Construction Challenges and Ideas

Tawal · Post by **Tawal** » August 25th, 2024, 11:04 am

It's not really a construction challenge, it's more of a research challenge.
As we have quite a few U-tuner to X converters (thanks to C28), we don't have many X to U-turner.
So let's find one X to U-turner with good clearance.
Perhaps the program Silk may be useful to find it.

Post by **dvgrn** » October 26th, 2024, 11:30 am

The new Mersenne prime find, M136279841, means that the prime-period oscillator in Golly's Very Large Patterns archive is no longer the largest prime period that we can easily build.*

We can fix that, though! FlutterWithKSparkler has already posted a period 2^136279841-1 oscillator that works very nicely in the INT rule B3-jknr4ity5ijk6i8/S23-a4city6c7c . There just isn't an equivalent pattern in Conway's Life yet.

The scripts from 2019 that produced the period-multiplier chain for the 2019 Mersenne-prime oscillator (2^82589933-1) turned out to be perfectly well up to the task of producing the somewhat larger period-multiplier chain for M136279841:

Code: Select all

[M2] (golly 4.3)
#R B3/S23
$$$$$$$....*..*$
4 0 0 0 1
$$$$$$$*$
4 0 0 3 0
5 0 0 2 4
6 0 0 0 5
6 0 0 5 5
7 0 0 6 7
7 0 0 7 7
8 0 0 8 9
8 0 0 9 9
9 0 0 10 11
9 0 0 11 11
10 0 0 12 13
10 0 0 13 13
11 0 0 14 15
11 0 0 15 15
12 0 0 16 17
12 0 0 17 17
13 0 0 18 19
13 0 0 19 19
14 0 0 20 21
14 0 0 21 21
15 0 0 22 23
15 0 0 23 23
16 0 0 24 25
16 0 0 25 25
17 0 0 26 27
6 0 0 5 0
7 0 0 29 0
8 0 0 9 30
9 0 0 31 0
10 0 0 13 32
11 0 0 33 0
12 0 0 17 34
13 0 0 35 0
14 0 0 21 36
15 0 0 23 37
16 0 0 25 38
17 0 0 39 0
18 0 0 28 40
$$$$$....**$....*$......*$
....****$$..******$.*$.**..**$.....**$
..*****$..*$.....***$.....*$$**$*..*.**$..**.**$
$$*$*....**$.....**$
4 42 43 44 45
.*$.*$*.**$*.*..*$*...**$**$
4 47 0 0 0
$$...*$.***$*$**$
$$$$$$$...**..*$
4 49 0 0 50
$$$$**$*$.***$...*$
$$..**.**$*..*.**$**$$.....*$.....***$
$$$$$.....**$*....**$*$
4 52 0 53 54
5 46 48 51 55
$$$$....**$.....*$...*$...**$
4 0 0 57 0
$$$$$$.......*$.......*$
$$$$$$*$..*$
4 0 0 59 60
.**...*$*..****$**.*$.*.*.**$.*.*.**$**.*$...*$...*.*$
$$$....**$....**$
....**$$$$......*$......**$
$...**$...*$**.*...*$.*.**..*$.*$.*.....*$.**$
4 62 63 64 65
.....*.*$.....**$
.**$*$*$***$...*$..**$
$$$*$*$$*$*$
$$$$$.....**$.....**$
4 67 68 69 70
5 58 61 66 71
$$$......*$......**$
..*.****$..*$**.*****$.*.*$...*.**$..**.**$
$$$.....**$.....**$
4 73 74 0 75
..*$..******$**...*$..*$.**$$$...*..*$
$*$*$$.....**$.**..**$.*$..******$
...*****$$...****$...*..*$$$.....**$.....**$
**$.*..****$....*..*$$$..**$*..*$**$
4 77 78 79 80
$$$$..**$...*$***$*$
$$.....**$.....**$$$...*..*$...****$
$$**$*..*$..**$$$....*..*$
4 0 82 83 84
$$*$***$...*$..**$
4 0 86 3 70
5 76 81 85 87
6 0 56 72 88
$$$......*$**....**$*...**$*.*..*$*.**$
.*$.*$*$
4 90 74 91 75
5 92 81 85 87
6 56 56 93 93
......*$......**$
4 0 95 0 0
$$$$$......**$......*$
$$$$..**.**$...*.**$.*.*$**.*****$
..*$..*.****$...**..*$
4 97 98 0 99
5 96 100 0 0
$...*****$...*..*$$$.**$..*$**...*$
.*..****$**$..******$.*$.**..**$.....**$$*$
..******$..*$.....***$.....*$$**$*..*.**$..**.**$
*$$*$*....**$.....**$
4 102 103 104 105
.*$.*$*.**$*.*..*$*...**$**....**$......*$
4 107 98 0 99
5 106 108 51 55
6 101 109 72 88
6 109 109 93 93
7 89 94 110 111
7 94 94 111 111
7 110 111 110 111
7 111 111 111 111
8 112 113 114 115
8 113 113 115 115
8 114 115 114 115
8 115 115 115 115
9 116 117 118 119
9 117 117 119 119
9 118 119 118 119
9 119 119 119 119
10 120 121 122 123
10 121 121 123 123
10 122 123 122 123
10 123 123 123 123
11 124 125 126 127
11 125 125 127 127
11 126 127 126 127
11 127 127 127 127
12 128 129 130 131
12 129 129 131 131
12 130 131 130 131
12 131 131 131 131
13 132 133 134 135
13 133 133 135 135
13 134 135 134 135
13 135 135 135 135
14 136 137 138 139
14 137 137 139 139
14 138 139 138 139
14 139 139 139 139
15 140 141 142 143
15 141 141 143 143
15 142 143 142 143
15 143 143 143 143
16 144 145 146 147
16 145 145 147 147
16 146 147 146 147
16 147 147 147 147
17 148 149 150 151
$$$$$$...**$.*..*$
4 0 0 153 0
$$$$......**$......*$$.......*$
$$$$$$*$*$
4 0 0 155 156
.**.*.*$...*.**$...*$.***$*$**$
$$$......**$......**$
$.......*$$...**$...**..*$$...**$...*$
4 158 159 0 160
.....*$.....***$$.....**$.....**$$$......*$
.**$*..*$*.**$*.*$*.*$*.**$*$*$
......**$*$*$*.**$*.*..*$..*.**$..*$.**$
4 162 163 164 0
5 154 157 161 165
4 0 86 3 0
5 92 81 85 167
$$$$**$*...**$*.*..*$*.**$
.....*$....**$$$$.......*$.......*$..**$
.*$.*.....*$*......*$$$$.....**$....*.*$
..*$*.*$..*.**$.**.*$....*$....**$
4 169 170 171 172
$$$$$*$$.*$
**$$**$**$
4 174 0 175 0
....*$.**.*$..*.*.**$..*.*.**$.**.*$.*..****$..**...*$....**$
$$.....**$.....**$
....*$......*$.....**$
4 177 178 179 0
**$
4 97 156 0 181
5 173 176 180 182
6 56 166 168 183
$$$$$.....**$......*$....*$
....**$$....**$....**$
4 0 185 0 186
$$$$$$$..**$
...*$...*.**$**.*..*$.*.**$.*$**$.......*$.......*$
$$$$$$*$.*$
4 188 0 189 190
$$$$$......**$.....*.*$.....*$
$$.......*$.......*$
....**$
4 192 193 194 0
$$*.....**$*.....**$$......**$......*$
.*$.*.**$.*.*$.*.*$.*.**$**..*$..**$**$
$.......*$.......*$
.*$$*$
4 196 197 198 199
5 187 191 195 200
6 201 0 0 0
5 106 48 51 55
6 203 166 168 183
7 184 202 204 202
7 204 202 204 202
8 113 205 115 206
8 115 206 115 206
9 207 0 208 0
9 208 0 208 0
10 121 209 123 210
10 123 210 123 210
11 211 0 212 0
11 212 0 212 0
12 129 213 131 214
12 131 214 131 214
13 215 0 216 0
13 216 0 216 0
14 137 217 139 218
14 139 218 139 218
15 141 219 143 220
15 143 220 143 220
16 145 221 147 222
16 147 222 147 222
17 223 0 224 0
$$**$*..*$..**$
4 0 82 83 226
4 0 86 0 70
5 76 81 227 228
6 101 109 72 229
5 92 81 227 228
6 109 109 231 231
7 110 111 230 232
7 111 111 232 232
8 114 115 233 234
8 115 115 234 234
$.....***$.....*$.......*$......**$.**$..*$**$
.*$**$
4 237 238 0 0
5 239 100 0 0
6 101 240 0 0
6 240 240 0 0
7 241 242 0 0
7 242 242 0 0
8 243 244 0 0
8 244 244 0 0
9 235 236 245 246
9 236 236 246 246
10 247 248 0 0
10 248 248 0 0
11 249 250 0 0
11 250 250 0 0
12 130 131 251 252
12 131 131 252 252
13 253 254 0 0
13 254 254 0 0
14 255 256 0 0
14 256 256 0 0
15 142 143 257 258
15 143 143 258 258
16 146 147 259 260
16 147 147 260 260
17 261 262 0 0
4 0 0 0 198
5 92 81 227 264
.....*$....**$
4 169 266 91 0
$$**$..*$.**$
4 0 0 268 0
5 267 0 269 0
6 203 166 265 270
7 204 202 271 202
8 115 206 234 272
$$$$.....**$.....*$.......*$
4 0 0 0 274
5 239 275 0 0
$$$$....**$....**$
$....**.*$....**.*$$$..*..*$..****$
$$$.**.**$..*.**$*.*$*.******$.*$
....****$....*$......*$.....**$**$.*$*$
4 277 278 279 280
$*$..*$.**$$$$*$
*$
4 282 0 283 0
.*.****$..**..*$
4 285 0 0 0
5 281 284 286 0
6 276 287 0 0
7 288 0 0 0
8 244 289 0 0
9 273 0 290 0
10 248 291 0 0
11 292 0 0 0
12 131 214 252 293
13 294 0 0 0
14 256 295 0 0
15 143 220 258 296
16 147 222 260 297
17 298 0 0 0
18 152 225 263 299
19 0 41 0 300

This is a chain of 68139984 quadri-Snarks. I've checked this by running a glider through the chain starting from the upper right corner, for just a bit over 2^32 ticks -- 4,634,248,960 ticks will do nicely -- and confirmed that the population went up by 68139984 times 6.

We only need 68,139,916 quadri-Snarks plus the same resettable period-2^9 loop that was used in the last Mersenne-prime oscillator.

So building an M136279841 oscillator will be a matter of shortening the last two or three boustrophedonic quadri-Snark chains at the top by a total of 68 quadri-Snarks, to make a little bit of space in the upper right corner to fit in the period-2^9 base loop connected to the beginning of the quadri-Snark chain, and the reset mechanism that ensures that the reset glider arrives at exactly the right time to speed up the signal in the period-2^9 base loop by exactly one tick.

The previous oscillator's reset mechanism includes a trombone slide and a custom 180-degree reflector, plus some extra stuff that I threw in to delay the glider by the right amount. Here's what the upper right corner of the M82589933 oscillator looks like at T = 2,802,630,000:

Code: Select all

x = 349, y = 287, rule = LifeHistory
103.2A154.2A3.2A$95.2A5.B2AB153.2A2.A.3A$96.A5.3B53.2A11.A91.A4.A$96.
A.AB3.B53.B2AB9.A.A86.4A.2A2.A$97.2A7B2.B49.3B9.A.A2.2A3.A78.A2.A.A.A
.2A$93.2A3.8B.B2A47.B.B9.2A.2A2.A2.A.A79.BABABA.A$94.A4.9B2A47.5B8.B
2.A.A3.A.A80.B2ABA.A$94.A.AB2.7B.B48.6B6.2ABA2.4A.A82.2B.BA$95.2AB.8B
5.2A43.8B4.2A.A.A3.A83.3B$97.9B6.A45.13B2.A.AB2.A73.2A6.4B$97.10B2.BA
.A43.13B5.A.A2B.A73.A6.B2A3B$97.10B2.B2A43.15B5.A2B.2A73.A.AB3.B2A3B$
97.13B45.15B4.3B78.2AB.10B$97.13B44.17B.B.2B18.2A61.13B13.A$95.2A13B
44.29B11.A62.14B10.3A$94.A.A12B44.13B2A16B7.BA.A62.15B8.A$94.A3.12B
42.14B2A16B2.B.2B.B2A4.2A59.8B2.4B7.2A$93.2A3.11B42.2AB3.27B.7B6.A60.
6B5.4B3.5B$98.10B42.A2.A4.33B4.BA.A59.9B4.4B2.3B$98.13B38.A.2A5.6B3.B
2.2B2.20B.B2A59.4B4.2A5.9B7.2A.2A$98.14B37.A7.6B14.19B60.4B5.A7.8B8.A
.2A$99.13B36.2A6.9B14.18B58.4B7.3A5.10B3.B.A$98.15B42.4B4.2A15.16B58.
4B10.A5.7B2A2B.B3A$98.15B4.2A35.4B5.A15.15B.B2A55.4B17.7B2A3BAB2.2A$
100.13B3.B2AB33.4B7.3A12.7B.7B.BA.A53.4B18.12B4A2.A$99.14B.B2.2B33.4B
10.A10.2AB.3B4.6B4.A8.A43.4B17.2AB.7B3.2B.A.2A$99.17B2.2B31.4B21.A.AB
9.6B3.2A5.3A42.4B17.A.AB.7B2.B3A2.A$97.2AB.20B29.4B22.A10.9B8.A44.4B
18.A5.4B4.A5.A$96.A.AB3.19B27.4B22.2A10.2A4.4B7.2A42.4B18.2A5.4B5.5A$
96.A6.19B26.4B36.A5.4B3.5B41.4B25.4B8.A$95.2A6.19B25.4B34.3A7.4B2.3B
42.4B25.4B$103.17B26.4B35.A10.9B7.2A.2A28.4B25.4B$101.2A17B25.4B48.8B
8.A.2A27.4B25.4B$100.A.A17B24.4B50.10B3.B.A29.4B25.4B$100.A4.15B23.4B
51.7B2A2B.B3A28.4B25.4B$99.2A5.15B21.4B52.7B2A3BAB2.2A25.4B25.4B$107.
10B.4B19.4B53.12B4A2.A23.4B25.4B$103.B.11B3.4B10.A6.4B52.2AB.7B3.2B.A
.2A22.4B25.4B$101.2A12B5.4B7.3A5.4B52.A.AB.7B2.B3A2.A22.4B25.4B$101.
2A12B6.4B5.A7.4B53.A5.4B4.A5.A21.4B25.4B$101.14B7.4B4.2A5.4B53.2A5.4B
5.5A21.4B25.4B$101.12B.B2A6.9B4.4B60.4B8.A22.4B25.4B$99.2AB.9B2.BA.A
6.6B5.4B60.4B31.4B25.4B$98.A.AB.8B6.A6.8B2.4B60.4B31.4B17.A7.4B$98.A
5.8B5.2A3.15B60.4B31.4B16.3A6.4B$97.2A6.7B10.14B60.4B31.4B16.A8.4B$
102.11B9.13B60.4B31.4B16.A.A6.4B$101.12B7.2AB.10B60.4B31.4B16.BA.A5.
4B$92.2A7.12B6.A.AB3.B2A3B61.4B31.4B16.3BA5.4B$91.A2.A2.2A2.11B7.A6.B
2A3B60.4B31.4B15.4B6.4B$92.2A2.A.A2.8B.4B4.2A6.4B61.4B31.4B14.6B5.4B$
94.2A.B3.7B4.2A13.3B60.4B31.4B14.7B4.4B$94.A2.2B2.7B4.A15.2B.BA56.4B
31.4B8.B.4B.8B2.4B$91.2A.A.BA2B.6B6.3A11.B2ABA.A54.4B31.4B8.2AB.17B$
91.A.2A.A.A8B8.A10.BABABA.A53.4B31.4B9.2A18B$95.A.A.8B17.A2.A.A.A.2A
51.4B31.4B11.2B.16B$92.2A2.A4.5B18.4A.2A2.A51.4B31.4B15.16B$90.3A.2A
4.6B22.A4.A50.4B31.4B17.15B$46.2A3.2A21.2A3.2A8.A4.B6.6B17.2A2.A.3A
50.4B31.4B19.12B.B2A20.2A11.A$46.2A2.A.3A19.2A2.A.3A7.3AB2AB3.7B17.2A
3.2A51.4B31.4B20.11B2.BA.A18.B2AB9.A.A$12.A2.2A33.A4.A22.A4.A8.A.2AB.
8B75.4B31.4B22.10B5.A19.3B9.A.A2.2A3.A$12.4A.A28.4A.2A2.A18.4A.2A2.A
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2.BA.A55.A8.4B31.4B21.3AB2AB3.7B24.13B2.A.AB2.A11.2A$4.2A7.2A.2A31.3B
25.3B15.12B.B2A55.2A7.4B31.4B21.A4.B6.6B22.13B5.A.A2B.A7.5B$4.A35.2A
6.4B16.2A6.4B14.15B57.5B3.4B22.A8.4B23.3A.2A4.6B22.15B5.A2B.2A6.4B$6.
A34.A6.B2A3B15.A6.B2A3B11.16B59.3B2.4B21.5A5.4B5.2A19.2A2.A4.5B22.15B
4.3B10.5B$2.5A34.A.AB3.B2A3B15.A.AB3.B2A3B8.2B.16B46.2A.2A7.9B21.A5.A
4.4B5.A23.A.A.8B20.17B.B.2B10.6B.B$2.A13.A25.2AB.10B14.2AB.10B5.2A18B
46.2A.A8.8B22.A2.3AB2.7B.BA.A19.A.2A.A.A8B8.A11.29B3.9B$5.4A6.A.A26.
13B15.13B4.2AB.17B48.A.B3.10B22.2A.A.2B3.7B.B2A20.2A.A.BA2B.6B6.3A10.
13B2A16B2.11B.B$5.A2.A6.A.A26.14B14.14B4.B.4B.8B2.4B47.3AB.2B2A7B22.A
2.4A12B25.A2.2B2.7B4.A12.14B2A16B2.12B2A$16.A27.15B10.A2.15B10.7B4.4B
44.2A2.BA3B2A7B23.2A2.BA3B2A7B25.2A.B3.7B4.2A10.2AB3.27B.13B2A$2A44.
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9.A2.A4.39B.B$A2.A.2A39.6B5.4B5.A7.6B5.4B11.4B6.4B41.2A.A.2B3.7B.B2A
23.A.B3.10B22.A2.A2.2A2.11B10.A.2A5.6B3.B2.2B2.22B$2.2A.2A3.A34.9B4.
4B4.2A5.9B4.4B12.3BA5.4B41.A2.3AB2.7B.BA.A19.2A.A8.8B22.2A7.12B9.A7.
6B14.20B$9.A.A32.4B4.2A5.9B4.4B4.2A5.4B12.BA.A5.4B40.A5.A4.4B5.A19.2A
.2A7.9B30.12B8.2A6.9B14.20B$10.A32.4B5.A7.6B5.4B5.A7.4B12.A.A6.4B40.
5A5.4B5.2A31.3B2.4B30.11B15.4B4.2A15.19B$3.A31.A6.4B7.3A4.8B2.4B7.3A
5.4B12.A8.4B41.A8.4B35.5B3.4B32.9B13.4B5.A15.19B$.3A29.3A5.4B10.A2.
15B10.A6.4B12.3A6.4B50.4B34.2A7.4B30.10B.2B9.4B7.3A12.17B2ABA.2A$A15.
2A14.A7.4B14.14B19.4B13.A7.4B50.4B34.A8.4B18.3B4.B.16B7.4B10.A10.2AB.
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2A2B21.A.AB6.11B$17.3A18.4B14.2AB.10B23.4B21.4B50.4B29.A13.4B15.2A29B
ABAB22.A8.10B$19.A17.4B14.A.AB3.B2A3B26.4B21.4B50.4B43.4B14.2A31BA22.
2A7.10B$26.A9.2A2B15.A6.B2A3B27.4B21.4B50.4B43.4B14.B.30B32.11B$25.A.
A7.ABAB15.2A6.4B30.4B21.4B50.4B43.4B15.29B33.11B$18.2A.2A3.A9.BA25.3B
31.4B21.4B50.4B43.4B16.26B33.13B$16.A2.A.2A41.2B.BA29.4B21.4B50.4B43.
4B16.B5.18B31.2B.13B.2B$16.2A45.B2ABA.A29.4B21.4B50.4B43.4B24.14B31.
21B$32.A29.BABABA.A30.4B21.4B50.4B42.4B24.14B29.25B$21.A2.A6.A.A26.A
2.A.A.A.2A30.4B21.4B50.4B41.5B24.2B4.5B31.25B$11.2A2.A5.4A6.A.A9.2A2.
A12.4A.2A2.A5.2A2.A22.4B21.4B50.4B39.9B20.2B5.4B23.2A6.27B$10.A.4A2.A
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Probably some new 180-degree reflector will need to be substituted in, to get the right mod-8 timing for the extremely tired glider escaping from the quadri-Snark chain. It should certainly be possible to improve on that silly oversized delay circuit that I used last time. simeks' and Goldtiger997's stamp collection will have something appropriate to swap in.

* calcyman has noted on Discord that

"> "built a Conway's Life oscillator with the largest prime period that it's currently possible to build" ...
This isn't actually true: you could build a computer that checks all numbers between N^3 and (N+1)^3 for the first prime P and returns to its original state in exactly P generations."

To which I say,

"Bah, humbug -- I don't have to believe that that's 'currently possible' until somebody actually builds it."

confocaloid · Post by **confocaloid** » October 26th, 2024, 11:38 am

The problem is interesting, especially if the aim is a pattern that's substantially more compact than would be achieved by just a reapplication of known approaches. How small a large prime period oscillator can be?

It's worth noting that the use of 'period-multiplier' is misleading in this context. The quadri-Snarks are pulse dividers; it's impossible to make a prime number period oscillator via period multiplication.

Post by **dvgrn** » October 26th, 2024, 2:30 pm

confocaloid wrote: October 26th, 2024, 11:38 am The problem is interesting, especially if the aim is a pattern that's substantially more compact than would be achieved by just a reapplication of known approaches. How small a large prime period oscillator can be?

Yup, I definitely didn't tighten up the quadri-Snark chains quite as far as I could have, on the grounds that aligning everything to a 32x64 grid would make it easier for Golly to work with the resulting pattern. The connections around the edges definitely aren't optimized either.

It would be really interesting to work out a data storage mechanism that could be run by a universal computer, that could store data at a greater density than this stupid-simple chain of quadri-Snarks posted above.

I think the only really complete 2D data storage mechanism we have is the "SQ" a.k.a. "B2D" unit in the Osqrtlogt pattern, which can store one bit of data in a diamond-shaped region of 512 cells.

The 32x64 tiles in the quadri-Snark chains are each holding 8 bits of data, so that's a factor of two better storage density than a B2D unit can manage-- and again, the quadri-Snarks can be packed down slightly smaller (I think).

Then... it seems like there's bound to be a way to program a universal computer to complete a task and reset in exactly 2^136279841-1 ticks, in some way other than simply implementing a binary counter that cycles through all combinations of ON and OFF states for (some number slightly less than) 136279841 bits of memory. I haven't thought about what clever calculation might be able to make that happen yet, so I don't have a guess at how much smaller a UC-based solution might turn out to be.

(?)

confocaloid wrote: October 26th, 2024, 11:38 amIt's worth noting that the use of 'period-multiplier' is misleading in this context. The quadri-Snarks are pulse dividers; it's impossible to make a prime number period oscillator via period multiplication.

... Yeah, we've been through this before a time or two.

In this case the objection doesn't seem to be valid. What I'm talking about above is attaching a chain of 68,139,916 period multipliers to a base period-2^9 gun. Each additional quadri-Snark multiplies the period by 4, so the entire structure is a perfectly operational period-2^136279841 gun. The quadri-Snarks are being used as period multipliers to reach the target period.

Now, the output of the period-2^136279841 gun will then get used to change its own phase by one tick -- but that's a function of the reset mechanism, not of the period-multiplier-based gun. The addition of the reset mechanism doesn't mean that the period-multiplying quadri-Snarks suddenly have to get re-labeled as pulse dividers.

confocaloid · Post by **confocaloid** » October 26th, 2024, 2:55 pm

dvgrn wrote: October 26th, 2024, 2:30 pm
confocaloid wrote: October 26th, 2024, 11:38 amIt's worth noting that the use of 'period-multiplier' is misleading in this context. The quadri-Snarks are pulse dividers; it's impossible to make a prime number period oscillator via period multiplication.
[...] What I'm talking about above is attaching a chain of 68,139,916 period multipliers to a base period-2^9 gun. Each additional quadri-Snark multiplies the period by 4, so the entire structure is a perfectly operational period-2^136279841 gun. The quadri-Snarks are being used as period multipliers to reach the target period.

Now, the output of the period-2^136279841 gun will then get used to change its own phase by one tick -- but that's a function of the reset mechanism, not of the period-multiplier-based gun. The addition of the reset mechanism doesn't mean that the period-multiplying quadri-Snarks suddenly have to get re-labeled as pulse dividers.

My objection is that it's misleading to describe quadri-Snarks or other pulse-dividing components as "period multipliers" in those cases when the device doesn't really function as a period multiplier.
In this case, the topic is a prime-period oscillator, so it immediately follows that one cannot use period multiplication to obtain that prime period.

The reactions happening inside any chosen quadri-Snark also can't happen at any "subperiod", because the only possibilities of "subperiods" in a prime-period oscillator are p1 (stator) and the full period (rotor).

My point is that your descriptions are misleading, at least without added extra explanations of this kind. On the other hand, with such explanations of "what you really meant in this case", the description becomes even more confusing (even if maybe less misleading).

In contrast, it's always correct and clear to describe a quadri-Snark as a pulse divider, because it's what it is as a component. It doesn't matter whether the incoming pulses come in a periodic stream or not.

If you need to give more details about how exactly a pulse divider is used in a certain pattern, then such details can and should go separately.

Post by **dvgrn** » October 26th, 2024, 4:23 pm

confocaloid wrote: October 26th, 2024, 2:55 pm My point is that your descriptions are misleading, at least without added extra explanations of this kind. On the other hand, with such explanations of "what you really meant in this case", the description becomes even more confusing (even if maybe less misleading).

In contrast, it's always correct and clear to describe a quadri-Snark as a pulse divider, because it's what it is as a component. It doesn't matter whether the incoming pulses come in a periodic stream or not.

Hmm, well, confusingness is in the eye of the beholder, I suppose.

A quadri-Snark is always a pulse divider, but quite often it's also a period multiplier. If a quadri-Snark is acting as a period multiplier, then it's needlessly vague to call it a pulse divider -- it's actually something more specific, and I think it's generally better to use a more specific term when I have a choice. I don't say "active object" when I can say "Herschel".

The quadri-Snarks in this case are components of a gun with a period that's a very high multiple of its base loop -- so "period multiplier" is a nice specific accurate label for them. I would use "pulse divider" for quadri-Snarks only when I wanted to highlight some situation where they were _not_ acting as period multipliers.

EDIT: This certainly isn't worth another post, but I've gone back and looked at all of the uses of "period-multiplier" in the post that confocaloid objected to. I think there's nothing wrong with my uses of the term. That post doesn't contain a prime-period oscillator. It contains a macrocell representation of a long chain of quadri-Snarks. That pattern is intended to be attached to a period-2^9 base loop, to multiply its period by 2^136279832 (after a few quadri-Snarks are removed).

The result will be a period-2^136279841 gun. In the context of that gun, the quadri-Snarks are all period multipliers -- and so I don't believe that it's either misleading or confusing to call them that.

confocaloid · Post by **confocaloid** » October 26th, 2024, 4:45 pm

Well, this might be an attempt to restate something I wrote, but I think this situation is indeed a case when the quadri-Snarks _aren't_ really acting as period multipliers. The topic/the pattern is a prime-period oscillator. Every cell in the pattern either is permanently off, or is permanently on, or oscillates at the same period as the entire contraption.
The base loop would have a lower period if it was not connected to anything, however, it no longer works at that period within the large-prime-period oscillator.

A glider loop based gun followed by a chain of pulse dividers, on its own, would be an example when the pulse dividers are used as period multipliers. The overall period of the resulting gun is the product of the period of the glider loop and all the pulse division coefficients.
However, a larger prime period oscillator (even if using the above as a component) is no longer an example of period multiplication.

My own interest in pulse dividers (as an interesting and useful type of component/device) is precisely because they don't require an uniformly-spaced stream of pulses. A xN pulse divider is a "counting device" that emits one pulse for every N incoming pulses.

Post by **dvgrn** » October 27th, 2024, 4:27 pm

dvgrn wrote: October 26th, 2024, 11:30 am The new Mersenne prime find, M136279841, means that the prime-period oscillator in Golly's Very Large Patterns archive is no longer the largest prime period that we can easily build.

We can fix that, though! ...

In case the longer post above wasn't clear, I'd be very happy if someone wanted to take on the challenge of building a CGoL M136279841 oscillator or gun.

The oscillator could either use the initial quadri-Snark chain that I suggested, or (preferably) some other method that I haven't thought of that will make a smaller oscillator than 191197 by 182547.

Just post a note here if you plan to work on it, and then I (and/or maybe others) will know not to spend time on the problem for a while.

confocaloid · Post by **confocaloid** » October 27th, 2024, 5:25 pm

dvgrn wrote: October 27th, 2024, 4:27 pm [...] The oscillator could either use the initial quadri-Snark chain that I suggested, or (preferably) some other method that I haven't thought of that will make a smaller oscillator than 191197 by 182547. [...]

I'm not currently volunteering for the design+construction work, but for some more unobtrusive handwaving, there should be a significantly smaller oscillator (measuring by either the lowest single-phase bounding box area or the lowest single-phase population) that doesn't really go all the way through universal technologies. Send a slow spaceship, wait, send a faster salvo that will collide with the slow spaceship later, wait until a glider arrives back from the collision, combine with other components. There are ridiculously long lasting engineered diehards starting in a small region of the Life universe, so it feels likely that there are also ridiculously high period engineered oscillators with one phase fitting in a reasonably small region of the Life universe. Then it would remain to find an example whose period is of the desired order of magnitude, and find a way to adjust the period exactly.

Post by **dvgrn** » October 27th, 2024, 9:50 pm

confocaloid wrote: October 27th, 2024, 5:25 pm Then it would remain to find an example whose period is of the desired order of magnitude, and find a way to adjust the period exactly.

I would totally love to see someone succeed in accomplishing this trick.

Just as a bit of fair warning to anyone who is thinking of attempting this, though: M136279841 is a number with 41,024,320 decimal digits.

Pattern engineers mostly don't have a lot of experience with hitting numbers that big right on the nose. Engineered diehards are designed to keep sailing right on past various ridiculously large milestones, for sure -- but they're definitely not designed to stop precisely on one specific chosen T value.

Imagine that someone manages to find an adjustable ridiculously long-lasting engineered oscillator with exactly the right order of magnitude, out of the millions of other "nearby" orders of magnitude that it might happen to hit instead.

The one known thing that's special about 2^136279841-1 is that it's only one tick away from a period that we can reach with period multipliers. If a hypothetical new mechanism doesn't use that handy fact somehow, then it's going to have a fairly serious problem locating this one particular needle-sized number in a much-larger-than-universe-sized numerical haystack (link is a YouTube video showing all of M136279841's digits).

Even if an oscillator with the exact right order of magnitude does show up, the "adjusting the period exactly" part will still probably require a mechanism that can count precisely to some (arbitrary, slightly smaller) 41,024,320-digit number. Maybe a 41,024,319-digit number if you're lucky, but the odds are against that.

confocaloid · Post by **confocaloid** » November 10th, 2024, 6:14 pm

confocaloid wrote: October 27th, 2024, 5:25 pm [...] there should be a significantly smaller oscillator (measuring by either the lowest single-phase bounding box area or the lowest single-phase population) [...]

Measuring "small" by lowest the single-phase bounding box area, the problem is reduced to building a stable pulse divider with coefficient 2^N, where N < 136279841 but "close enough", with an additional requirement that the pulse divider should have a "small" state. (Without this requirement, one could continue as before with a giant packed array of chained pulse dividers.)

That should be possible using as a component a (much simpler) pulse divider with coefficient (N - 2). A reasonably convenient choice would be (N - 2 = 136279584 = 2^5 x 3^4 x 7^2 x 29 x 37) because that can be composed using several low-coefficient pulse dividers, while also being "close enough" to 136279841. I think it is possible to construct a large-prime-period oscillator using two sliding blocks (nonnegative integer variables), three demultiplexers, a permanent on/off switch, a bunch of low-coefficient stable pulse dividers, and a bunch of stable stateless components.

CARuler · Post by **CARuler** » January 1st, 2025, 2:08 am

a puffer whose output is adjustable

Post by **dvgrn** » January 1st, 2025, 11:48 am

CARuler wrote: January 1st, 2025, 2:08 am a puffer whose output is adjustable

This is still much too vague to be comprehensible. We ran into this problem with clarity a few weeks back.

We have lots of high-period puffers with adjustable output already. What specifically are you suggesting, that is different from all of the high-period adjustable puffers that we already know about?

... Looking at your example rule from the linked thread -- do you want something along the lines of GilGil's printer patterns? Here's an example in .MC format, complete with encryption and decryption technology:

Code: Select all

[M2] (golly 3.1)
#R B3/S23
$$$$....**$....**$
4 0 1 0 0
5 0 2 0 0
6 3 0 0 0
7 0 0 4 0
8 0 5 0 0
9 0 0 6 0
10 7 0 0 0
11 8 0 0 0
6 0 0 3 0
7 10 0 0 0
8 0 11 0 0
9 12 0 0 0
10 13 0 0 0
11 14 0 0 0
12 0 9 0 15
13 0 0 0 16
7 0 0 10 0
8 0 0 0 18
9 0 0 19 0
10 20 0 0 0
11 0 0 21 0
8 0 0 0 5
9 23 0 0 0
10 24 0 0 0
11 0 0 25 0
12 0 22 0 26
7 4 0 0 0
8 0 0 0 28
9 29 0 0 0
10 0 0 30 0
11 31 0 0 0
12 0 0 0 32
13 0 27 0 33
14 0 17 0 34
15 0 0 0 35
8 5 0 0 0
9 0 0 37 0
10 38 0 0 0
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22 0 0 25723 0

b-engine · Post by **b-engine** » January 11th, 2025, 6:23 am

A "true" wandering spaceship. This can been made by making a "replicator" that destructs itself upon successful replication, and the construction arm depends on a pseudo-random number generator which is extended by each replication, to switch the direction of the construction arm. The PRNG gets longer a bit by each replication, therefore making the result a "true" wandering spaceship.

confocaloid · Post by **confocaloid** » January 11th, 2025, 7:53 am

b-engine wrote: January 11th, 2025, 6:23 am A "true" wandering spaceship. This can been made by making a "replicator" that destructs itself upon successful replication, and the construction arm depends on a pseudo-random number generator which is extended by each replication, to switch the direction of the construction arm. The PRNG gets longer a bit by each replication, therefore making the result a "true" wandering spaceship.

I'm not sure if I understand the idea behind the word 'true'. It sounds like the PRNG would grow forever and there would be a non-periodic sequence somewhere, however, it would still remain a pseudo-random sequence (true randomness cannot be achieved solely through computations).

As far as I understand "spaceship" also needs to be put in quotes, since it would never repeat and wouldn't move in any single direction. (Actually the same also applies to the earlier "wandering spaceships" in OCA, too. Those are non-spaceships that can sometimes be obtained from a pair of spaceships in different CA.)

b-engine · Post by **b-engine** » January 12th, 2025, 4:49 am

confocaloid wrote: January 11th, 2025, 7:53 am I'm not sure if I understand the idea behind the word 'true'. It sounds like the PRNG would grow forever and there would be a non-periodic sequence somewhere, however, it would still remain a pseudo-random sequence (true randomness cannot be achieved solely through computations).

That's true - what I mean is that the PRNG will grow forever, and therefore the "spaceship" would never be a spaceship with a fixed direction and speed.

If the PRNG is removed before the construction of child begins, the "spaceship" would never halt, or else the PRNG would eventually be long enough to interfere and therefore reducing both the child and parent into ashes.

CARuler · Post by **CARuler** » January 24th, 2025, 12:36 am

dvgrn wrote: January 1st, 2025, 11:48 am

CARuler wrote: January 1st, 2025, 2:08 am a puffer whose output is adjustable

This is still much too vague to be comprehensible. We ran into this problem with clarity a few weeks back.

We have lots of high-period puffers with adjustable output already. What specifically are you suggesting, that is different from all of the high-period adjustable puffers that we already know about?

... Looking at your example rule from the linked thread -- do you want something along the lines of GilGil's printer patterns? Here's an example in .MC format, complete with encryption and decryption technology:

Code: Select all

[M2] (golly 3.1)
#R B3/S23
$$$$....**$....**$
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5 0 2 0 0
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11 19722 0 0 19653
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14 25637 25643 0 0
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11 20004 0 0 0
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13 25651 25653 0 0
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15 25601 25632 25644 25655
12 23673 0 23720 23579
12 0 0 23425 23590
11 0 0 19679 0
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11 0 0 19698 0
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12 0 23734 0 23607
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11 0 0 19190 0
12 25674 0 0 23567
12 0 23797 0 25322
11 0 0 19998 0
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12 25327 25616 25328 25329
13 25675 25676 25679 25680
14 25663 25668 25673 25681
12 23640 23499 0 0
12 23774 0 23702 25316
11 0 19163 0 0
12 0 0 25685 23699
11 0 0 0 19174
12 23703 23704 23799 25687
13 25683 25684 25686 25688
12 0 23532 23557 23575
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12 25633 0 0 25347
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11 0 20009 0 0
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13 25714 0 0 0
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17 25718 0 0 0
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19 0 25720 0 0
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22 0 0 25723 0

this is what i meant, even though i didn't know it existed

LuveelVoom · Post by **LuveelVoom** » February 18th, 2025, 9:17 pm

There’s been some discussion about pi climber pairs/groups in thread for your unsure discoveries. Since these groups can produce some fairly clean and glider making combinations, I wonder if a 9c/30o (3c/10) piship (or some multiple of that) could be constructed. Is this feasible? How would such a thing be done? My basic concept was to have combinations of pi climbers that fire gliders to form spaceships which then collide with forward fired gliders and fire more gliders back to make blocks for the climbers, but this is probably not that well thought out, as I’m not really a constructed ship maker.

hth3 · Post by **hth3** » February 23rd, 2025, 9:08 am

Can we build a retro Geminoid like Remini but with p46 technology (twin bee) instead of p30 (queen bee)?

Post by **dvgrn** » February 23rd, 2025, 6:49 pm

hth3 wrote: February 23rd, 2025, 9:08 am Can we build a retro Geminoid like Remini but with p46 technology (twin bee) instead of p30 (queen bee)?

Possibly. Would need to run a fresh set of searches to see if the presence or absence of gliders in an intermittent p46 stream is enough to allow for controlling an elbow to do universal construction. I don't think that that search has been done yet.

If it turns out that PUSH, PULL and FIRE recipes do exist for some choice of target elbow, I'd expect them to be quite a bit less efficient -- somewhere between half as efficient and one-tenth as efficient, maybe? That's just an unjustified guess, though, and the recipes might not exist at all.

LittleLWSS · Post by **LittleLWSS** » March 15th, 2025, 7:24 am

A computer that uses low-level "language"
A diagonoid
An obliquedoid
A "dinosaur"
A "mammal"
"Busy beaver"
A metacell in a metacell

User:HotdogPi/My discoveries · Post by **hotdogPi** » March 15th, 2025, 7:27 am

LittleLWSS wrote: March 15th, 2025, 7:24 am A computer that uses low-level "language"

APGsembly

LittleLWSS wrote: March 15th, 2025, 7:24 am A diagonoid

Demonoid

LittleLWSS wrote: March 15th, 2025, 7:24 am An obliquedoid

Not yet.

LittleLWSS wrote: March 15th, 2025, 7:24 am A "dinosaur"

There are a few members here that fit that description.

LittleLWSS wrote: March 15th, 2025, 7:24 am A "mammal"

Seal

LittleLWSS wrote: March 15th, 2025, 7:24 am "Busy beaver"

Impossible by definition; busy beaver is uncomputable.

LittleLWSS wrote: March 15th, 2025, 7:24 am A metacell in a metacell

Already been done.

b-engine · Post by **b-engine** » March 15th, 2025, 7:56 am

LittleLWSS wrote: March 15th, 2025, 7:24 am An obliquedoid

Gemini is a geminoid and an oblique spaceship.

EDIT: I challenge you all to make a constructed shuttle, bounding box ideally smaller than 8192 × 8192.

confocaloid · Post by **confocaloid** » March 15th, 2025, 5:10 pm

b-engine wrote: March 15th, 2025, 7:56 am [...] EDIT: I challenge you all to make a constructed shuttle, bounding box ideally smaller than 8192 × 8192.

A constructed shuttle? Just a shuttle oscillator? Something seems to be missing to make this into a challenge. The twin bees shuttle looks like a good existing example (variations copied from the wiki page shown below), and of course a pair of Jubjub reflectors with a single glider endlessly going back and forth between them would unambiguously count as a constructed shuttle.

Code: Select all

x = 81, y = 69, rule = B3/S23
50bo25bo$49bobo23bobo$49bobo23bobo$2o27b2o16b3ob2o21b2ob3o$bo27bo16bo
33bo$bobo23bobo17b3ob2o21b2ob3o$2b2o8bo14b2o20bob2o7bo13b2obo$11b2o46b
2o$10b2o46b2o$11b2o2b2o42b2o2b2o4$11b2o2b2o42b2o2b2o$10b2o46b2o$11b2o
46b2o$2b2o8bo14b2o31bo$bobo23bobo$bo27bo18b2o27b2o$2o27b2o18bo27bo$46b
3o29b3o$46bo33bo6$52b2o19b2o$52b2o19b2o2$12bo47bo$11b2o38b2o6b2o13b2o
$10b2o39b2o5b2o14b2o$4bo6b2o2b2o9bo32b2o2b2o$2b3o21b3o$bo27bo$2b3o21b
3o$4bo6b2o2b2o9bo32b2o2b2o$10b2o39b2o5b2o14b2o$11b2o38b2o6b2o13b2o$12b
o47bo2$52b2o19b2o$52b2o19b2o7$7b2o13b2o31b2o13b2o$6bobo13bobo29bobo13b
obo$7bo15bo31bo15bo2$12bo47bo$4b2o5b2o12b2o25b2o5b2o12b2o$4b2o4b2o13b
2o25b2o4b2o13b2o$11b2o2b2o42b2o2b2o4$11b2o2b2o42b2o2b2o$4b2o4b2o13b2o
21b2o8b2o17b2o$4b2o5b2o12b2o21b2o9b2o16b2o$12bo47bo2$7bo15bo28bo21bo$
6bobo13bobo26bobo19bobo$7b2o13b2o28b2o19b2o!

b-engine · Post by **b-engine** » March 15th, 2025, 8:08 pm

confocaloid wrote: March 15th, 2025, 5:10 pm A constructed shuttle? Just a shuttle oscillator? Something seems to be missing to make this into a challenge. The twin bees shuttle looks like a good existing example (variations copied from the wiki page shown below), and of course a pair of Jubjub reflectors with a single glider endlessly going back and forth between them would unambiguously count as a constructed shuttle.

I mean, a constructed shuttle that construct itself at different place with different orientation before self-destructing. More like a meta-pattern.

ConwayLife.com

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