A Simple Rule

bprentice · Post by **bprentice** » August 6th, 2017, 9:35 pm

The rule tree:

@RULE BWP1

@TREE

num_states=4
num_neighbors=8
num_nodes=280
1 0 2 0 3
2 0 0 0 0
3 1 1 1 1
4 2 2 2 2
5 3 3 3 3
1 1 2 0 3
2 0 5 0 5
2 5 0 0 0
3 6 7 1 7
4 8 8 8 8
5 9 9 9 9
2 0 5 0 0
3 11 7 1 1
4 12 12 12 12
5 13 13 13 13
6 4 10 4 14
3 6 6 6 6
3 7 7 7 7
4 16 17 2 17
5 18 18 18 18
2 5 5 0 5
3 6 20 6 20
3 20 7 7 7
4 21 22 8 22
5 23 23 23 23
3 6 20 6 6
2 5 5 0 0
3 26 7 7 7
4 25 27 12 27
5 28 28 28 28
6 19 24 19 29
3 11 11 11 11
4 31 17 2 2
5 32 32 32 32
3 6 26 11 26
4 34 22 8 8
5 35 35 35 35
3 11 26 11 11
4 37 27 12 12
5 38 38 38 38
6 33 36 33 39
7 15 30 15 40
2 5 5 5 5
3 1 42 1 42
4 43 43 43 43
3 42 1 1 1
4 45 45 45 45
5 44 46 3 46
3 6 42 1 42
4 48 48 48 48
3 42 7 1 7
4 50 50 50 50
5 49 51 9 51
3 11 42 1 42
4 53 53 53 53
3 42 7 1 1
4 55 55 55 55
5 54 56 13 56
6 47 52 47 57
3 6 42 6 42
3 7 42 7 42
4 59 60 43 60
3 42 6 6 6
3 42 7 7 7
4 62 63 45 63
5 61 64 18 64
3 20 42 7 42
4 59 66 48 66
3 42 20 6 20
4 68 63 50 63
5 67 69 23 69
3 26 42 7 42
4 59 71 53 71
3 42 20 6 6
4 73 63 55 63
5 72 74 28 74
6 65 70 65 75
3 11 42 11 42
4 77 60 43 43
3 42 11 11 11
4 79 63 45 45
5 78 80 32 80
3 6 42 11 42
4 82 66 48 48
3 42 26 11 26
4 84 63 50 50
5 83 85 35 85
4 77 71 53 53
3 42 26 11 11
4 88 63 55 55
5 87 89 38 89
6 81 86 81 90
7 58 76 58 91
3 1 42 1 1
4 93 93 93 93
5 94 46 3 3
3 6 42 1 7
4 96 96 96 96
5 97 51 9 9
3 11 42 1 1
4 99 99 99 99
5 100 56 13 13
6 95 98 95 101
3 6 42 6 6
3 7 42 7 7
4 103 104 93 104
5 105 64 18 18
3 6 42 6 20
3 20 42 7 7
4 107 108 96 108
5 109 69 23 23
3 26 42 7 7
4 103 111 99 111
5 112 74 28 28
6 106 110 106 113
3 11 42 11 11
4 115 104 93 93
5 116 80 32 32
3 6 42 11 26
4 118 108 96 96
5 119 85 35 35
4 115 111 99 99
5 121 89 38 38
6 117 120 117 122
7 102 114 102 123
8 41 92 41 124
3 42 42 42 42
4 2 126 2 126
4 126 2 2 2
5 127 128 3 128
4 8 126 8 126
4 126 8 8 8
5 130 131 9 131
4 12 126 12 126
4 126 12 12 12
5 133 134 13 134
6 129 132 129 135
4 16 126 2 126
4 126 17 2 17
5 137 138 18 138
4 21 126 8 126
4 126 22 8 22
5 140 141 23 141
4 25 126 12 126
4 126 27 12 27
5 143 144 28 144
6 139 142 139 145
4 31 126 2 126
4 126 17 2 2
5 147 148 32 148
4 34 126 8 126
4 126 22 8 8
5 150 151 35 151
4 37 126 12 126
4 126 27 12 12
5 153 154 38 154
6 149 152 149 155
7 136 146 136 156
4 43 126 43 126
4 126 45 45 45
5 158 159 3 159
4 48 126 48 126
4 126 50 50 50
5 161 162 9 162
4 53 126 53 126
4 126 55 55 55
5 164 165 13 165
6 160 163 160 166
4 59 126 43 126
4 126 63 45 63
5 168 169 18 169
4 59 126 48 126
4 126 63 50 63
5 171 172 23 172
4 59 126 53 126
4 126 63 55 63
5 174 175 28 175
6 170 173 170 176
4 77 126 43 126
4 126 63 45 45
5 178 179 32 179
4 82 126 48 126
4 126 63 50 50
5 181 182 35 182
4 77 126 53 126
4 126 63 55 55
5 184 185 38 185
6 180 183 180 186
7 167 177 167 187
4 93 126 93 126
5 189 159 3 128
4 96 126 96 126
5 191 162 9 131
4 99 126 99 126
5 193 165 13 134
6 190 192 190 194
4 103 126 93 126
5 196 169 18 138
4 107 126 96 126
5 198 172 23 141
4 103 126 99 126
5 200 175 28 144
6 197 199 197 201
4 115 126 93 126
5 203 179 32 148
4 118 126 96 126
5 205 182 35 151
4 115 126 99 126
5 207 185 38 154
6 204 206 204 208
7 195 202 195 209
8 157 188 157 210
4 2 126 2 2
5 212 128 3 3
4 8 126 8 8
5 214 131 9 9
4 12 126 12 12
5 216 134 13 13
6 213 215 213 217
4 16 126 2 17
5 219 138 18 18
4 21 126 8 22
5 221 141 23 23
4 25 126 12 27
5 223 144 28 28
6 220 222 220 224
4 31 126 2 2
5 226 148 32 32
4 34 126 8 8
5 228 151 35 35
4 37 126 12 12
5 230 154 38 38
6 227 229 227 231
7 218 225 218 232
4 43 126 43 43
5 234 159 3 46
4 48 126 48 48
5 236 162 9 51
4 53 126 53 53
5 238 165 13 56
6 235 237 235 239
4 59 126 43 60
5 241 169 18 64
4 59 126 48 66
5 243 172 23 69
4 59 126 53 71
5 245 175 28 74
6 242 244 242 246
4 77 126 43 43
5 248 179 32 80
4 82 126 48 48
5 250 182 35 85
4 77 126 53 53
5 252 185 38 89
6 249 251 249 253
7 240 247 240 254
4 93 126 93 93
5 256 159 3 3
4 96 126 96 96
5 258 162 9 9
4 99 126 99 99
5 260 165 13 13
6 257 259 257 261
4 103 126 93 104
5 263 169 18 18
4 107 126 96 108
5 265 172 23 23
4 103 126 99 111
5 267 175 28 28
6 264 266 264 268
4 115 126 93 93
5 270 179 32 32
4 118 126 96 96
5 272 182 35 35
4 115 126 99 99
5 274 185 38 38
6 271 273 271 275
7 262 269 262 276
8 233 255 233 277
9 125 211 125 278

Example guns:

Code: Select all

x = 13, y = 13, rule = BWP1
C10.2C$C3$11.2A$11.2B6$12.C$2C10.C!

Code: Select all

x = 17, y = 17, rule = BWP1
13.2C2$C.C10.2C$C.C3$13.2A$13.2B6$14.C.C$2.2C10.C.C2$2.2C!

Code: Select all

x = 19, y = 19, rule = BWP1
2.4C2$18.C$3.C10.2C2.C$3.C14.C$18.C3$14.2A$14.2B4$C$C14.C$C2.2C10.C
$C2$13.4C!

Code: Select all

x = 18, y = 19, rule = BWP1
2.4C$14.2C2$.C.C10.2C$.C.C4$14.2A$14.2B4$C$C14.C.C$C2.2C10.C.C$C$3.
2C$13.4C!

Code: Select all

x = 19, y = 19, rule = BWP1
2.4C$.C10.6C$.C16.C$.C.C10.2C2.C$.C.C14.C$.C16.C$.C2$14.2A$14.2B4$C
$C14.C$C2.2C10.C$C$.6C$13.4C!

Code: Select all

x = 19, y = 20, rule = BWP1
2.4C$.C10.6C$.C16.C$.C.C10.2C2.C$.C.C14.C$.C16.C$.C2$14.2A$14.2B4$C
$C14.C.C$C2.2C10.C.C$C$.6C6.4C2$15.4C!

Code: Select all

x = 55, y = 29, rule = BWP1
2.6C$4.2A$C3.2B$C5.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA$CAB2.
CBA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA$CAB2.2A7.BA2.BA2.BA2.BA
2.BA2.BA2.BA2.BA2.BA$C10.2A13.BA2.BA2.BA2.BA2.BA2.BA$C10.2B10.2A13.
BA2.BA2.BA$5.2B16.2B10.2A$5.2A28.2B10.2A$3.6C2.2A34.2B$11.2B10.2A$23.
2B10.2A$35.2B10.2A$11.2A34.2B$11.2B10.2A$23.2B10.2A$18.C16.2B10.2A$
8.C2.2A5.C11.C16.2B$8.C2.2BA2.BAC.C2.2A5.C11.C$8.CAB.CA2.BAC.C2.2BA
2.BAC.C2.2A5.C11.C$8.CAB7.C.CAB.CA2.BAC.C2.2BA2.BAC.C2.2A5.C$8.C9.C
.CAB7.C.CAB.CA2.BAC.C2.2BA2.BAC$8.C3.2B6.C9.C.CAB7.C.CAB.CA2.BAC$12.
2A6.C3.2B6.C9.C.CAB7.C$10.6C8.2A6.C3.2B6.C9.C$22.6C8.2A6.C3.2B$34.6C
8.2A$46.6C!

Code: Select all

x = 53, y = 26, rule = BWP1
52.C$48.C2.2C$44.C2.2C$40.C2.2C$36.C2.2C$32.C2.2C$28.C2.2C$2.4C18.C
2.2C$14.2C4.C2.2C$19.2C$.C.C10.2C$.C.C$19.2C$20.C2.2C$24.C2.2C$14.2A
12.C2.2C$14.2B16.C2.2C$36.C2.2C$40.C2.2C$44.C2.2C$C47.C2.2C$C14.C.C
34.C$C2.2C10.C.C$C$3.2C$13.4C!

Brian Prentice

bprentice · Post by **bprentice** » August 7th, 2017, 2:38 am

Oscillators with periods 3, 4, 5, 11, 12 and 13:

Code: Select all

x = 44, y = 62, rule = BWP1
2.4C$7.2C$3.2A6.C$.C.CB.A2CA.C$.C.CB.A2BA33.C$C2.2A38.C$C6.2A.BA.BA
.BA.BA.BA.BA.BA.BA.BA.BA.BA.C$C.A2BA.BC.BA.BA.BA.BA.BA.BA.BA.BA.BA.
BA.BA.C$C.A2BA.BC.BA.BA.BA.BA.BA.BA.BA.BA.BA.BA.BA.C$C6.2A.BA.BA.BA
.BA.BA.BA.BA.BA.BA.BA.BA.C$C2.2A38.C$.C.CB.A2BA33.C$.C.CB.A2CA.C$3.
2A6.C$7.2C$2.4C5$2.4C$8.2C$12.C$.C.CAB2.2C2.C$.C.CAB2.2A$8.2B33.C$C
42.C$C2.2B6.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.C$C2.2A2.BAC.BA2.BA2.BA
2.BA2.BA2.BA2.BA2.BA2.C$C2.2A2.BAC.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.
C$C2.2B6.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.C$C42.C$8.2B33.C$.C.CAB2.2A
$.C.CAB2.2C2.C$12.C$8.2C$2.4C5$2.4C$9.2C$13.C$.C.CAB3.2C2.C$.C.CAB3.
2A$9.2B$43.C$C42.C$C2.2B8.BA3.BA3.BA3.BA3.BA3.BA3.C$C2.2A3.BAC2.BA3.
BA3.BA3.BA3.BA3.BA3.C$C2.2A3.BAC2.BA3.BA3.BA3.BA3.BA3.BA3.C$C2.2B8.
BA3.BA3.BA3.BA3.BA3.BA3.C$C42.C$43.C$9.2B$.C.CAB3.2A$.C.CAB3.2C2.C$
13.C$9.2C$2.4C!

Code: Select all

x = 155, y = 36, rule = BWP1
110.4C$54.4C67.2C$.4C63.2C59.C$14.2C56.C36.C.CAB11.2C2.C$18.C34.C.C
AB10.2C2.C36.C.CAB11.2A2.C$C.CAB9.2C2.C34.C.CAB10.2A2.C52.2B2.C$C.C
AB9.2A2.C49.2B2.C$14.2B2.C7$39.C55.C58.C$C38.C13.C41.C13.C44.C$C.2B
20.BA9.BA2.C13.C.2B22.BA10.BA2.C13.C.2B24.BA11.BA2.C$C.2A9.BAC8.BA9.
BA2.C13.C.2A10.BAC9.BA10.BA2.C13.C.2A11.BAC10.BA11.BA2.C$C.2A9.BAC8.
BA9.BA2.C13.C.2A10.BAC9.BA10.BA2.C13.C.2A11.BAC10.BA11.BA2.C$C.2B20.
BA9.BA2.C13.C.2B22.BA10.BA2.C13.C.2B24.BA11.BA2.C$C38.C13.C41.C13.C
44.C$39.C55.C58.C7$14.2B2.C$C.CAB9.2A2.C49.2B2.C$C.CAB9.2C2.C34.C.C
AB10.2A2.C52.2B2.C$18.C34.C.CAB10.2C2.C36.C.CAB11.2A2.C$14.2C56.C36.
C.CAB11.2C2.C$.4C63.2C59.C$54.4C67.2C$110.4C!

It seems that guns and oscillators can be constructed with any period greater than two.

Brian Prentice

Saka · Post by **Saka** » August 7th, 2017, 9:30 am

This rule IS very fun

Code: Select all

x = 57, y = 40, rule = BWP1
36.6C$4.4C2$C$C42.C$C4.C5.AB25.2C3.C$C4.C5.AB30.C$C42.C$C4$38.2A$38.
2B6$38.2A$38.2B2$5.2B$5.2A3$54.3C$51.3C$48.3C3.C$45.3C3.C$48.C$.C43.C
$.C20.BA15.C$.C3.2C15.BA15.C$.C43.C$48.C$45.3C3.C$37.4C7.3C3.C$3.6C
42.3C$54.3C!

-------------EDITS--------------
Smallest possible "square-based" gun?

Code: Select all

x = 4, y = 5, rule = BWP1
C.2C$C.2A$2.BC$2CBC$2.2A!

p83 squaretrack

Code: Select all

x = 30, y = 29, rule = BWP1
6.C$5.C5.16C$4.C3.BA17.C$3.C2.C.BA18.C$2.C2.C5.16C2.C$.C2.C22.C$.C2.C
$.C2.C$.C2.C$.C2.C$.C2.C$.C2.C$.C2.C$.C2.C$.C2.C$.C2.C21.C2.C$26.C2.C
$26.C2.C$26.C2.C$26.C2.C$26.C2.C$26.C2.C$C2.C21.C2.C$.C2.C19.C2.C$2.C
2.C17.C2.C$3.C2.7C9.C2.C$4.C16.C2.C$5.C17.C$6.7C9.C!

bprentice · Post by **bprentice** » August 7th, 2017, 10:54 am

Saka wrote:Smallest possible "square-based" gun?

x = 4, y = 5, rule = BWP1
C.2C$C.2A$2.BC$2CBC$2.2A!

Code: Select all

x = 3, y = 3, rule = BWP1
2A$2BA$.CA!

Brian Prentice

BlinkerSpawn · Post by **BlinkerSpawn** » August 7th, 2017, 2:31 pm

p3+:

Code: Select all

x = 39, y = 8, rule = BWP1
30.2C$20.2C9.2BA$10.2C9.2BA8.CA4.C$2C9.2BA8.CA3.C2.C2.C4.C$.2BA8.CA2.
C3.C2.C3.C2.C3.C3.C$2.CA.C4.C2.C2.C3.C3.C2.C2.C4.C2.C$C.AC6.C2.AC5.C
3.AC4.C4.AC$2.A2B8.A2B8.A2B8.A2B!

EDIT: Alternative method:

Code: Select all

x = 37, y = 16, rule = BWP1
3.C9.C9.C9.C$2.2CA7.2CA7.2CA7.2CA$2.CBA.C5.CBA.C5.CBA.C5.CBA.C$3.BA2C
6.BA2C6.BA2C6.BA2C$.2A$.2B.2B5.2A$4.2A5.2B.2B5.2A$2CAB10.2A5.2B.2B5.
2A$C.ABC19.2A5.2B.2B$2.A2C5.2CAB20.2A$10.C.ABC$12.A2C5.2CAB$20.C.ABC$
22.A2C5.2CAB$30.C.ABC$32.A2C!

EDIT 2: More compact version of the arbitrarily-long-photon gun:

Code: Select all

x = 17, y = 13, rule = BWP1
2.C9.C$2.C.BA6.C$4.BA3.3C$2C8.C$8.C$8.3C$11.C$12.C$13.C$14.C$15.C$16.
C$16.C!

bprentice · Post by **bprentice** » August 7th, 2017, 3:20 pm

BlinkerSpawn wrote:p3+:

Very good!

Brian Prentice

Saka · Post by **Saka** » August 8th, 2017, 1:07 am

Interesting...

Code: Select all

x = 44, y = 38, rule = BWP1
13.C$13.C$6.2C$33.C$33.C$23.2C4$2C5.C4.2C$7.C16.C$24.C4$2.C21.2C15.C$
2.C29.2C7.C3$17.4C3.C13.2C$24.C$15.C$15.C2.2A$15.C2.CBA$15.C3.BA17.2C
$17.2B$17.2A2$28.2C7.C$16.4C17.C6$42.2C$30.C$30.C!

bprentice wrote:
Code: Select all
x = 3, y = 3, rule = BWP1
2A$2BA$.CA!
Brian Prentice

It's not based on square reflections by 2-cell dominoes.

Dunno how what to call this. "Self working" gun

Code: Select all

x = 14, y = 22, rule = BWP1
10.4C2$C$C$C10.C$C9.C$C8.C$C7.C$C6.C$C5.C$C2.BA$C2.BA$C5.C$C6.C$C7.C$
C8.C$C9.C$C10.C$C$C2$10.4C!

EDIT:
Another weird self-working gun that uses the opposite reaction

Code: Select all

x = 16, y = 17, rule = BWP1
4.4C$15.C$15.C$BA4.C8.C$BA5.C7.C$BA6.C6.C$BA7.C5.C$BA8.C4.C$BA13.C$BA
8.C4.C$BA7.C5.C$BA6.C6.C$BA5.C7.C$6.C8.C$15.C$15.C$4.4C!

bprentice · Post by **bprentice** » August 8th, 2017, 6:21 am

Saka wrote:Interesting...

x = 44, y = 38, rule = BWP1
13.C$13.C$6.2C$33.C$33.C$23.2C4$2C5.C4.2C$7.C16.C$24.C4$2.C21.2C15.C$
2.C29.2C7.C3$17.4C3.C13.2C$24.C$15.C$15.C2.2A$15.C2.CBA$15.C3.BA17.2C
$17.2B$17.2A2$28.2C7.C$16.4C17.C6$42.2C$30.C$30.C!

I agree. That is exactly what the rule was designed to do. Try finding something similar with an odd period.

Brian Prentice

Saka · Post by **Saka** » August 8th, 2017, 6:39 am

An interesting in-line photon duplicator that does a +1 operation if you put too many at a time (distance added so it's clear)

Code: Select all

x = 54, y = 17, rule = BWP1
49.5C3$48.C$48.C3$46.2C$46.C3.C$BA.BA26.BA4.BA10.C$BA.BA26.BA4.BA10.C
$46.C3.C$46.2C2$52.2C$48.C$48.C!

Also, why do you remove the code tags?

bprentice · Post by **bprentice** » August 8th, 2017, 8:36 am

Saka wrote:An interesting in-line photon duplicator that does a +1 operation if you put too many at a time (distance added so it's clear)

x = 54, y = 17, rule = BWP1
49.5C3$48.C$48.C3$46.2C$46.C3.C$BA.BA26.BA4.BA10.C$BA.BA26.BA4.BA10.C
$46.C3.C$46.2C2$52.2C$48.C$48.C!

This concept needs some work to be useful.

Brian Prentice

Saka · Post by **Saka** » August 8th, 2017, 9:20 am

Actually, if you let the duplicator space them, it functions as a good +1 adder. It's also pretty fun to watch the photons fill up the loop one by one. (P313)

Code: Select all

x = 70, y = 51, rule = BWP1
20.5C3$19.C$19.C$68.2C2$17.2C$2.C14.C3.C$2.C7.BA8.C$10.BA8.C33.C$17.C
3.C32.C$17.2C21.2C2$23.2C$19.C$19.C2$27.2C12.C$41.C7$20.2C6.C$28.C8$
22.C17.2C$22.C12$2C51.2C$39.C27.C$39.C27.C!

EDIT:
Strange extender

Code: Select all

x = 17, y = 10, rule = BWP1
13.4C$11.4C$9.4C$7.4C4.C$13.C.C$11.C.C$BA7.C.C$BA7.C$.BA$.BA!

bprentice · Post by **bprentice** » August 10th, 2017, 3:18 pm

Rule BWP1 does not seem to have a period 2 oscillator. Rule BWP2:

Code: Select all

@RULE BWP2

@TREE

num_states=5
num_neighbors=8
num_nodes=284
1 0 2 0 3 4
1 1 0 0 3 4
2 0 0 0 0 1
2 1 1 1 1 1
3 2 2 2 2 3
3 3 3 3 3 3
4 4 4 4 4 5
4 5 5 5 5 5
5 6 6 6 6 7
1 1 2 0 3 4
2 0 9 0 9 1
2 9 0 0 0 1
3 10 11 2 11 3
4 12 12 12 12 5
5 13 13 13 13 7
2 0 9 0 0 1
3 15 11 2 2 3
4 16 16 16 16 5
5 17 17 17 17 7
6 8 14 8 18 8
3 10 10 10 10 3
3 11 11 11 11 3
4 20 21 4 21 5
5 22 22 22 22 7
2 9 9 0 9 1
3 10 24 10 24 3
3 24 11 11 11 3
4 25 26 12 26 5
5 27 27 27 27 7
3 10 24 10 10 3
2 9 9 0 0 1
3 30 11 11 11 3
4 29 31 16 31 5
5 32 32 32 32 7
6 23 28 23 33 23
3 15 15 15 15 3
4 35 21 4 4 5
5 36 36 36 36 7
3 10 30 15 30 3
4 38 26 12 12 5
5 39 39 39 39 7
3 15 30 15 15 3
4 41 31 16 16 5
5 42 42 42 42 7
6 37 40 37 43 37
7 19 34 19 44 19
2 9 9 9 9 1
3 2 46 2 46 3
4 47 47 47 47 5
3 46 2 2 2 3
4 49 49 49 49 5
5 48 50 6 50 7
3 10 46 2 46 3
4 52 52 52 52 5
3 46 11 2 11 3
4 54 54 54 54 5
5 53 55 13 55 7
3 15 46 2 46 3
4 57 57 57 57 5
3 46 11 2 2 3
4 59 59 59 59 5
5 58 60 17 60 7
6 51 56 51 61 51
3 10 46 10 46 3
3 11 46 11 46 3
4 63 64 47 64 5
3 46 10 10 10 3
3 46 11 11 11 3
4 66 67 49 67 5
5 65 68 22 68 7
3 24 46 11 46 3
4 63 70 52 70 5
3 46 24 10 24 3
4 72 67 54 67 5
5 71 73 27 73 7
3 30 46 11 46 3
4 63 75 57 75 5
3 46 24 10 10 3
4 77 67 59 67 5
5 76 78 32 78 7
6 69 74 69 79 69
3 15 46 15 46 3
4 81 64 47 47 5
3 46 15 15 15 3
4 83 67 49 49 5
5 82 84 36 84 7
3 10 46 15 46 3
4 86 70 52 52 5
3 46 30 15 30 3
4 88 67 54 54 5
5 87 89 39 89 7
4 81 75 57 57 5
3 46 30 15 15 3
4 92 67 59 59 5
5 91 93 42 93 7
6 85 90 85 94 85
7 62 80 62 95 62
3 2 46 2 2 3
4 97 97 97 97 5
5 98 50 6 6 7
3 10 46 2 11 3
4 100 100 100 100 5
5 101 55 13 13 7
3 15 46 2 2 3
4 103 103 103 103 5
5 104 60 17 17 7
6 99 102 99 105 99
3 10 46 10 10 3
3 11 46 11 11 3
4 107 108 97 108 5
5 109 68 22 22 7
3 10 46 10 24 3
3 24 46 11 11 3
4 111 112 100 112 5
5 113 73 27 27 7
3 30 46 11 11 3
4 107 115 103 115 5
5 116 78 32 32 7
6 110 114 110 117 110
3 15 46 15 15 3
4 119 108 97 97 5
5 120 84 36 36 7
3 10 46 15 30 3
4 122 112 100 100 5
5 123 89 39 39 7
4 119 115 103 103 5
5 125 93 42 42 7
6 121 124 121 126 121
7 106 118 106 127 106
8 45 96 45 128 45
3 46 46 46 46 3
4 4 130 4 130 5
4 130 4 4 4 5
5 131 132 6 132 7
4 12 130 12 130 5
4 130 12 12 12 5
5 134 135 13 135 7
4 16 130 16 130 5
4 130 16 16 16 5
5 137 138 17 138 7
6 133 136 133 139 133
4 20 130 4 130 5
4 130 21 4 21 5
5 141 142 22 142 7
4 25 130 12 130 5
4 130 26 12 26 5
5 144 145 27 145 7
4 29 130 16 130 5
4 130 31 16 31 5
5 147 148 32 148 7
6 143 146 143 149 143
4 35 130 4 130 5
4 130 21 4 4 5
5 151 152 36 152 7
4 38 130 12 130 5
4 130 26 12 12 5
5 154 155 39 155 7
4 41 130 16 130 5
4 130 31 16 16 5
5 157 158 42 158 7
6 153 156 153 159 153
7 140 150 140 160 140
4 47 130 47 130 5
4 130 49 49 49 5
5 162 163 6 163 7
4 52 130 52 130 5
4 130 54 54 54 5
5 165 166 13 166 7
4 57 130 57 130 5
4 130 59 59 59 5
5 168 169 17 169 7
6 164 167 164 170 164
4 63 130 47 130 5
4 130 67 49 67 5
5 172 173 22 173 7
4 63 130 52 130 5
4 130 67 54 67 5
5 175 176 27 176 7
4 63 130 57 130 5
4 130 67 59 67 5
5 178 179 32 179 7
6 174 177 174 180 174
4 81 130 47 130 5
4 130 67 49 49 5
5 182 183 36 183 7
4 86 130 52 130 5
4 130 67 54 54 5
5 185 186 39 186 7
4 81 130 57 130 5
4 130 67 59 59 5
5 188 189 42 189 7
6 184 187 184 190 184
7 171 181 171 191 171
4 97 130 97 130 5
5 193 163 6 132 7
4 100 130 100 130 5
5 195 166 13 135 7
4 103 130 103 130 5
5 197 169 17 138 7
6 194 196 194 198 194
4 107 130 97 130 5
5 200 173 22 142 7
4 111 130 100 130 5
5 202 176 27 145 7
4 107 130 103 130 5
5 204 179 32 148 7
6 201 203 201 205 201
4 119 130 97 130 5
5 207 183 36 152 7
4 122 130 100 130 5
5 209 186 39 155 7
4 119 130 103 130 5
5 211 189 42 158 7
6 208 210 208 212 208
7 199 206 199 213 199
8 161 192 161 214 161
4 4 130 4 4 5
5 216 132 6 6 7
4 12 130 12 12 5
5 218 135 13 13 7
4 16 130 16 16 5
5 220 138 17 17 7
6 217 219 217 221 217
4 20 130 4 21 5
5 223 142 22 22 7
4 25 130 12 26 5
5 225 145 27 27 7
4 29 130 16 31 5
5 227 148 32 32 7
6 224 226 224 228 224
4 35 130 4 4 5
5 230 152 36 36 7
4 38 130 12 12 5
5 232 155 39 39 7
4 41 130 16 16 5
5 234 158 42 42 7
6 231 233 231 235 231
7 222 229 222 236 222
4 47 130 47 47 5
5 238 163 6 50 7
4 52 130 52 52 5
5 240 166 13 55 7
4 57 130 57 57 5
5 242 169 17 60 7
6 239 241 239 243 239
4 63 130 47 64 5
5 245 173 22 68 7
4 63 130 52 70 5
5 247 176 27 73 7
4 63 130 57 75 5
5 249 179 32 78 7
6 246 248 246 250 246
4 81 130 47 47 5
5 252 183 36 84 7
4 86 130 52 52 5
5 254 186 39 89 7
4 81 130 57 57 5
5 256 189 42 93 7
6 253 255 253 257 253
7 244 251 244 258 244
4 97 130 97 97 5
5 260 163 6 6 7
4 100 130 100 100 5
5 262 166 13 13 7
4 103 130 103 103 5
5 264 169 17 17 7
6 261 263 261 265 261
4 107 130 97 108 5
5 267 173 22 22 7
4 111 130 100 112 5
5 269 176 27 27 7
4 107 130 103 115 5
5 271 179 32 32 7
6 268 270 268 272 268
4 119 130 97 97 5
5 274 183 36 36 7
4 122 130 100 100 5
5 276 186 39 39 7
4 119 130 103 103 5
5 278 189 42 42 7
6 275 277 275 279 275
7 266 273 266 280 266
8 237 259 237 281 237
9 129 215 129 282 129

does have such an oscillator:

Code: Select all

x = 1, y = 1, rule = BWP2
D!

and is omniperiodic since it runs all patterns that run on BWP1. This also means that guns of any period greater than 2 are supported. As a bonus, guns like this this:

Code: Select all

x = 1, y = 8, rule = BWP2
C$D$D$D$D$D$D$C!

can be constructed and patterns like this can still be enjoyed:

Code: Select all

x = 174, y = 101, rule = BWP2
153.C$153.C$60.2C3$159.C$159.C4$165.C$165.C4$171.C$171.C3$148.C$141.
AB5.C$136.2C3.AB7$66.C$67.C$68.C6.C$69.2C4.C34.AB37.2C$75.C34.AB25.
2C$75.C20.2C39.2C$75.C14.2C$75.C8.2C$61.9B5.C2.2C$61.9A5.C$99.15C4$
76.A2BA74.2C$2C74.A2BA4$82.A2BA74.2C$6.2C74.A2BA4$88.A2BA74.2C$12.2C
74.A2BA4$94.A2BA74.2C$18.2C74.A2BA4$60.15C$98.C5.9A$94.2C2.C5.9B$88.
2C8.C$82.2C14.C$35.2C39.2C20.C$35.2C25.BA34.C$23.2C37.BA34.C4.2C$98.
C6.C$106.C$107.C7$31.BA3.2C$25.C5.BA$25.C3$2.C$2.C4$8.C$8.C4$14.C$14.
C3$112.2C$20.C$20.C!

In case anyone would like to explore other rule variants, rule BWP2 was generated with this Java program:

Code: Select all

import java.util.*;

public class RuleTreeGen
{
  /* Put your state count, neighbor count, and function here */
  final static int numStates = 5;
  final static int numNeighbors = 8;

  /* 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 NW = a[0];
    int NE = a[1];
    int SW = a[2];
    int SE = a[3];
    int N = a[4];
    int W = a[5];
    int E = a[6];
    int S = a[7];
    int cell = a[8];
    if ((cell == 0) && (S == 1))
    {
      if ((SE == 1) && (E == 0))
        return 1;
      if ((SW == 1) && (W == 0))
        return 1;
    }
    if ((cell == 0) && (W == 1))
    {
      if ((NW == 1) && (N == 0))
        return 1;
      if ((SW == 1) && (S == 0))
        return 1;
    }
    if ((cell == 0) && (N == 1))
    {
      if ((NE == 1) && (E == 0))
        return 1;
      if ((NW == 1) && (W == 0))
        return 1;
    }
    if ((cell == 0) && (E == 1))
    {
      if ((NE == 1) && (N == 0))
        return 1;
      if ((SE == 1) && (S == 0))
        return 1;
    }

    if ((cell == 0) && (S == 0))
    {
      if ((E == 3) && (SE == 1))
        return 1;
      if ((W == 3) && (SW == 1))
        return 1;
    }
    if ((cell == 0) && (N == 0))
    {
      if ((NE == 3) && (E == 1))
        return 1;
      if ((NW == 3) && (W == 1))
        return 1;
    }

    if ((cell == 0) && (W == 0))
    {
      if ((S == 3) && (SW == 1))
        return 1;
      if ((N == 3) && (NW == 1))
        return 1;
    }
    if ((cell == 0) && (E == 0))
    {
      if ((SE == 3) && (S == 1))
        return 1;
      if ((NE == 3) && (N == 1))
        return 1;
    }

    if ((cell == 0) && (N == 0))
    {
      if ((E == 3) && (NE == 1))
        return 1;
      if ((W == 3) && (NW == 1))
        return 1;
    }
    if ((cell == 0) && (S == 0))
    {
      if ((SE == 3) && (E == 1))
        return 1;
      if ((SW == 3) && (W == 1))
        return 1;
    }

    if ((cell == 0) && (E == 0))
    {
      if ((S == 3) && (SE == 1))
        return 1;
      if ((N == 3) && (NE == 1))
        return 1;
    }
    if ((cell == 0) && (W == 0))
    {
      if ((SW == 3) && (S == 1))
        return 1;
      if ((NW == 3) && (N == 1))
        return 1;
    }
    if ((cell == 3) || (cell == 4))
      return cell;
    if ((cell == 0) && ((N == 4) || (S == 4) || (E == 4) || (W == 4)))
      return 1;
    if ((cell == 1) && ((N == 4) || (S == 4) || (E == 4) || (W == 4)))
      return 0;
    if (cell == 1)
      return 2;
    if (cell == 2)
      return 0;
    return 0;
  }

  final static int numParams = numNeighbors + 1;
  HashMap<String, Integer> world = new HashMap<String, Integer>();
  ArrayList<String> r = new ArrayList<String>();
  int[] params = new int[numParams];
  int nodeSeq = 0;

  int getNode(String n)
  {
    Integer found = world.get(n);
    if (found == null)
    {
      found = nodeSeq++;
      r.add(n);
      world.put(n, found);
    }
    return found;
  }

  int recur(int at)
  {
    if (at == 0)
      return f(params);
    String n = "" + at;
    for (int i=0; i<numStates; i++)
    {
      params[numParams-at] = i;
      n += " " + recur(at-1);
    }
    return getNode(n);
  }

  void writeRuleTree()
  {
    System.out.println("@RULE BWP2\n");
    System.out.println("@TREE\n");
    System.out.println("num_states=" + numStates);
    System.out.println("num_neighbors=" + numNeighbors);
    System.out.println("num_nodes=" + r.size());
    for (int i=0; i<r.size(); i++)
      System.out.println(r.get(i));
  }

  public static void main(String[] args) throws Exception
  {
    RuleTreeGen rtg = new RuleTreeGen();
    rtg.recur(numParams);
    rtg.writeRuleTree();
  }
}

Brian Prentice

Post by **AforAmpere** » August 11th, 2017, 5:26 pm

Almost a working half-adder in the first rule. It adds correctly, but the timing is slightly different for 1+0 and 0+1.

Code: Select all

x = 51, y = 43, rule = BWP1
$35.C$35.C$7.2C31.2C$8.C17.C$24.3C8.2C$37.C$16.2C11.2C6.C2.C$17.C6.3C
10.C2.C$26.C2.2C6.C8$28.C$28.C$41.2C2$4.C18.C$4.C18.C$4.C23.2C$4.C25.
C$4.C18.2C11.C10.C$4.C3.C27.C10.C$4.C3.C38.C3$17.C5.2C$.BA4.2C8.C$.BA
26.2C16.2C$23.C17.C$23.C17.C$.BA13.2C$.BA33.2C$29.C$29.C$28.2C$38.4C!

I need to find a XOR gate with the right timing.

ConwayLife.com

A Simple Rule

A Simple Rule

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Re: A Simple Rule

Re: A Simple Rule

Re: A Simple Rule

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Re: A Simple Rule

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Re: A Simple Rule