2D115.C2AC45.2B189.C2AC
45.2B189.C2AC45.2B189.C2AC45.2B$38.2AB.2E.2C4.ABCDE7.2C116.2D45.4A189.
2D45.4A189.2D45.4A189.2D45.4A$36.5ACACD.D4.ABCDE7.2B115.E2CE45.2A189.
E2CE45.2A189.E2CE45.2A189.E2CE45.2A$36.5ACD2E18.2A2.2E168.2E238.2E238.
2E238.2E$38.3A.EDE22.2D112.2E238.2E238.2E238.2E$13.B.D23.2A2BD.EDE19.
2C104.2A61.E2CE173.2A61.E2CE173.2A61.E2CE173.2A61.E2CE$11.3ACBED3.A
BCDE15.2A.E2D19.BA104.4A61.2D173.4A61.2D173.4A61.2D173.4A61.2D$11.3A
CBED2.ABCDE19.3E4.A7.A6.AB3.2E100.2B61.C2AC173.2B61.C2AC173.2B61.C2A
C173.2B61.C2AC$13.B.DA.CAECAEC.E14.2A.E2D24.2D99.C2AC61.2B173.C2AC61.
2B173.C2AC61.2B173.C2AC61.2B$16.ABCDE.A2BCE12.2A2BD.EDE23.2C100.2D61.
4A173.2D61.4A173.2D61.4A173.2D61.4A$3.A3.EDC7.BACD.B.A2.2D9.3A.EDE26.
2B99.E2CE61.2A173.E2CE61.2A173.E2CE61.2A173.E2CE61.2A$2.2AB.2E.2C4.
ABCDE7.2C7.5ACD2E26.2A172.2E238.2E238.2E238.2E$5ACACD.D4.ABCDE7.2B7.
5ACACD.D126.2E238.2E238.2E238.2E$5ACD2E18.2A2.2E5.2AB.2E.2C118.2A77.
E2CE157.2A77.E2CE157.2A77.E2CE157.2A77.E2CE$2.3A.EDE22.2D6.A3.EDC118.
4A77.2D157.4A77.2D157.4A77.2D157.4A77.2D$3.2A2BD.EDE19.2C46.2E84.2B
77.C2AC157.2B77.C2AC157.2B77.C2AC157.2B77.C2AC$5.2A.E2D19.BA47.2D83.
C2AC77.2B157.C2AC77.2B157.C2AC77.2B157.C2AC77.2B$8.3E4.A7.A6.AB3.2E
42.2C84.2D77.4A157.2D77.4A157.2D77.4A157.2D77.4A$5.2A.E2D24.2D42.2B
83.E2CE77.2A157.E2CE77.2A157.E2CE77.2A157.E2CE77.2A$3.2A2BD.EDE23.2C
42.2A172.2E238.2E238.2E238.2E$2.3A.EDE26.2B128.2E238.2E238.2E238.2E
$5ACD2E26.2A120.2A93.E2CE141.2A93.E2CE141.2A93.E2CE141.2A93.E2CE$5A
CACD.D145.4A93.2D141.4A93.2D141.4A93.2D141.4A93.2D$2.2AB.2E.2C76.2E
68.2B93.C2AC141.2B93.C2AC141.2B93.C2AC141.2B93.C2AC$3.A3.EDC8.AB.CE
.D62.2D67.C2AC93.2B141.C2AC93.2B141.C2AC93.2B141.C2AC93.2B$19.2A2D2C
18.2E42.2C68.2D93.4A141.2D93.4A141.2D93.4A141.2D93.4A$16.A.CB2A2.DE
17.2D42.2B67.E2CE93.2A141.E2CE93.2A141.E2CE93.2A141.E2CE93.2A$14.5A
B2DC21.BC41.2A172.2E238.2E238.2E238.2E30.A.C.E$14.6ADEDC4.A7.A7.CB111.
2E238.2E238.2E238.2E133.2ABADC.E2.ABCDE$16.4AE2D126.2A109.E2CE125.2A
109.E2CE125.2A109.E2CE125.2A109.E2CE28.2ABADC.E.ABCDE$17.2A2B2D125.
4A109.2D125.4A109.2D125.4A109.2D125.4A109.2D30.A.C.EBADB.DB.D$19.AC
2AC71.2E52.2B109.C2AC125.2B109.C2AC125.2B109.C2AC125.2B109.C2AC33.A
BCDE.2ABD2E$21.2B.B69.DC52.C2AC109.2B125.C2AC109.2B125.C2AC109.2B125.
C2AC109.2B24.DCB7.A.BCEA3.E2C$20.3A.AB5.A7.A7.A7.A7.A7.A7.A7.A6.CD53.
2D109.4A125.2D109.4A125.2D109.4A125.2D109.4A18.A.A.2DE2B5.ABCDE6.2B
$21.2A8.2E115.E2CE109.2A125.E2CE109.2A125.E2CE109.2A125.E2CE109.2A18.
4ABABC.C5.ABCDE6.2A2.2E$29.2E.C236.2E238.2E238.2E250.4ABC2D22.2D$31.
CA7.A7.A7.A7.A7.A7.A7.A7.A8.E43.2E238.2E238.2E238.2E110.2A19.A.A.DB
D22.2C$28.E2CE72.E36.2A125.E2CE109.2A125.E2CE109.2A125.E2CE109.2A117.
4A21.A.2A2E20.2B$29.2D109.4A125.2D109.4A125.2D109.4A125.2D109.4A117.
2B22.3A.2D20.2A.ED$28.C2AC109.2B125.C2AC109.2B125.C2AC109.2B125.C2A
C109.2B117.C2AC22.2AC2.A7.A7.A6.DE$29.2B32.DCB29.2A43.C2AC125.2B109.
C2AC125.2B109.C2AC125.2B109.C2AC117.2D22.3A.2D$28.4A26.A.A.2DE2B28.
2B44.2D125.4A109.2D125.4A109.2D125.4A109.2D117.E2CE21.A.2A2E$29.2A26.
4ABABC.C28.2C43.E2CE125.2A109.E2CE125.2A109.E2CE125.2A109.E2CE138.A
.A.DBD30.2E$37.2E18.4ABC2D30.2D180.2E238.2E238.2E222.2E18.4ABC2D30.
2D$58.A.A.DBD30.2E44.2E238.2E238.2E238.2E110.2A26.4ABABC.C28.2C$36.
E2CE21.A.2A2E66.2A141.E2CE93.2A141.E2CE93.2A141.E2CE93.2A117.4A26.A
.A.2DE2B28.2B$37.2D22.3A.2D65.4A141.2D93.4A141.2D93.4A141.2D93.4A117.
2B32.DCB29.2A$36.C2AC22.2AC2.A7.A7.A6.DE41.2B141.C2AC93.2B141.C2AC93.
2B141.C2AC93.2B117.C2AC$37.2B22.3A.2D20.2A.ED40.C2AC141.2B93.C2AC141.
2B93.C2AC141.2B93.C2AC117.2D$36.4A21.A.2A2E20.2B44.2D141.4A93.2D141.
4A93.2D141.4A93.2D117.E2CE72.E$37.2A19.A.A.DBD22.2C43.E2CE141.2A93.
E2CE141.2A93.E2CE141.2A93.E2CE119.CA7.A7.A7.A7.A7.A7.A7.A7.A8.E$45.
2E10.4ABC2D22.2D196.2E238.2E238.2E206.2E.C$57.4ABABC.C5.ABCDE6.2A2.
2E44.2E238.2E238.2E238.2E110.2A8.2E$44.E2CE10.A.A.2DE2B5.ABCDE6.2B40.
2A157.E2CE77.2A157.E2CE77.2A157.E2CE77.2A117.3A.AB5.A7.A7.A7.A7.A7.
A7.A7.A6.CD$45.2D16.DCB7.A.BCEA3.E2C39.4A157.2D77.4A157.2D77.4A157.
2D77.4A117.2B.B69.DC$44.C2AC25.ABCDE.2ABD2E40.2B157.C2AC77.2B157.C2A
C77.2B157.C2AC77.2B116.AC2AC71.2E$45.2B22.A.C.EBADB.DB.D41.C2AC157.
2B77.C2AC157.2B77.C2AC157.2B77.C2AC113.2A2B2D$44.4A20.2ABADC.E.ABCD
E43.2D157.4A77.2D157.4A77.2D157.4A77.2D113.4AE2D$45.2A21.2ABADC.E2.
ABCDE41.E2CE157.2A77.E2CE157.2A77.E2CE157.2A77.E2CE110.6ADEDC4.A7.A
7.CB$53.2E14.A.C.E219.2E238.2E238.2E183.5AB2DC21.BC41.2A$125.2E238.
2E238.2E238.2E113.A.CB2A2.DE17.2D42.2B$52.E2CE61.2A173.E2CE61.2A173.
E2CE61.2A173.E2CE61.2A124.2A2D2C18.2E42.2C$53.2D61.4A173.2D61.4A173.
2D61.4A173.2D61.4A107.A3.EDC8.AB.CE.D62.2D$52.C2AC61.2B173.C2AC61.2B
173.C2AC61.2B173.C2AC61.2B107.2AB.2E.2C76.2E$53.2B61.C2AC173.2B61.C
2AC173.2B61.C2AC173.2B61.C2AC104.5ACACD.D$52.4A61.2D173.4A61.2D173.
4A61.2D173.4A61.2D105.5ACD2E26.2A$53.2A61.E2CE173.2A61.E2CE173.2A61.
E2CE173.2A61.E2CE106.3A.EDE26.2B$61.2E238.2E238.2E238.2E164.2A2BD.E
DE23.2C42.2A$117.2E238.2E238.2E238.2E110.2A.E2D24.2D42.2B$60.E2CE45.
2A189.E2CE45.2A189.E2CE45.2A189.E2CE45.2A121.3E4.A7.A6.AB3.2E42.2C$
61.2D45.4A189.2D45.4A189.2D45.4A189.2D45.4A117.2A.E2D19.BA47.2D$60.
C2AC45.2B189.C2AC45.2B189.C2AC45.2B189.C2AC45.2B116.2A2BD.EDE19.2C46.
2E$61.2B45.C2AC189.2B45.C2AC189.2B45.C2AC189.2B45.C2AC114.3A.EDE22.
2D6.A3.EDC$60.4A45.2D189.4A45.2D189.4A45.2D189.4A45.2D113.5ACD2E18.
2A2.2E5.2AB.2E.2C44.B.D$61.2A45.E2CE189.2A45.E2CE189.2A45.E2CE189.2A
45.E2CE112.5ACACD.D4.ABCDE7.2B7.5ACACD.D42.3ACBED3.ABCDE$69.2E238.2E
238.2E238.2E155.2AB.2E.2C4.ABCDE7.2C7.5ACD2E26.2A16.3ACBED2.ABCDE$109.
2E238.2E238.2E238.2E116.A3.EDC7.BACD.B.A2.2D9.3A.EDE26.2B18.B.DA.CA
ECAEC.E$68.E2CE29.2A205.E2CE29.2A205.E2CE29.2A205.E2CE29.2A137.ABCD
E.A2BCE12.2A2BD.EDE23.2C21.ABCDE.A2BCE$69.2D29.4A205.2D29.4A205.2D29.
4A205.2D29.4A133.B.DA.CAECAEC.E14.2A.E2D24.2D8.A3.EDC7.BACD.B.A2.2D
$68.C2AC29.2B205.C2AC29.2B205.C2AC29.2B205.C2AC29.2B132.3ACBED2.ABC
DE19.3E4.A7.A6.AB3.2E7.2AB.2E.2C4.ABCDE7.2C$69.2B29.C2AC205.2B29.C2A
C205.2B29.C2AC205.2B29.C2AC131.3ACBED3.ABCDE15.2A.E2D19.BA10.5ACACD
.D4.ABCDE7.2B$68.4A29.2D205.4A29.2D205.4A29.2D205.4A29.2D134.B.D23.
2A2BD.EDE19.2C9.5ACD2E18.2A2.2E$69.2A29.E2CE205.2A29.E2CE205.2A29.E
2CE205.2A29.E2CE158.3A.EDE22.2D11.3A.ECE22.2D$77.2E238.2E238.2E238.
2E181.5ACD2E18.2A2.2E12.A.3AB22.2C$101.2E238.2E238.2E238.2E157.5ACA
CD.D4.ABCDE7.2B17.3AB.2E20.2B2.E$76.E2CE13.2A221.E2CE13.2A221.E2CE13.
2A221.E2CE13.2A167.2AB.2E.2C4.ABCDE7.2C17.3ABD2.A7.A7.A3.2A.E$77.2D
13.4A221.2D13.4A221.2D13.4A221.2D13.4A167.A3.EDC7.BACD.B.A2.2D17.3A
B.2E$76.C2AC13.2B221.C2AC13.2B221.C2AC13.2B221.C2AC13.2B181.ABCDE.A
2BCE18.A.3AB$77.2B13.C2AC221.2B13.C2AC221.2B13.C2AC221.2B13.C2AC177.
B.DA.CAECAEC.E17.3A.ECE$5.CBA3.E64.4A13.2D221.4A13.2D221.4A13.2D221.
4A13.2D176.3ACBED2.ABCDE17.5ACD2E30.2E$2.A.2CD2A2.2E64.2A13.E2CE221.
2A13.E2CE221.2A13.E2CE221.2A13.E2CE175.3ACBED3.ABCDE16.5ACACD.D28.2D
$6ABEBE75.2E238.2E238.2E238.2E186.B.D28.2AB.2E.2C28.2C$4AB2CE85.2E238.
2E238.2E238.2E210.A3.EDC29.2B$2.A.CBC2.E74.E2AE236.E2AE236.E2AE236.
E2AE253.2A$4.AB.CBCD73.B2AC236.B2AC236.B2AC236.B2AC$6.C2BD73.AD2.B235.
AD2.B235.AD2.B235.AD2.B$6.3CD3.A7.A7.A7.A7.A7.A7.A7.A7.A6.AD7.A7.A7.
A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A
7.A7.A7.A7.A6.AD7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A
7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A6.AD7.A7.A7.A7.A7.A7.A7.A7.A7.A
7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A6.AD7.A
7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.A7.
A7.A7.A7.A7.A7.A7.A7.A7.A$6.C2BD$4.AB.CBCD$2.A.CBC2.E$4AB2CE$6ABEBE
$2.A.2CD2A2.2E$5.CBA3.E!
The following archive contains a collection of patterns that can be run on Golly:
Snake.zip
(220.29 KiB) Downloaded 417 times
The patterns were originally generated many years ago using MCell.

http://www.mirekw.com/ca/index.html

The oscillators are of particular interest. There are no guns in the archive. This does not mean that the Snake rule does not support guns. It simply means that I was unable to find any.

A method of extending Generations rules was introduced here:

viewtopic.php?f=11&t=1624#p16952

The following rule definition:

Code: Select all

  final static int numStates = 11;
  final static int numOscillators = 5;
  final static int numNeighbors = 8;
  final static int ruleTable[][] =
    {
      {0,0,1,0,0,1,0,0,0},
      {1,2,2,1,1,2,1,1,2},
      {3,3,3,3,3,3,3,3,3},
      {4,4,4,4,4,4,4,4,4},
      {5,5,5,5,5,5,5,5,5},
      {0,0,0,0,0,0,0,0,0}
    };

  /* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
  /* order for five neighbors is n, w, e, s, c */

  int adjustNeighbor(int n)
  {
    if (n >= (numStates - numOscillators))
      return n - numStates + numOscillators + 1;
    return n; 
  }

  int f(int[] a)
  {
    int cell = a[8];
    int count = 0;
    for (int i = 0; i < 8; i++)
    {
      int t = adjustNeighbor(a[i]);
      if (t == 1)
        count += t;
    }
    if (cell >= (numStates - numOscillators))
    {
      if (cell == (numStates - 1))
        return numStates - numOscillators;
      return cell + 1;
    }
    return ruleTable[cell][count];
  }
was inserted into the Golly provided file RuleTreeGen.java and used to generate this Golly rule tree:

Code: Select all

@RULE Snake_O5
@TREE
num_states=11
num_neighbors=8
num_nodes=35
1 0 1 3 4 5 0 7 8 9 10 6
1 0 2 3 4 5 0 7 8 9 10 6
2 0 1 0 0 0 0 1 0 0 0 0
1 1 2 3 4 5 0 7 8 9 10 6
2 1 3 1 1 1 1 3 1 1 1 1
3 2 4 2 2 2 2 4 2 2 2 2
2 3 0 3 3 3 3 0 3 3 3 3
3 4 6 4 4 4 4 6 4 4 4 4
4 5 7 5 5 5 5 7 5 5 5 5
2 0 0 0 0 0 0 0 0 0 0 0
3 6 9 6 6 6 6 9 6 6 6 6
4 7 10 7 7 7 7 10 7 7 7 7
5 8 11 8 8 8 8 11 8 8 8 8
2 0 3 0 0 0 0 3 0 0 0 0
3 9 13 9 9 9 9 13 9 9 9 9
4 10 14 10 10 10 10 14 10 10 10 10
5 11 15 11 11 11 11 15 11 11 11 11
6 12 16 12 12 12 12 16 12 12 12 12
3 13 6 13 13 13 13 6 13 13 13 13
4 14 18 14 14 14 14 18 14 14 14 14
5 15 19 15 15 15 15 19 15 15 15 15
6 16 20 16 16 16 16 20 16 16 16 16
7 17 21 17 17 17 17 21 17 17 17 17
4 18 10 18 18 18 18 10 18 18 18 18
5 19 23 19 19 19 19 23 19 19 19 19
6 20 24 20 20 20 20 24 20 20 20 20
7 21 25 21 21 21 21 25 21 21 21 21
8 22 26 22 22 22 22 26 22 22 22 22
3 9 2 9 9 9 9 2 9 9 9 9
4 10 28 10 10 10 10 28 10 10 10 10
5 23 29 23 23 23 23 29 23 23 23 23
6 24 30 24 24 24 24 30 24 24 24 24
7 25 31 25 25 25 25 31 25 25 25 25
8 26 32 26 26 26 26 32 26 26 26 26
9 27 33 27 27 27 27 33 27 27 27 27
@COLORS
 0   0   0   0
 1 255   0   0
 2   0 255   0
 3   0   0 255
 4 255 255   0
 5   0 255 255
 6 255   0 255
 7  92  36 110
 8   0  99 140
 9 176 196 222
10 115  61  26
This rule extends the Snake rule by adding period 5 oscillators which can be used to construct guns. Some examples follow:

Code: Select all

x = 1, y = 2, rule = Snake_O5
F$F!

Code: Select all

x = 3, y = 2, rule = Snake_O5
3F$.F!

Code: Select all

x = 5, y = 3, rule = Snake_O5
F3.F$.3F$2.F!

Code: Select all

x = 2, y = 3, rule = Snake_O5
.F$2F$F!

Code: Select all

x = 5, y = 1, rule = Snake_O5
2F.2F!

Code: Select all

x = 5, y = 7, rule = Snake_O5
2.F$2.F2$2F.2F2$2.F$2.F!

Code: Select all

x = 5, y = 5, rule = Snake_O5
2.F2$F3.F2$2.F!

Code: Select all

x = 4, y = 2, rule = Snake_O5
F.FI$.F!

Code: Select all

x = 5, y = 5, rule = Snake_O5
J$.J$2.J$3.J$4.J!

Code: Select all

x = 10, y = 10, rule = Snake_O5
J$.J$2.J$3.J$4.J$5.J$6.J$7.J$8.J$9.J!
Most small symmetrical patterns consisting only of states 6 thru 10 are guns!

Brian Prentice
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