IntegerLife (R1,I8,S2-3,B3,NM)

[lemon41625]

The thread for Mark Niemiec's rule, Integer Life, defined here:

I keep hearing mentions of INT rules, but I'm not sure what that term means, and can't find any references to it. Where is it defined?

It's just an abbreviation for isotropic non-totalistic.

Back in the 1990s, I played with a rule I called Integer Life.
1) Assume a Moore neighborhood, except every cell has an integer value
2) At every step, a cell's neighborhood is the arithmetic sum of the values of its 8 neighbors.
3) If a cell is dead (i.e. value=0), and has a neighborhood of exactly 3n, a new cell of value n is born there; otherwise it stays dead.
4) If a cell is alive (i.e. value=n, n!=0), and has exactly 2n or 3n neighbors, it remains alive; otherwise, it dies. (As it happens, the n!=0 condition is redundant).
5) There is some room for experimentation with regards to what happens with neighborhoods aren't exact multiples of n; I have found that "round down" works the best, i.e. survival in the range [2n...4n); some other more permissive combinations can make a rule that is explosive.

This rule behaves very similarly to life, with some minor exceptions. The exteriors of soups behave much as in Life, but the interiors work very differently; it's a bit like the interior of a star, with high temperatures causing creation of heavier elements. Most stable patterns and oscillators tend to be of one state, but a fair number of hybrids of multiple states (most commonly, 2 in the interior and 1 on the outside) occur

One interesting feature is scaling; any pattern containing cells of states 1, 2, 3, ... is isomorphic to a similar pattern containing cells of states n, 2n, 3n... for any integer n that is not a multiple of 3. One can even extend this from integers to rational numbers whose denominators are not multiples of 3.

Besides supporting most patterns from Life (notably excluding anything involving dead cells with 6 neighbors, as does HighLife, e.g. ship and dead spark coil), there is also a natural 2c/6 orthogonal spaceship:

Code: Select all

.111
1.2.
122.
1.2.
...1

I'll also add in the condition that if a cell hits the max state (in this case 8, it dies) because I don't feel like waiting for an eternal for a 255 state ruletree to compile.

Use the ruletree below with Golly.
Alternatively, Integer Rules (generalised to HROT) are supported by CAViewer and Caterer on the discord.

Anyway, here's the ruletree

Code: Select all

@RULE R1_I8_S2-3_B3_NM

@TREE
num_states=8
num_neighbors=8
num_nodes=180
1 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0
1 0 0 2 0 0 0 0 0
1 2 0 2 3 0 0 0 0
1 0 0 2 3 0 0 0 0
2 0 0 1 2 3 3 4 5
1 0 0 0 3 4 0 0 0
2 0 1 2 3 3 4 5 7
1 3 0 0 3 4 0 0 0
2 1 2 3 3 4 5 7 9
1 0 0 0 3 4 5 0 0
2 2 3 3 4 5 7 9 11
2 3 3 4 5 7 9 11 11
1 4 0 0 0 4 5 6 0
2 3 4 5 7 9 11 11 14
1 0 0 0 0 4 5 6 0
2 4 5 7 9 11 11 14 16
1 0 0 0 0 4 5 6 7
2 5 7 9 11 11 14 16 18
3 6 8 10 12 13 15 17 19
1 5 0 0 0 4 5 6 7
2 7 9 11 11 14 16 18 21
3 8 10 12 13 15 17 19 22
1 0 0 0 0 0 5 6 7
2 9 11 11 14 16 18 21 24
3 10 12 13 15 17 19 22 25
2 11 11 14 16 18 21 24 24
3 12 13 15 17 19 22 25 27
1 6 0 0 0 0 5 6 7
2 11 14 16 18 21 24 24 29
3 13 15 17 19 22 25 27 30
2 14 16 18 21 24 24 29 24
3 15 17 19 22 25 27 30 32
1 0 0 0 0 0 0 6 7
2 16 18 21 24 24 29 24 34
3 17 19 22 25 27 30 32 35
1 7 0 0 0 0 0 6 7
2 18 21 24 24 29 24 34 37
3 19 22 25 27 30 32 35 38
4 20 23 26 28 31 33 36 39
2 21 24 24 29 24 34 37 34
3 22 25 27 30 32 35 38 41
4 23 26 28 31 33 36 39 42
2 24 24 29 24 34 37 34 34
3 25 27 30 32 35 38 41 44
4 26 28 31 33 36 39 42 45
1 0 0 0 0 0 0 0 7
2 24 29 24 34 37 34 34 47
3 27 30 32 35 38 41 44 48
4 28 31 33 36 39 42 45 49
2 29 24 34 37 34 34 47 47
3 30 32 35 38 41 44 48 51
4 31 33 36 39 42 45 49 52
2 24 34 37 34 34 47 47 47
3 32 35 38 41 44 48 51 54
4 33 36 39 42 45 49 52 55
2 34 37 34 34 47 47 47 47
3 35 38 41 44 48 51 54 57
4 36 39 42 45 49 52 55 58
2 37 34 34 47 47 47 47 0
3 38 41 44 48 51 54 57 60
4 39 42 45 49 52 55 58 61
5 40 43 46 50 53 56 59 62
2 34 34 47 47 47 47 0 0
3 41 44 48 51 54 57 60 64
4 42 45 49 52 55 58 61 65
5 43 46 50 53 56 59 62 66
2 34 47 47 47 47 0 0 0
3 44 48 51 54 57 60 64 68
4 45 49 52 55 58 61 65 69
5 46 50 53 56 59 62 66 70
2 47 47 47 47 0 0 0 0
3 48 51 54 57 60 64 68 72
4 49 52 55 58 61 65 69 73
5 50 53 56 59 62 66 70 74
2 47 47 47 0 0 0 0 0
3 51 54 57 60 64 68 72 76
4 52 55 58 61 65 69 73 77
5 53 56 59 62 66 70 74 78
2 47 47 0 0 0 0 0 0
3 54 57 60 64 68 72 76 80
4 55 58 61 65 69 73 77 81
5 56 59 62 66 70 74 78 82
2 47 0 0 0 0 0 0 0
3 57 60 64 68 72 76 80 84
4 58 61 65 69 73 77 81 85
5 59 62 66 70 74 78 82 86
2 0 0 0 0 0 0 0 0
3 60 64 68 72 76 80 84 88
4 61 65 69 73 77 81 85 89
5 62 66 70 74 78 82 86 90
6 63 67 71 75 79 83 87 91
3 64 68 72 76 80 84 88 88
4 65 69 73 77 81 85 89 93
5 66 70 74 78 82 86 90 94
6 67 71 75 79 83 87 91 95
3 68 72 76 80 84 88 88 88
4 69 73 77 81 85 89 93 97
5 70 74 78 82 86 90 94 98
6 71 75 79 83 87 91 95 99
3 72 76 80 84 88 88 88 88
4 73 77 81 85 89 93 97 101
5 74 78 82 86 90 94 98 102
6 75 79 83 87 91 95 99 103
3 76 80 84 88 88 88 88 88
4 77 81 85 89 93 97 101 105
5 78 82 86 90 94 98 102 106
6 79 83 87 91 95 99 103 107
3 80 84 88 88 88 88 88 88
4 81 85 89 93 97 101 105 109
5 82 86 90 94 98 102 106 110
6 83 87 91 95 99 103 107 111
3 84 88 88 88 88 88 88 88
4 85 89 93 97 101 105 109 113
5 86 90 94 98 102 106 110 114
6 87 91 95 99 103 107 111 115
3 88 88 88 88 88 88 88 88
4 89 93 97 101 105 109 113 117
5 90 94 98 102 106 110 114 118
6 91 95 99 103 107 111 115 119
7 92 96 100 104 108 112 116 120
4 93 97 101 105 109 113 117 117
5 94 98 102 106 110 114 118 122
6 95 99 103 107 111 115 119 123
7 96 100 104 108 112 116 120 124
4 97 101 105 109 113 117 117 117
5 98 102 106 110 114 118 122 126
6 99 103 107 111 115 119 123 127
7 100 104 108 112 116 120 124 128
4 101 105 109 113 117 117 117 117
5 102 106 110 114 118 122 126 130
6 103 107 111 115 119 123 127 131
7 104 108 112 116 120 124 128 132
4 105 109 113 117 117 117 117 117
5 106 110 114 118 122 126 130 134
6 107 111 115 119 123 127 131 135
7 108 112 116 120 124 128 132 136
4 109 113 117 117 117 117 117 117
5 110 114 118 122 126 130 134 138
6 111 115 119 123 127 131 135 139
7 112 116 120 124 128 132 136 140
4 113 117 117 117 117 117 117 117
5 114 118 122 126 130 134 138 142
6 115 119 123 127 131 135 139 143
7 116 120 124 128 132 136 140 144
4 117 117 117 117 117 117 117 117
5 118 122 126 130 134 138 142 146
6 119 123 127 131 135 139 143 147
7 120 124 128 132 136 140 144 148
8 121 125 129 133 137 141 145 149
5 122 126 130 134 138 142 146 146
6 123 127 131 135 139 143 147 151
7 124 128 132 136 140 144 148 152
8 125 129 133 137 141 145 149 153
5 126 130 134 138 142 146 146 146
6 127 131 135 139 143 147 151 155
7 128 132 136 140 144 148 152 156
8 129 133 137 141 145 149 153 157
5 130 134 138 142 146 146 146 146
6 131 135 139 143 147 151 155 159
7 132 136 140 144 148 152 156 160
8 133 137 141 145 149 153 157 161
5 134 138 142 146 146 146 146 146
6 135 139 143 147 151 155 159 163
7 136 140 144 148 152 156 160 164
8 137 141 145 149 153 157 161 165
5 138 142 146 146 146 146 146 146
6 139 143 147 151 155 159 163 167
7 140 144 148 152 156 160 164 168
8 141 145 149 153 157 161 165 169
5 142 146 146 146 146 146 146 146
6 143 147 151 155 159 163 167 171
7 144 148 152 156 160 164 168 172
8 145 149 153 157 161 165 169 173
5 146 146 146 146 146 146 146 146
6 147 151 155 159 163 167 171 175
7 148 152 156 160 164 168 172 176
8 149 153 157 161 165 169 173 177
9 150 154 158 162 166 170 174 178

And the catagolue census: https://catagolue.appspot.com/census/x1 ... 3_b3_nm/C1

==========================
Stuff I've found

P58

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
oobobobobbbooooo$
obobobbobobbbbbb$
boobobbooobbbbob$
bboboboooobobbob$
ooobbbbobobobbbb$
boooboooobbbbobb$
bobbbbbooooobboo$
oobbboobboobbooo$
boobbboboooooooo$
boobobboooobbbbo$
oobooboboobobbbo$
boboboobbobooobb$
bboooboboooobbob$
oobbooooboobooob$
bobooboboobboobo$
obbooboboobbbbbo!

P5

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
bbbbboooooobbobb$
ooobbbooobbooobo$
ooooboooboobobbb$
bbbbobbobbooobob$
booobbbbobbooobb$
booobbbbbbobbobb$
obooobobobobbooo$
bobooobbbobbboob$
boooooobbobboboo$
bbobobbobbbbobbo$
obbboboboooboobb$
oboobbooooboobob$
boboobboobobboob$
bbbbobbboooboobb$
boooobbboboobbob$
oooboboooboobbbo!

Linear Growth!

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
bbboobobbboooobo$
oobobbbbbboooboo$
ooboobbbooobooob$
bbobobbooobboobb$
bboboobbobooobbo$
obobbboooooboboo$
boobooobooboobob$
booobooobobobobb$
oobbbboobobobbob$
bobobooboobobbbb$
oobbbooobboooobb$
bbooobobbooobobo$
bbboobbboobbboob$
ooooobobbbbobooo$
bbbobooobbbbooob$
booobobobobooboo!

3c/11o

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
bbobobboobboooob$
bbbboooobbboboob$
oooobbobbooobboo$
obbbbobobbobobob$
bboboobbbbbbbooo$
oobobbbbbbbboooo$
bbbobooobobbbobo$
ooobbobobboobbbb$
bbbbboobobobobob$
booobbbboobooboo$
bbobobbboobboobb$
ooobbobooooboboo$
obbbbbbobooooooo$
obbobbbboobbbbbo$
bbbbbboooobbbbob$
obobbobbbbbobbbb!

P8

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
oooooooboobooobb$
obooobobobobbooo$
obooooooobobooob$
bobooobbooboobbo$
boboobbobooooobb$
obooobbbobobboob$
oboooooobbobobbo$
oobbobbbooboobbb$
bbbbobbobboooboo$
oobbbbbboooooooo$
obbobooboooboobo$
obboobobbobobbbb$
obobbbobbobobboo$
booobbooobbooobo$
bbobbboobobboobb$
boobbobooobbbboo!

c/3o

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
obooboooooobboob$
bboboobobbbbbbob$
ooooobooobbooboo$
bboobobbbbbobooo$
obbbobobobobbbbo$
bbbbobbooobobobb$
ooobbbbooboobooo$
bobboboooobooobo$
bbbbooobbooboboo$
bboobooboboooobo$
bbbbobobbbbobboo$
oobbboooboooobbo$
obboboooobobbbbb$
oobbbbbbbboobbbb$
bboooobboobooboo$
obobbboobboooobo!

P4

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
bobboobobobobbbo$
ooboobbooobobobo$
oooboooobobbbbbo$
obbobbbobbbbbbbb$
ooboobbbboboobob$
bbobbbbboboboobb$
bobbbbbboboboobb$
ooooooobobboobbb$
bboooobooooboobb$
bboboobbbboobboo$
boooobboobooobob$
oooooooooooobobo$
oboboooobobooboo$
booobbobbboboobo$
ooobobobbbobbbbo$
bbbbbobbbboobobb!

P44 (Gun Pls)

Code: Select all

x = 16, y = 16, rule = R1_I8_S2-3_B3_NM
bbobbobobooooobb$
bbboooooboobooob$
oooobbbbbboobboo$
obooboobbobbbbob$
bobbbboobbbbbbob$
boobobbbobbboooo$
boooobbbboobboob$
ooobbobobbobooob$
bboobobobbobbboo$
booobbobbbbooboo$
ooboobbbooobboob$
oobobbobobbobbbo$
obboobbbbbbbobob$
bbooobbooboboooo$
oobobobbooobbooo$
oboooooboobobobo!

[Layz Boi]

~gun

Code: Select all

x = 24, y = 21, rule = R1_I8_S2-3_B3_NM
6.AB.A$7.B.C$6.A3B$5.2A2.B.A$5.2A$6.2A2$12.A$11.A11.A$11.3A8.2A$19.A.
3A$20.B.2A$19.3B.A$23.A$19.4A$21.2A$22.A2$.A$A$3A!

Edit: period doubling and tripping:

Code: Select all

x = 42, y = 152, rule = R1_I8_S2-3_B3_NM
A10$17.A$17.A$14.A2.B$15.B$16.B.3A$14.AB2.A.A2$22.A$21.A$21.3A3$30.2A
$29.A.A$25.A.AB.B$26.2AB2.A$27.A3.A2$11.A$10.A$10.3A18$8.2A$8.A.A$8.A
2$23.A2.A$23.B.B$24.B$26.B2A$23.2A$24.A$23.2A$19.2A$19.A.A$19.A2$14.A
$13.A$12.3A$13.2B$15.A$14.B.A$12.2A.2A27$17.A2.A2$14.A2.2B.BA$13.A2.B
.B.2A$14.A2.D$14.A.CD$16.B2.A$16.A2.A$16.3A5$19.A.A$19.2A5.A.A$20.A4.
A.2B$27.BCA$24.A.CB3.A$23.A3.2B2.A$23.A3.4A$24.4A4$8.A.A$8.2A$9.A6$8.
A$8.A$8.A3$10.3A$10.A9.2A$11.A7.A.A$18.3A$18.2AB.C.BA$19.A5.B$21.BDC$
19.A2.B2.A$20.A.A$21.A$16.2A$16.2A$18.A$12.A2.C.B.A$11.2AB.3DB$12.A.B
C2.B$13.A2.A2$41.A!

[FWKnightship]

P2,P3,P7,P9:

Code: Select all

x = 51, y = 48, rule = R1_I8_S2-3_B3_NM
2E4.2E9.A.A$.F4.F11.B$.GF2.FG12.B$2.D2.D12.A.A10.4C11.F2.F$31.E2.E10.
F.2G.F$28.2A.E2GE.2A8.G2.G$28.2A.D2.D.2A8.G2.G$45.F.2G.F$19.A26.F2.F$
2B18.B$B.B3.2E9.A3.A$2.B3.F11.B$B.B2.FG12.A$2B3.D4$20.A$17.A.B$18.B.A
$18.B.A$17.A.B$20.A5$17.A2.A2$15.A.B2.B.A3$15.A.B2.B.A2$17.A2.A6$18.
2D$17.DE5$17.DE$18.2D!

[Jackk]

Cute 2c/6 orthogonal:

Code: Select all

x = 5, y = 4, rule = R1_I8_S2-3_B3_NM
.3A$A.B$A3B$A3.A!

EDIT: Heisenburg reaction with a glider

Code: Select all

x = 11, y = 7, rule = R1_I8_S2-3_B3_NM
7.3A$6.A.B$6.A3B$6.A3.A$A.A$.2A$.A!

[mniemiec]

I'll also add in the condition that if a cell hits the max state (in this case 8, it dies) because I don't feel like waiting for an eternal for a 255 state ruletree to compile.

I'm a bit more of a purist; in my own implentation, I supported 255 living states, and the program automatically halts if it encounters any births that would creates states higher than this.
For example, the following two do so at generations 224 and 1407 respectively. (Note that these won't run correctly in the 8-state version).

Code: Select all

x = 9, y = 13, rule = R1_I8_S2-3_B3_NM
5bobo$5boo$6bo$$booboo$obobobo$bo5bo$8bo$7boo$$7boo$6bobo$7bo!

Code: Select all

x = 13, y = 17, rule = R1_I8_S2-3_B3_NM
bboo$ooboo$4o$boo9$9b3o$9bobbo$9bo$9bo$10bobo!

A better approach might be to have the rule be a subset of Integer Life, with all births equal to or above the number of supported states (e.g. 8 ) going to an extra disallowed state; that state would infect all adjacent cells (i.e. if any parents are disallowed, the child also becomes disallowed), so any pattern containing a disallowed cell would soon fill the universe with disallowed cells. Any patterns that don't do this (which will be the vast majority of them) would be guaranteed to work correctly in true Integer Life, or any other subset with the same or more supported states.

One thing that I've found is that patterns in this rule behave very much like they do in Life around the exteriors, but interiors that have large neighborhoods more closely resemble exploding rules like B2/S2 or B34/S34. The interiors don't fragment from over-population as they do in life; rather, they just fulminate randomly until the interiors are exposed to the cooling effect of empty space. If such regions are sufficiently large, the state numbers in the interiors can grow rapidly.

Other than the P58, all of the other discoveries posted in this thread appear to be new.

Most of the hybrid state patterns I had found in the past (mostly from running glider collisions) were still-lifes and pseudo-still-lifes, which are interesting from a synthesis perspective, but generally boring otherwise. Here are a few others from my collection:

The 2c/6 orthogonal glider, 5 P2s, 2 P3s, P4, P5, and the P58. All the dates on my files are from around 2012-12, when I had attempted a more thorough exploration of this rule (which I had first investigated around 1993).

Code: Select all

x = 116, y = 84, rule = R1_I8_S2-3_B3_NM
A.A.A3.A.A.A18.AB.A$32.BB$A7.A$30.A.B.A$A.A.A3.A.A.A20.A$32.A$4.A7.A$$
A.A.A3.A.A.A7$A.A.A3.A.A.A17.DD19.B19.BB17.AA18.A$30.D..A16.B.B17.B.C
19.A18.BB$A3.A7.A20.A17.BB.A15.BC18.AB19.BB$31.AA20.B37.A21.BB$A.A.A3.
A.A.A39.A60.BB$115.A$A7.A$$A7.A.A.A7$A.A.A3.A.A.A19.A17.A$31.B19.B.A$A
3.A7.A17.A3.A15.A.B$33.B19.A$A.A.A3.A.A.A19.A$$A11.A$$A7.A.A.A7$A.A.A
3.A3.A17.A$31.B.A$A3.A3.A3.A17.A.B$33.A$A.A.A3.A.A.A19.A$$A11.A$$A11.A
7$A.A.A3.A.A.A21.D$33.D.D$A3.A3.A25.D$34.B$A.A.A3.A.A.A20.A.A$30.3A3.
3A$A11.A$$A7.A.A.A7$A.A.A3.A.A.A3.A.A.A12.CC$30.A6.A$A3.A3.A7.A3.A$31.
AB..BA$A.A.A3.A.A.A3.A.A.A$$A11.A3.A3.A$$A7.A.A.A3.A.A.A!

Most of these can be synthesized from gliders*.

Code: Select all

x = 165, y = 85, rule = R1_I8_S2-3_B3_NM
4.AA19.A19.A$3.AA19.A.A17.A.A$5.A17.A..A16.A..A$3A21.AA18.AA$..A$.A40.
AA$41.A.A$43.A$62.AB.A$63.BB$$61.A.B.A$64.A$63.A5$141.A.A$.A39.A99.AA$
..B.A34.AA101.A$..BBA35.AA$..B.A32.A22.BB18.BB18.BB4.A13.BB18.BB$.3A
33.AA20.B..B16.B..B16.B..B3.A.A10.B..B..AA12.B..B..AA$21.BB13.A.A..BB
16.B..B16.B..B16.B..B3.AA11.B..B.A.A8.AA..B..B.A.A$A..A17.B.B17.B.B16.
BB3.A.A12.3B.A15.3B.A15.3B..A10.AA..3B..A17.BB$.B..A17.B19.B22.AA16.B
19.B31.A26.B.C$BB.B.A60.A15.A19.A18.A19.A20.BC$A61.AA56.A.A17.A.A$3.A
59.AA34.3A18.AA18.AA$62.A38.A$100.A$$25.AA$25.AA$$27.AA$27.A.A$27.A8$
104.A3.A$102.A.A3.A.A$103.AA3.AA$$5.3A32.A.A20.A41.A.A$6.B.A32.AA19.B
20.A3.A18.B$5.3BA9.BB21.A3.A15.A3.A17.A3B19.D19.D19.D$4.A3.A11.B23.AA
18.B18.A.B19.D.D17.D.D17.D.D$18.BD24.A.A16.A20.3A19.D19.D19.D$AA17.B
86.B19.B19.B$.AA77.A.BA21.A.A17.A.A17.A.A$A80.BB38.3A5.3A10.3A3.3A$
123.A5.A$80.A.B.A37.A7.A$81.A$82.A9$.A$..A$3A$4.A$3.A$3.3A17.AA59.CC$
23.AA17.BB18.BB17.A6.A$28.3A11.B19.B$23.AA..A.B15.B19.B16.AB..BA$5.AA
16.A.A.A3B13.BB18.BB$4.AA18.A..A3.A16.B20.A$6.A41.B19.AA$48.B3.AA14.A.
A$52.A.A$52.A!

Unfortunately, a couple of the syntheses created intermediate steps with state 8, so they won't work with this version of the rule:

Code: Select all

x = 181, y = 67, rule = R1_I8_S2-3_B3_NM
106.A$105.A$105.3A$102.AA33.A$102.AA18.A14.A.A$121.A15.AA22.A$121.3A
32.B4.A.A$.3A40.A.A14.A..A.A66.3A..D18.DD..AA15.AA$..B.A40.B13.A.A3.B
32.HH18.HH15.A.D.D17.D.D17.A$.3BA15.A3.A20.B..A11.AA3.B..A10.AA17.H.H
17.H.H13.A3.D19.D18.A..D$A3.A16.A.A.A14.A.A3.BB15.A.3B11.A.A17.H19.H
59.DD$6.AA11.3A..A.A14.AA5.A15.B3.A11.A.A32.AA38.3A$7.AA16.A15.A23.A
15.AA31.A.A40.A$6.A37.AA37.AA31.A39.A$24.AA17.AA21.3A14.A.A$24.A.A18.A
20.A12.3A..A.A$24.A42.A13.A3.AA$80.A30$4.A119.A$.A.B86.A.A32.A$.ABB46.
A40.AA14.A15.3A$.A.B44.A.A40.A16.A4.A13.AA..A19.A$..3A44.AA55.3A..DC
14.AA3.BB18.BB$33.BB18.BB17.D17.D.D17.D.D19.BB18.BB$..A..A26.B.B17.B.B
12.A3.D.D17.H19.H4.A17.BB18.BB$.A..B28.B19.B14.AA.D..D16.H..D..AA12.H
..DC18.BB18.BB$A.B.BB61.AA3.DD18.HH..AA14.HH.D20.A19.A$5.A49.3A36.D3.A
15.D$..A52.A16.A$56.A14.AA42.AA18.AA$71.A.A41.A.A17.AA$115.A$29.AA106.
AA$29.AA106.A.A$137.A$27.AA$26.A.A$28.A!

*The syntheses in the first list don't all work correctly for the same reason;
e.g. the first step on line two makes a cell of state 9 in step 12, so everything after that diverges in this implementation. Also, on the bottom line, the collision of the c/3 into the block-on-boat normally makes a 2-beacon and a 2-blinker, but at generation 16, one of the cells is of state 10.

[Layz Boi]

Yellow is pretty stable, and can be contained with orange.

Code: Select all

x = 89, y = 114, rule = R1_I8_S2-3_B3_NM
9.EFE69.2G$10.G32.2E5.2E12.2G16.G$10.G31.E.F.FGF.F.E12.G2.2G9.G2.F2.2G
$8.2G.E15.E14.EFD.F.F.DFE9.G2.F2.G10.2GF3.G$7.G4.E2.E9.2GF18.BDB13.2G
FDB.F2.G13.F2.G$7.G5.2GF9.G2.F14.2FB3.B2F13.B.BDF2G14.F2G$5.2G.C3.G2.
E12.G14.G.D3.D.G12.B3.B8.2GF$4.G2.C.C2.G15.2GF12.2FB3.B2F9.2GFDB.B9.G
2.F$.E2.G3.C.2G19.FE13.BDB12.G2.F.BDF2G9.G3.F2G$.F2G5.G21.G10.EFD.F.F
.DFE11.G2.F2.G8.2G2.F2.G$.E2.E4.G20.2G10.E.F.FGF.F.E10.2G2.G15.G$5.E.
2G34.2E5.2E15.2G14.2G$6.G$6.G$5.EFE7$75.D$62.B10.DF.FD$44.DF.G.FD22.F
.D.F$44.F.GFG.F11.D9.D.D.D.D$45.F3.F9.B.D.D.B7.F.D.F$62.D10.DF.FD$75.
D$45.F3.F12.B$44.F.GFG.F$44.DF.G.FD15$4.D2.D$4.D2FD$23.D2.E2.E2.E2.E2.
E2.E2.E2.D$5.2F16.D2FE2FE2FE2FE2FE2FE2FE2FD$2D2.F2.F2.2D9.2D25.2D$.F.
F.2B.F.F11.F25.F$.F.F.2B.F.F11.F9.3G13.F$2D2.F2.F2.2D9.2E9.G.G13.2E$5.
2F15.F9.3G13.F17.D2.E2.E2.E2.E2.D$22.F25.F17.D2FE2FE2FE2FE2FD$4.D2FD13.
2D25.2D$4.D2.D15.D2FE2FE2FE2FE2FE2FE2FE2FD$23.D2.E2.E2.E2.E2.E2.E2.E2.
D14.2D6.3G11.2D$63.F6.G.G11.F$63.F6.3G11.F$62.2D20.2D3$22.D2.D.D2.D$22.
D2FD.D2FD$43.D2.E2.E2.D9.2D20.2D$43.D2FE2FE2FD10.F6.3G11.F$23.G5.G11.
2D10.2D8.F6.G.G11.F$22.3G3.3G11.F10.F8.2D6.3G11.2D$21.2G.2G.2G.2G10.F
5.3G2.F$22.3G3.3G10.2E5.G.G2.2E$23.G5.G12.F5.3G2.F12.D2FE2FE2FE2FE2FD
$42.F10.F12.D2.E2.E2.E2.E2.D$41.2D10.2D$22.D2FD.D2FD12.D2FE2FE2FD$22.
D2.D.D2.D12.D2.E2.E2.D16$29.D2.E2.D2.D2.E2.D2.D2.E2.D2.D2.E2.D2.D2.E2.
D2.D2.E2.D$29.D2FE2FD2.D2FE2FD2.D2FE2FD2.D2FE2FD2.D2FE2FD2.D2FE2FD6$14.
G$14.6G$13.G2.2G.G11.G55.2D$11.G.G9.2G6.2G54.F$11.G2.G.3G3.3G8.G53.F$
11.G.G9.2G6.2G54.2D$13.G2.2G.G11.G$14.6G$14.G6$29.D2FE2FD2.D2FE2FD2.D
2FE2FD2.D2FE2FD2.D2FE2FD2.D2FE2FD$29.D2.E2.D2.D2.E2.D2.D2.E2.D2.D2.E2.
D2.D2.E2.D2.D2.E2.D!

[LaundryPizza03]

Yellow (state 7) behaves exactly like standard Life. IntegerLife actually appears to be more stable than standard Life, since the extra states make it more similar to Highlife and Flock and eliminates many of Life's methuselahs.

Code: Select all

x = 3, y = 3, rule = R1_I8_S2-3_B3_NM
.2G$2G$.G!

Code: Select all

x = 3, y = 3, rule = R1_I8_S2-3_B3_NM
.2A$2A$.A!

There are some exceptions, however. For example, the lifespan of the teardrop increases from 20 generations to 75:

Code: Select all

x = 4, y = 4, rule = R1_I8_S2-3_B3_NM
3A$A2.A$A2.A$.2A!

[yujh]

Yellow (state 7) behaves exactly like standard Life. IntegerLife actually appears to be more stable than standard Life, since the extra states make it more similar to Highlife and Flock and eliminates many of Life's methuselahs.

Code: Select all

x = 3, y = 3, rule = R1_I8_S2-3_B3_NM
.2G$2G$.G!

State 5 seems to be life as well

Code: Select all

x = 3, y = 3, rule = R1_I8_S2-3_B3_NM
.2E$2E$.E!

4 too

Code: Select all

x = 3, y = 3, rule = R1_I8_S2-3_B3_NM
.2D$2D$.D!

[mniemiec]

Yellow (state 7) behaves exactly like standard Life. IntegerLife actually appears to be more stable than standard Life, since the extra states make it more similar to Highlife and Flock and eliminates many of Life's methuselahs. ...

State 5 seems to be life as well ... 4 too ...

Actually, the way I designed the original rule, any pattern consisting of states 1, 2, 3, ... is isomorphic with a similar pattern consisting of states n, 2n, 3n, ... for any integer n that is not a multiple of 3. This finite implementation of the rule causes all states 8+ to change to 0, which causes some anomalous horizon effects that may vary slightly between one base state and another, but otherwise, small patterns (i.e. ones that don't have large interiors) should evolve approximately the same as they do in Life.

[FWKnightship]

P4,P7:

Code: Select all

x = 18, y = 7, rule = R1_I8_S2-3_B3_NM
13.B$.A9.B.F$B.A9.3F$.B$B.A11.3F$.A13.F.B$15.B!