Bit Counts

[bprentice]

One of the rule families supported by Square Cell is called Bit Counts. Rules in this family can have up to 16 states and are selected with an input dialog. An example dialog is shown below:

BitCounts.png (27.37 KiB) Viewed 6281 times

Each step, the bits of the neighbor states are counted and this count is used to index a rule table to obtain the next state. A cells neighborhood is divided into 4 planes. The 9 bits in each plane can be individually selected to participate in the neighborhood count. In the example above all bits are selected for each neighbor and no bits are selected for the cell itself.

Randomly generated rule tables can be tested to find an interesting rule.

The following Golly rule tree:

Code: Select all

@RULE BitCounts003
@TREE
num_states=8
num_neighbors=8
num_nodes=98
1 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0
1 5 5 5 5 5 5 5 5
2 0 0 0 0 0 0 0 2
2 0 0 0 2 0 2 2 0
3 1 1 1 3 1 3 3 4
1 7 7 7 7 7 7 7 7
2 0 2 2 0 2 0 0 6
3 1 3 3 4 3 4 4 7
2 2 0 0 6 0 6 6 0
3 3 4 4 7 4 7 7 9
2 0 6 6 0 6 0 0 0
3 4 7 7 9 7 9 9 11
4 5 8 8 10 8 10 10 12
1 6 6 6 6 6 6 6 6
2 6 0 0 0 0 0 0 14
3 7 9 9 11 9 11 11 15
4 8 10 10 12 10 12 12 16
2 0 0 0 14 0 14 14 0
3 9 11 11 15 11 15 15 18
4 10 12 12 16 12 16 16 19
1 2 2 2 2 2 2 2 2
2 0 14 14 0 14 0 0 21
3 11 15 15 18 15 18 18 22
4 12 16 16 19 16 19 19 23
5 13 17 17 20 17 20 20 24
2 14 0 0 21 0 21 21 14
3 15 18 18 22 18 22 22 26
4 16 19 19 23 19 23 23 27
5 17 20 20 24 20 24 24 28
2 0 21 21 14 21 14 14 0
3 18 22 22 26 22 26 26 30
4 19 23 23 27 23 27 27 31
5 20 24 24 28 24 28 28 32
2 21 14 14 0 14 0 0 0
3 22 26 26 30 26 30 30 34
4 23 27 27 31 27 31 31 35
5 24 28 28 32 28 32 32 36
6 25 29 29 33 29 33 33 37
2 14 0 0 0 0 0 0 0
3 26 30 30 34 30 34 34 39
4 27 31 31 35 31 35 35 40
5 28 32 32 36 32 36 36 41
6 29 33 33 37 33 37 37 42
1 4 4 4 4 4 4 4 4
2 0 0 0 0 0 0 0 44
3 30 34 34 39 34 39 39 45
4 31 35 35 40 35 40 40 46
5 32 36 36 41 36 41 41 47
6 33 37 37 42 37 42 42 48
2 0 0 0 44 0 44 44 0
3 34 39 39 45 39 45 45 50
4 35 40 40 46 40 46 46 51
5 36 41 41 47 41 47 47 52
6 37 42 42 48 42 48 48 53
7 38 43 43 49 43 49 49 54
1 3 3 3 3 3 3 3 3
2 0 44 44 0 44 0 0 56
3 39 45 45 50 45 50 50 57
4 40 46 46 51 46 51 51 58
5 41 47 47 52 47 52 52 59
6 42 48 48 53 48 53 53 60
7 43 49 49 54 49 54 54 61
2 44 0 0 56 0 56 56 0
3 45 50 50 57 50 57 57 63
4 46 51 51 58 51 58 58 64
5 47 52 52 59 52 59 59 65
6 48 53 53 60 53 60 60 66
7 49 54 54 61 54 61 61 67
2 0 56 56 0 56 0 0 0
3 50 57 57 63 57 63 63 69
4 51 58 58 64 58 64 64 70
5 52 59 59 65 59 65 65 71
6 53 60 60 66 60 66 66 72
7 54 61 61 67 61 67 67 73
8 55 62 62 68 62 68 68 74
2 56 0 0 0 0 0 0 6
3 57 63 63 69 63 69 69 76
4 58 64 64 70 64 70 70 77
5 59 65 65 71 65 71 71 78
6 60 66 66 72 66 72 72 79
7 61 67 67 73 67 73 73 80
8 62 68 68 74 68 74 74 81
2 0 0 0 6 0 6 6 0
3 63 69 69 76 69 76 76 83
4 64 70 70 77 70 77 77 84
5 65 71 71 78 71 78 78 85
6 66 72 72 79 72 79 79 86
7 67 73 73 80 73 80 80 87
8 68 74 74 81 74 81 81 88
2 0 6 6 0 6 0 0 2
3 69 76 76 83 76 83 83 90
4 70 77 77 84 77 84 84 91
5 71 78 78 85 78 85 85 92
6 72 79 79 86 79 86 86 93
7 73 80 80 87 80 87 87 94
8 74 81 81 88 81 88 88 95
9 75 82 82 89 82 89 89 96
@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

was generated by the Java file RuleTreeGen.java which is included with Golly.

This code was used:

Code: Select all

  /* Put your state count, neighbor count, and function here */
  final static int numStates = 8;
  final static int numNeighbors = 8;
  final static int neighborSelector[][] =
  {
    {1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1},
  };
  final static int ruleTable[] =
    {0,0,0,0,0,5,0,7,0,0,6,0,2,6,0,0,0,4,0,3,0,0,7,0,5,6,0,7,0,0,5,0,0,0,0,0,0};

  /* 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 f(int[] a)
  {
    int bitCount =
      ((a[0]     ) & neighborSelector[0][0]) +
      ((a[0] >> 1) & neighborSelector[1][0]) +
      ((a[0] >> 2) & neighborSelector[2][0]) +
      ((a[0] >> 3) & neighborSelector[3][0]) +
      ((a[4]     ) & neighborSelector[0][1]) +
      ((a[4] >> 1) & neighborSelector[1][1]) +
      ((a[4] >> 2) & neighborSelector[2][1]) +
      ((a[4] >> 3) & neighborSelector[3][1]) +
      ((a[1]     ) & neighborSelector[0][2]) +
      ((a[1] >> 1) & neighborSelector[1][2]) +
      ((a[1] >> 2) & neighborSelector[2][2]) +
      ((a[1] >> 3) & neighborSelector[3][2]) +

      ((a[5]     ) & neighborSelector[0][3]) +
      ((a[5] >> 1) & neighborSelector[1][3]) +
      ((a[5] >> 2) & neighborSelector[2][3]) +
      ((a[5] >> 3) & neighborSelector[3][3]) +
      ((a[8]     ) & neighborSelector[0][4]) +
      ((a[8] >> 1) & neighborSelector[1][4]) +
      ((a[8] >> 2) & neighborSelector[2][4]) +
      ((a[8] >> 3) & neighborSelector[3][4]) +
      ((a[6]     ) & neighborSelector[0][5]) +
      ((a[6] >> 1) & neighborSelector[1][5]) +
      ((a[6] >> 2) & neighborSelector[2][5]) +
      ((a[6] >> 3) & neighborSelector[3][5]) +

      ((a[2]     ) & neighborSelector[0][6]) +
      ((a[2] >> 1) & neighborSelector[1][6]) +
      ((a[2] >> 2) & neighborSelector[2][6]) +
      ((a[2] >> 3) & neighborSelector[3][6]) +
      ((a[7]     ) & neighborSelector[0][7]) +
      ((a[7] >> 1) & neighborSelector[1][7]) +
      ((a[7] >> 2) & neighborSelector[2][7]) +
      ((a[7] >> 3) & neighborSelector[3][7]) +
      ((a[3]     ) & neighborSelector[0][8]) +
      ((a[3] >> 1) & neighborSelector[1][8]) +
      ((a[3] >> 2) & neighborSelector[2][8]) +
      ((a[3] >> 3) & neighborSelector[3][8]);
    return ruleTable[bitCount];
  }

The rule has a common replicator. Can this replicator be used to construct guns?

Brian Prentice

[c0b0p0]

The rule has a common replicator. Can this replicator be used to construct guns?

Here is an 8-replicator gun.

Code: Select all

x = 103, y = 65, rule = BitCounts003
13.E.F.E$13.G3.G$13.E.F.E10$EGE2$F.F2$EGE29$94.E.F.E$94.G3.G$94.E.F.E
$63.EGE$100.EGE$63.F.F$100.F.F$63.EGE$86.EGE11.EGE2$86.F.F2$86.EGE2$
90.E.F.E$90.G3.G$90.E.F.E$48.E.F.E$48.G3.G$48.E.F.E!

Unfortunately this rule does not have any oscillators other than replicator-based ones and the oscillator below, which cannot function as an eater.

Code: Select all

x = 3, y = 2, rule = BitCounts003
.G$E.E!

[bprentice]

Unfortunately this rule does not have any oscillators other than replicator-based ones and the oscillator below, which cannot function as an eater.

Code: Select all

x = 168, y = 29, rule = BitCounts003
86.E$82.E.B.E$82.2E.E21$166.2E$2E163.E$2.E108.E.E7.E.E7.E.E7.E.E22.
B$.B22.E.E7.E.E7.E.E7.E.E54.G.G7.G.G7.G.G7.G.G21.E$2.E21.G.G7.G.G7.
G.G7.G.G54.E.E7.E.E7.E.E7.E.E21.2E$.2E21.E.E7.E.E7.E.E7.E.E!

Code: Select all

x = 27, y = 28, rule = BitCounts003
2E$2.E$.B2.E.F.E5.E.F.E$2.E.G3.G5.G3.G$.2E.E.F.E5.E.F.E5$24.EGE2$24.
F.F2$24.EGE6$24.EGE2$24.F.F2$24.EGE2$23.E.2E$22.E.B.E$22.E!

Brian Prentice

[bprentice]

The parameters and rule tree for this 16 state Bit Counts rule are:

Code: Select all

  final static int numStates = 16;
  final static int numNeighbors = 8;
  final static int neighborSelector[][] =
  {
    {1,1,1,1,1,1,1,1,1},
    {1,1,1,1,0,1,1,1,1},
    {1,1,1,1,0,1,1,1,1},
    {1,1,1,1,1,1,1,1,1},
  };
  final static int ruleTable[] =
    {0,0,0,0,1,0,0,14,3,0,0,10,0,6,1,0,3,14,0,0,10,1,15,6,4,13,0,0,8,7,2,7,0,5,7,0,0};

Code: Select all

@RULE BitCounts004
@TREE
num_states=16
num_neighbors=8
num_nodes=151
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0
1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0
2 0 0 0 1 0 1 1 2 0 1 1 2 1 2 2 3
1 0 0 0 0 0 0 0 0 0 14 0 14 0 14 0 14
2 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 5
1 0 14 0 14 0 14 0 14 14 3 14 3 14 3 14 3
2 1 2 2 3 2 3 3 5 2 3 3 5 3 5 5 7
1 14 3 14 3 14 3 14 3 3 0 3 0 3 0 3 0
2 2 3 3 5 3 5 5 7 3 5 5 7 5 7 7 9
1 3 0 3 0 3 0 3 0 0 0 0 0 0 0 0 0
2 3 5 5 7 5 7 7 9 5 7 7 9 7 9 9 11
3 4 6 6 8 6 8 8 10 6 8 8 10 8 10 10 12
1 0 0 0 0 0 0 0 0 0 10 0 10 0 10 0 10
2 5 7 7 9 7 9 9 11 7 9 9 11 9 11 11 14
3 6 8 8 10 8 10 10 12 8 10 10 12 10 12 12 15
1 0 10 0 10 0 10 0 10 10 0 10 0 10 0 10 0
2 7 9 9 11 9 11 11 14 9 11 11 14 11 14 14 17
3 8 10 10 12 10 12 12 15 10 12 12 15 12 15 15 18
1 10 0 10 0 10 0 10 0 0 6 0 6 0 6 0 6
2 9 11 11 14 11 14 14 17 11 14 14 17 14 17 17 20
3 10 12 12 15 12 15 15 18 12 15 15 18 15 18 18 21
1 0 6 0 6 0 6 0 6 6 1 6 1 6 1 6 1
2 11 14 14 17 14 17 17 20 14 17 17 20 17 20 20 23
3 12 15 15 18 15 18 18 21 15 18 18 21 18 21 21 24
4 13 16 16 19 16 19 19 22 16 19 19 22 19 22 22 25
1 6 1 6 1 6 1 6 1 1 0 1 0 1 0 1 0
2 14 17 17 20 17 20 20 23 17 20 20 23 20 23 23 27
3 15 18 18 21 18 21 21 24 18 21 21 24 21 24 24 28
4 16 19 19 22 19 22 22 25 19 22 22 25 22 25 25 29
1 1 0 1 0 1 0 1 0 0 3 0 3 0 3 0 3
2 17 20 20 23 20 23 23 27 20 23 23 27 23 27 27 31
3 18 21 21 24 21 24 24 28 21 24 24 28 24 28 28 32
4 19 22 22 25 22 25 25 29 22 25 25 29 25 29 29 33
1 0 3 0 3 0 3 0 3 3 14 3 14 3 14 3 14
2 20 23 23 27 23 27 27 31 23 27 27 31 27 31 31 35
3 21 24 24 28 24 28 28 32 24 28 28 32 28 32 32 36
4 22 25 25 29 25 29 29 33 25 29 29 33 29 33 33 37
1 3 14 3 14 3 14 3 14 14 0 14 0 14 0 14 0
2 23 27 27 31 27 31 31 35 27 31 31 35 31 35 35 39
3 24 28 28 32 28 32 32 36 28 32 32 36 32 36 36 40
4 25 29 29 33 29 33 33 37 29 33 33 37 33 37 37 41
5 26 30 30 34 30 34 34 38 30 34 34 38 34 38 38 42
1 14 0 14 0 14 0 14 0 0 0 0 0 0 0 0 0
2 27 31 31 35 31 35 35 39 31 35 35 39 35 39 39 44
3 28 32 32 36 32 36 36 40 32 36 36 40 36 40 40 45
4 29 33 33 37 33 37 37 41 33 37 37 41 37 41 41 46
5 30 34 34 38 34 38 38 42 34 38 38 42 38 42 42 47
2 31 35 35 39 35 39 39 44 35 39 39 44 39 44 44 14
3 32 36 36 40 36 40 40 45 36 40 40 45 40 45 45 49
4 33 37 37 41 37 41 41 46 37 41 41 46 41 46 46 50
5 34 38 38 42 38 42 42 47 38 42 42 47 42 47 47 51
1 0 10 0 10 0 10 0 10 10 1 10 1 10 1 10 1
2 35 39 39 44 39 44 44 14 39 44 44 14 44 14 14 53
3 36 40 40 45 40 45 45 49 40 45 45 49 45 49 49 54
4 37 41 41 46 41 46 46 50 41 46 46 50 46 50 50 55
5 38 42 42 47 42 47 47 51 42 47 47 51 47 51 51 56
1 10 1 10 1 10 1 10 1 1 15 1 15 1 15 1 15
2 39 44 44 14 44 14 14 53 44 14 14 53 14 53 53 58
3 40 45 45 49 45 49 49 54 45 49 49 54 49 54 54 59
4 41 46 46 50 46 50 50 55 46 50 50 55 50 55 55 60
5 42 47 47 51 47 51 51 56 47 51 51 56 51 56 56 61
6 43 48 48 52 48 52 52 57 48 52 52 57 52 57 57 62
1 1 15 1 15 1 15 1 15 15 6 15 6 15 6 15 6
2 44 14 14 53 14 53 53 58 14 53 53 58 53 58 58 64
3 45 49 49 54 49 54 54 59 49 54 54 59 54 59 59 65
4 46 50 50 55 50 55 55 60 50 55 55 60 55 60 60 66
5 47 51 51 56 51 56 56 61 51 56 56 61 56 61 61 67
6 48 52 52 57 52 57 57 62 52 57 57 62 57 62 62 68
1 15 6 15 6 15 6 15 6 6 4 6 4 6 4 6 4
2 14 53 53 58 53 58 58 64 53 58 58 64 58 64 64 70
3 49 54 54 59 54 59 59 65 54 59 59 65 59 65 65 71
4 50 55 55 60 55 60 60 66 55 60 60 66 60 66 66 72
5 51 56 56 61 56 61 61 67 56 61 61 67 61 67 67 73
6 52 57 57 62 57 62 62 68 57 62 62 68 62 68 68 74
1 6 4 6 4 6 4 6 4 4 13 4 13 4 13 4 13
2 53 58 58 64 58 64 64 70 58 64 64 70 64 70 70 76
3 54 59 59 65 59 65 65 71 59 65 65 71 65 71 71 77
4 55 60 60 66 60 66 66 72 60 66 66 72 66 72 72 78
5 56 61 61 67 61 67 67 73 61 67 67 73 67 73 73 79
6 57 62 62 68 62 68 68 74 62 68 68 74 68 74 74 80
1 4 13 4 13 4 13 4 13 13 0 13 0 13 0 13 0
2 58 64 64 70 64 70 70 76 64 70 70 76 70 76 76 82
3 59 65 65 71 65 71 71 77 65 71 71 77 71 77 77 83
4 60 66 66 72 66 72 72 78 66 72 72 78 72 78 78 84
5 61 67 67 73 67 73 73 79 67 73 73 79 73 79 79 85
6 62 68 68 74 68 74 74 80 68 74 74 80 74 80 80 86
7 63 69 69 75 69 75 75 81 69 75 75 81 75 81 81 87
1 13 0 13 0 13 0 13 0 0 0 0 0 0 0 0 0
2 64 70 70 76 70 76 76 82 70 76 76 82 76 82 82 89
3 65 71 71 77 71 77 77 83 71 77 77 83 77 83 83 90
4 66 72 72 78 72 78 78 84 72 78 78 84 78 84 84 91
5 67 73 73 79 73 79 79 85 73 79 79 85 79 85 85 92
6 68 74 74 80 74 80 80 86 74 80 80 86 80 86 86 93
7 69 75 75 81 75 81 81 87 75 81 81 87 81 87 87 94
1 0 0 0 0 0 0 0 0 0 8 0 8 0 8 0 8
2 70 76 76 82 76 82 82 89 76 82 82 89 82 89 89 96
3 71 77 77 83 77 83 83 90 77 83 83 90 83 90 90 97
4 72 78 78 84 78 84 84 91 78 84 84 91 84 91 91 98
5 73 79 79 85 79 85 85 92 79 85 85 92 85 92 92 99
6 74 80 80 86 80 86 86 93 80 86 86 93 86 93 93 100
7 75 81 81 87 81 87 87 94 81 87 87 94 87 94 94 101
1 0 8 0 8 0 8 0 8 8 7 8 7 8 7 8 7
2 76 82 82 89 82 89 89 96 82 89 89 96 89 96 96 103
3 77 83 83 90 83 90 90 97 83 90 90 97 90 97 97 104
4 78 84 84 91 84 91 91 98 84 91 91 98 91 98 98 105
5 79 85 85 92 85 92 92 99 85 92 92 99 92 99 99 106
6 80 86 86 93 86 93 93 100 86 93 93 100 93 100 100 107
7 81 87 87 94 87 94 94 101 87 94 94 101 94 101 101 108
1 8 7 8 7 8 7 8 7 7 2 7 2 7 2 7 2
2 82 89 89 96 89 96 96 103 89 96 96 103 96 103 103 110
3 83 90 90 97 90 97 97 104 90 97 97 104 97 104 104 111
4 84 91 91 98 91 98 98 105 91 98 98 105 98 105 105 112
5 85 92 92 99 92 99 99 106 92 99 99 106 99 106 106 113
6 86 93 93 100 93 100 100 107 93 100 100 107 100 107 107 114
7 87 94 94 101 94 101 101 108 94 101 101 108 101 108 108 115
8 88 95 95 102 95 102 102 109 95 102 102 109 102 109 109 116
1 7 2 7 2 7 2 7 2 2 7 2 7 2 7 2 7
2 89 96 96 103 96 103 103 110 96 103 103 110 103 110 110 118
3 90 97 97 104 97 104 104 111 97 104 104 111 104 111 111 119
4 91 98 98 105 98 105 105 112 98 105 105 112 105 112 112 120
5 92 99 99 106 99 106 106 113 99 106 106 113 106 113 113 121
6 93 100 100 107 100 107 107 114 100 107 107 114 107 114 114 122
7 94 101 101 108 101 108 108 115 101 108 108 115 108 115 115 123
8 95 102 102 109 102 109 109 116 102 109 109 116 109 116 116 124
1 2 7 2 7 2 7 2 7 7 0 7 0 7 0 7 0
2 96 103 103 110 103 110 110 118 103 110 110 118 110 118 118 126
3 97 104 104 111 104 111 111 119 104 111 111 119 111 119 119 127
4 98 105 105 112 105 112 112 120 105 112 112 120 112 120 120 128
5 99 106 106 113 106 113 113 121 106 113 113 121 113 121 121 129
6 100 107 107 114 107 114 114 122 107 114 114 122 114 122 122 130
7 101 108 108 115 108 115 115 123 108 115 115 123 115 123 123 131
8 102 109 109 116 109 116 116 124 109 116 116 124 116 124 124 132
1 7 0 7 0 7 0 7 0 0 5 0 5 0 5 0 5
2 103 110 110 118 110 118 118 126 110 118 118 126 118 126 126 134
3 104 111 111 119 111 119 119 127 111 119 119 127 119 127 127 135
4 105 112 112 120 112 120 120 128 112 120 120 128 120 128 128 136
5 106 113 113 121 113 121 121 129 113 121 121 129 121 129 129 137
6 107 114 114 122 114 122 122 130 114 122 122 130 122 130 130 138
7 108 115 115 123 115 123 123 131 115 123 123 131 123 131 131 139
8 109 116 116 124 116 124 124 132 116 124 124 132 124 132 132 140
1 0 5 0 5 0 5 0 5 5 7 5 7 5 7 5 7
2 110 118 118 126 118 126 126 134 118 126 126 134 126 134 134 142
3 111 119 119 127 119 127 127 135 119 127 127 135 127 135 135 143
4 112 120 120 128 120 128 128 136 120 128 128 136 128 136 136 144
5 113 121 121 129 121 129 129 137 121 129 129 137 129 137 137 145
6 114 122 122 130 122 130 130 138 122 130 130 138 130 138 138 146
7 115 123 123 131 123 131 131 139 123 131 131 139 131 139 139 147
8 116 124 124 132 124 132 132 140 124 132 132 140 132 140 140 148
9 117 125 125 133 125 133 133 141 125 133 133 141 133 141 141 149
@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
11 189 183 107
12 205 133  63
13  47  79  79
14 255 128   0
15 255 215   0

Some example guns:

Code: Select all

x = 36, y = 76, rule = BitCounts004
33.2A$33.2A9$32.A2NA$32.A2.A$32.A2NA2$32.A2NA$32.A2.A$32.A2NA3$28.3A
.3A$18.2A8.N.N.N.N$18.2A8.N.N.N.N$28.3A.3A13$33.2A$33.2A15$32.A2NA$
32.A2.A$32.A2NA2$32.A2NA$32.A2.A$32.A2NA6$32.A2NA$32.A2.A$32.A2NA2$
32.A2NA$32.A2.A$32.A2NA3$16.3A.3A5.3A.3A$2A14.N.N.N.N5.N.N.N.N$2A14.
N.N.N.N5.N.N.N.N$16.3A.3A5.3A.3A!

Code: Select all

x = 41, y = 44, rule = BitCounts004
33.2A3.2A$33.2A3.2A21$32.A2NA.A2NA$35.A.A$34.FN.NF$34.A3.A$32.CA5.A
C$34.A3.A$34.FN.NF$35.A.A$32.A2NA.A2NA5$21.3A5.3A$2A19.N9.N$2A19.N.
F.N.N.F.N$21.A9.A$22.A.C3.C.A$21.A9.A$2A19.N.F.N.N.F.N$2A19.N9.N$21.
3A5.3A!

Code: Select all

x = 41, y = 42, rule = BitCounts004
33.2A3.2A$33.2A3.2A21$32.A2NA.A2NA$35.A.A$34.FN.NF$34.A3.A$32.CA5.A
C$34.A3.A$34.FN.NF$35.A.A$32.A2NA.A2NA3$21.3A5.3A$2A19.N9.N$2A19.N.
F.N.N.F.N$21.A9.A$22.A.C3.C.A$21.A9.A$2A19.N.F.N.N.F.N$2A19.N9.N$21.
3A5.3A!

Code: Select all

x = 40, y = 50, rule = BitCounts004
32.2A3.2A$32.2A3.2A21$31.A2NA.A2NA$34.A.A$33.FN.NF$33.A3.A$31.CA5.A
C$33.A3.A$33.FN.NF$34.A.A$31.A2NA.A2NA11$22.A3.C3.A$2A20.N3.A3.N$2A
20.N.FA.AF.N$22.2AN3.N2A2$22.2AN3.N2A$2A20.N.FA.AF.N$2A20.N3.A3.N$22.
A3.C3.A!

The performance of Golly when running this rule is excellent, but it took approximately four hours to generate the rule tree on my 2.93 GHz IMac.

Brian Prentice

[Whiterose1]

Most Life-life rules support some oscillators, but there are a few exceptions. Obviously there must be both birth and death, so B/* is out and so is */S012345678. B0 just confuses me, and anything with B1 just explodes.
Now two living cells diagonally adjacent make a period-2 oscillator in everything from B2/ to B2345678/S02345678, or everything with B2 and without S1. I don't think B2/S1 can have oscillators.
A few minutes work can find a p2 oscillator in almost any B3 rule except B3/S123456. Are there any oscillators in this rule?
What is known about this question? Is there any impossibility proof in a non-obvious case like B3/S123456?

[Scorbie]

What is known about this question? Is there any impossibility proof in a non-obvious case like B3/S123456?

I'm no expert, but a simple attempt of gsearch gave me this:

No gliders can exist: with S123456, connected patterns can not shrink.

Ooooor... I'm not sure if this is on-topic.

[bprentice]

Are there any oscillators in this rule?

Yes:

Code: Select all

x = 89, y = 39, rule = BitCounts004
4.3A.3A2.A40.3A.3A5.3A.3A$4.N.N.N.N6.2A35.N.N.N.N5.N.N.N.N$4.N.N.N.
N5.A2.A34.N.N.N.N5.N.N.N.N$4.3A.3A3.2A3.A34.3A.3A5.3A.3A$A2NA12.A.A
31.A2NA$A2.A13.A32.A2.A$A2NA13.A32.A2NA$20.A$A2NA46.A2NA$A2.A46.A2.
A$A2NA13.A2NA29.A2NA$17.A2.A$17.A2NA$A$3.A13.A2NA$3.A13.A2.A$2.A.A12.
A2NA29.A2NA31.A2NA$.A3.2A3.3A.3A33.A2.A31.A2.A$.A2.A5.N.N.N.N33.A2N
A31.A2NA$2.2A6.N.N.N.N$7.A2.3A.3A33.A2NA31.A2NA$50.A2.A31.A2.A$50.A
2NA31.A2NA6$85.A2NA$85.A2.A$85.A2NA2$85.A2NA$85.A2.A$85.A2NA$66.3A.
3A5.3A.3A$66.N.N.N.N5.N.N.N.N$66.N.N.N.N5.N.N.N.N$66.3A.3A5.3A.3A!

Code: Select all

x = 57, y = 4, rule = BitCounts004
4.3A.3A$2A2.N.N.N.N8.A11.A11.A11.2A$2A2.N.N.N.N8.A11.A11.A11.2A$4.3A
.3A!

Code: Select all

x = 154, y = 81, rule = BitCounts004
9.A3.C3.A64.A3.C3.A$9.N3.A3.N64.N3.A3.N$9.N.FA.AF.N64.N.FA.AF.N$9.2A
N3.N2A64.2AN3.N2A2$9.2AN3.N2A64.2AN3.N2A$9.N.FA.AF.N64.N.FA.AF.N$9.
N3.A3.N64.N3.A3.N$9.A3.C3.A64.A3.C3.A$A2NA.A2NA64.A2NA.A2NA$3.A.A70.
A.A$2.FN.NF68.FN.NF$2.A3.A68.A3.A$CA5.AC64.CA5.AC$2.A3.A68.A3.A$2.F
N.NF68.FN.NF$3.A.A70.A.A$A2NA.A2NA64.A2NA.A2NA10$36.A2NA.A2NA$39.A.
A$38.FN.NF$38.A3.A$36.CA5.AC$38.A3.A$38.FN.NF$39.A.A$36.A2NA.A2NA$27.
A3.C3.A$27.N3.A3.N$27.N.FA.AF.N$27.2AN3.N2A2$27.2AN3.N2A$27.N.FA.AF
.N$27.N3.A3.N$27.A3.C3.A19$145.A2NA.A2NA$148.A.A$147.FN.NF$147.A3.A
$145.CA5.AC$147.A3.A$147.FN.NF$148.A.A$145.A2NA.A2NA$136.A3.C3.A$136.
N3.A3.N$136.N.FA.AF.N$136.2AN3.N2A2$136.2AN3.N2A$136.N.FA.AF.N$136.
N3.A3.N$136.A3.C3.A!

Code: Select all

x = 71, y = 34, rule = BitCounts004
4.A3.C3.A$2A2.N3.A3.N20.2A$2A2.N.FA.AF.N20.2A$4.2AN3.N2A2$4.2AN3.N2A
$2A2.N.FA.AF.N20.2A$2A2.N3.A3.N20.2A$4.A3.C3.A17$4.A3.C3.A$2A2.N3.A
3.N56.2A$2A2.N.FA.AF.N56.2A$4.2AN3.N2A2$4.2AN3.N2A$2A2.N.FA.AF.N56.
2A$2A2.N3.A3.N56.2A$4.A3.C3.A!

Code: Select all

x = 40, y = 40, rule = BitCounts004
32.2A3.2A$32.2A3.2A21$31.A2NA.A2NA$34.A.A$33.FN.NF$33.A3.A$31.CA5.A
C$33.A3.A$33.FN.NF$34.A.A$31.A2NA.A2NA$22.A3.C3.A$2A20.N3.A3.N$2A20.
N.FA.AF.N$22.2AN3.N2A2$22.2AN3.N2A$2A20.N.FA.AF.N$2A20.N3.A3.N$22.A
3.C3.A!

Brian Prentice

[unname66609]

Most Life-life rules support some oscillators, but there are a few exceptions. Obviously there must be both birth and death, so B/* is out and so is */S012345678. B0 just confuses me, and anything with B1 just explodes.
Now two living cells diagonally adjacent make a period-2 oscillator in everything from B2/ to B2345678/S02345678, or everything with B2 and without S1. I don't think B2/S1 can have oscillators.
A few minutes work can find a p2 oscillator in almost any B3 rule except B3/S123456. Are there any oscillators in this rule?
What is known about this question? Is there any impossibility proof in a non-obvious case like B3/S123456?

I don’t know.

[gameoflifeboy]

Self-descriptive population plot is BitCounts004:

Code: Select all

x = 542, y = 536, rule = BitCounts004
238.4A3.3A2.4A2.A3.A.A6.3A2.5A2.3A3.3A2.A3.A7.4A2.A6.3A2.5A$238.A3.A.
A3.A.A3.A.A3.A.A5.A3.A3.A5.A3.A3.A.2A2.A7.A3.A.A5.A3.A3.A$238.A3.A.A
3.A.A3.A.A3.A.A5.A3.A3.A5.A3.A3.A.A.A.A7.A3.A.A5.A3.A3.A$238.4A2.A3.A
.4A2.A3.A.A5.5A3.A5.A3.A3.A.A2.2A7.4A2.A5.A3.A3.A$238.A5.A3.A.A5.A3.A
.A5.A3.A3.A5.A3.A3.A.A3.A7.A5.A5.A3.A3.A$238.A5.A3.A.A5.A3.A.A5.A3.A
3.A5.A3.A3.A.A3.A7.A5.A5.A3.A3.A$238.A6.3A2.A6.3A2.5A.A3.A3.A4.3A3.3A
2.A3.A7.A5.5A2.3A4.A8$.3A3.3A3.3A3.3A$A3.A.A3.A.A5.A$4.A.A2.2A.A5.A$
3.A2.A.A.A.4A2.4A11.A$2.A3.2A2.A.A3.A.A3.A10.A$.A4.A3.A.A3.A.A3.A10.A
$5A2.3A3.3A3.3A11.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A
$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.
A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$
33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A
$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.
A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$
33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A
$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.
A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$
33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A
$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.
A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$
33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A
$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.
A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$33.A$
33.A$33.A$33.A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$16.7A10.2A$19.A13.2A$18.A14.2A$17.A15.2A$16.
7A10.2A$33.2A$17.5A11.2A$16.A5.A10.2A$16.A5.A10.2A$16.A5.A10.2A$17.5A
11.2A$33.2A$33.2A$16.A5.A10.2A$16.7A10.2A$16.A5.A10.2A$33.2A$33.2A$
16.A16.2A$16.A16.2A$16.7A10.2A$16.A16.2A$16.A16.2A$33.2A$17.6A10.2A$
16.A2.A13.2A$16.A2.A13.2A$16.A2.A13.2A$17.6A10.2A$33.2A$22.A10.2A$22.
A10.2A$22.A10.2A$22.A10.2A$16.7A10.2A$33.2A$16.6A11.2A$22.A10.2A$22.A
10.2A$22.A10.2A$16.6A11.2A$33.2A$17.2A14.2A$16.A2.A13.2A$16.A2.A13.2A
$16.A2.A13.2A$16.7A10.2A$33.2A$17.5A11.2A$16.A5.A10.2A$16.A5.A10.2A$
16.A5.A10.2A$17.5A11.2A$33.2A$17.2A14.2A$16.A2.A13.2A$16.A2.A13.2A$
16.A2.A13.2A$16.7A10.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$
33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.2A$33.
A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$
33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A
$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.
A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A.A$33.A
.A$33.A2.A$33.A2.A$33.A2.A$33.A2.A$33.A2.A$33.A2.A$33.A2.A$33.A2.A$
21.A11.A2.A$20.2A11.A2.A$19.A.A11.A3.A$18.A2.A11.A3.A$18.5A10.501A$
21.A$21.A8$31.3A188.3A2.5A.A3.A.5A.4A3.3A2.5A2.3A3.3A2.A3.A10.A33.3A
4.A4.3A3.A182.5A2.3A3.3A$30.A3.A186.A3.A.A5.2A2.A.A5.A3.A.A3.A3.A5.A
3.A3.A.2A2.A9.A11.A21.A3.A2.A.A2.A3.A3.A181.A5.A3.A.A3.A$30.A2.2A186.
A5.A5.A.A.A.A5.A3.A.A3.A3.A5.A3.A3.A.A.A.A9.A4.4A.5A2.3A2.4A2.5A.A3.A
.A3.A.A2.2A3.A181.A5.A2.2A.A2.2A$30.A.A.A186.A2.2A.3A3.A2.2A.3A3.4A2.
5A3.A5.A3.A3.A.A2.2A9.A3.A7.A3.A3.A.A3.A8.3A8.A.A.A3.A182.3A2.A.A.A.A
.A.A$30.2A2.A186.A3.A.A5.A3.A.A5.A2.A2.A3.A3.A5.A3.A3.A.A3.A9.A4.3A4.
A3.5A.A3.A.5A.A3.A7.2A2.A3.A185.A.2A2.A.2A2.A$30.A3.A186.A3.A.A5.A3.A
.A5.A3.A.A3.A3.A5.A3.A3.A.A3.A9.A7.A3.A3.A5.A3.A7.A3.A7.A3.A3.A181.A
3.A.A3.A.A3.A$31.3A188.3A2.5A.A3.A.5A.A3.A.A3.A3.A4.3A3.3A2.A3.A10.A
2.4A5.2A2.4A.4A9.3A9.3A3.A183.3A3.3A3.3A$311.A$311.A!

The pattern is the same as its population plot for 500 generations.