666 rules
Posted: October 13th, 2024, 1:40 am
Nothing really diabolic. I came up with this idea, because I wanted to define hexagonal rules with photons. That requires a larger neighborhood, which can not be fully emulated in Golly, but a large subset of this rulespace can be defined as follows using Golly's weighted Larger-than-Life rules with the following custom neighborhood:
NW31073100000701010700310100013100070101070000310731H

That's where 666 comes from: it is 7^3-1=342 in base 7. Although Golly rulestrings are decimal, it is easier to memorize, for example, that survival of two immediate neighbors plus three edge neighbors plus five range-2 neighbors is 7-base 532 rather than 268. 666 (base 7) in the highest possible neighbor number,
Besides regular photons, we can have "hyperphotons", such as these ones in explosive rules that resemble Seeds:
A Sierpiński triangle builder:
Hyperphotonic rules can be stabilized by adding generations:
Here is one with stable splitters that can be used as guns:
And AND gate:
A "flying gun" rake in a "swarming" explosive rule, where photons breed like bugs:
Some rules are abundant with natural guns and reflectors:
Some oscillators:
Here are "regular" photons:
A replicator producing a Sierpiński triangle of photons:
NW31073100000701010700310100013100070101070000310731H

That's where 666 comes from: it is 7^3-1=342 in base 7. Although Golly rulestrings are decimal, it is easier to memorize, for example, that survival of two immediate neighbors plus three edge neighbors plus five range-2 neighbors is 7-base 532 rather than 268. 666 (base 7) in the highest possible neighbor number,
Besides regular photons, we can have "hyperphotons", such as these ones in explosive rules that resemble Seeds:
Code: Select all
x = 11, y = 11, rule = R2,C0,S,B14,56,NW31073100000701010700310100013100070101070000310731H
4$4b2o$3bo3bo!
Code: Select all
x = 12, y = 12, rule = R2,C0,S,B56-57,NW31073100000701010700310100013100070101070000310731H
3$3b2o2$3bo2bo!Code: Select all
x = 8, y = 9, rule = R2,C0,S0,B56-57,NW31073100000701010700310100013100070101070000310731H
3$2b2o$4bo!Here is one with stable splitters that can be used as guns:
Code: Select all
x = 145, y = 136, rule = R2,C3,S0,7,14,49,98,112,B56,99,NW31073100000701010700310100013100070101070000310731H
9$48.A$44.A$50.A4$52.A$44.A26.A$56.A$44.A30.B$58.A16.B$85.A2$46.A40.A
2$44.A$64.A$44.A10.A.A.A.A27.A$55.A.B2.B.A$57.B.A.B31.A2$55.A.A5.A.A
29.A6$78.A$77.B.A$78.B2$96.2B$85.A$92.A4.2A$85.A3.B$90.B3$87.A$58.2B$
85.A$59.2A48.A$85.A2$61.A27.2B$24.A$29.A27.A.A5.A.A22.2A12.A$24.A3.B.
A$29.B70.A.A5.A.A3$26.A2$24.A2$24.A2$28.2B2$29.2A6$55.A$55.A.B$57.B
10$38.A3$107.2B2$108.2A$91.A$91.A.B$93.B5$120.A5$115.A2$111.A.A5.A.A!
Code: Select all
x = 78, y = 84, rule = R2,C3,S0,7,14,49,98,112,B56,99,NW31073100000701010700310100013100070101070000310731H
14$14.A$10.A51.A$16.A42.B$60.B2$16.A$18.A$10.A5.B37.A$17.B.A2.A30.B.A
$10.A43.B$24.A2$13.A$12.A35.A$15.B31.B.A$10.A2.A.B32.B$23.2B5.A$10.A$
23.A2.A$25.A16.A$41.B.A$21.A.A5.A.A10.B2$16.2B2$17.2A17.A$35.B.A$36.B
4$30.A10.A$29.B.A14.A$30.B10.A2$22.2B$44.A$23.2A18.A$25.A20.B5.A$25.A
.B13.A2.A.B$27.B26.A$41.A2$54.A$37.A18.A$37.A.B14.B$39.B15.B.A2.A$47.
2B$62.A$47.A2.A$49.A2$45.A.A5.A.A5.A!Code: Select all
x = 26, y = 23, rule = R2,C3,S1,8,B9,50-51,NW31073100000701010700310100013100070101070000310731H
2$4.A8.ABA$3.A.B$3.ABA8.ABA$5.A$4.ABA$4.B.A12.A$5.A13.B.A$19.A.B$21.A
7$16.2A$15.A.B2AB$16.BA.B.A$19.2A!Code: Select all
x = 49, y = 56, rule = R2,C3,S1,9,B9,50-51,NW31073100000701010700310100013100070101070000310731H
6$20.A$19.AB$13.A6.B$14.A6.B$14.AB6.A$15.A$15.AB3.AB$16.A.B$10.BA8.B$
20.A$11.BA2$22.2B.A$25.B$18.3A2.2B.A6$30.A2.A$22.B5.BA.B.B$29.A2.2B2$
26.B4.B2.B$32.A.A$35.A$17.AB11.B4.BA$30.A3.BA$18.AB14.2A$30.A.B$31.B
2.BA$21.A10.A$22.B11.ABA$20.ABA$19.AB10.A$20.B2.BA5.A.B$20.AB2.B6.B$
24.BA$22.ABA$22.B$23.A!Code: Select all
x = 173, y = 132, rule = R2,C3,S100-342,B9,50-51,NW31073100000701010700310100013100070101070000310731H
10$9.A$10.B3.A$11.5A.A$17.2A.A$11.4A2.A.A$17.A.2A$11.5A.A2.A$14.A.A$
11.A.A$14.A.A$13.A.A2B38$126.AB8.A$133.A2.B$108.4A14.B2.A.A.4A$106.AB
A.A12.BA.A$110.2A.A2.A.A2.ABA.A3.A.3A.3A$99.B7.A2.A.A13.A.A$97.A.3A.
2A2.2A.2A4.4A.A.A.A.A3.2A.A.2A$121.A.A2.A3.A3.A2.A$97.2A.5A4.3A.2A2.
2A.2A7.4A.A4.B$100.A.A3.A.A12.A.A.A2.A.A$97.2A.A2.4A.4A.2A4.A3.4A.2A.
3A.A$102.A.A.A.A.A3.A6.A.A7.A.A$68.A28.A.5A2.A.2A4.A.A4.A.2A2.9A$67.A
.B29.A.A2.3A.A5.A.A2.A6.A6.A.A$68.B30.A2.2A.A2.2A6.A.3A.3A.A.10ABA$
99.A.A3.3A2.A2.B2.A.2A.2A3.A.A6.A$98.A4.A.4A.2A.2A2.6A3.2A3.A.A2.2A$
98.BA.A.A.2A2.A.2A5.A.A.6A.A3.A.A$105.A.4A.2A.A3.A2.2A.5A3.A.A$99.A.A
4.3A2.4A3.A.A.A4.A.A5.A$103.A.A6.5A.2A.3A.8A.4A$98.2BA.A2.A.A10.A.A8.
A3.A.A.2A$99.A3.A.A.4A.A.3A3.A.A.2A.2A.A.2A.2A$96.A5.A.A2.A4.A7.A10.A
3.A$97.A.A.2A3.2A.2A.A3.A.A.A.A11.4A$98.A.A.A21.5A4.A.A.2A$97.A.A.6A.
2A2.A.2A.A.2A.A6.A.A4.A$97.2A.A11.A3.A9.5A$98.2A.A.2A3.5A.A.7A.2A5.A.
A$104.BA3.A2.A.A.3A7.A3.3A.B$113.A.A.A2.3A.2A.A$116.4A5.A2.A2.2A3.A$
104.2AB6.A.A.A6.A3.5A.A.B$88.A5.BA7.A.B.A.2A.A.A10.A2.A.2A.A$89.B.B9.
3A5.A3.A.A7.BA.3A2.4A$90.B2A4.B11.A2.3A.A.A4.A6.A.2A$98.A.2A.A.A.A.A.
A.A.A.A.A3.2A.A3.A.A$100.A.A.A8.3A.2A8.4A.A$100.A8.A.A4.A.5A3.A3.A$
100.A.A.A4.2AB5.2A.A7.2A$92.B5.A.4A14.A2.6A3.A$100.A23.A3.A3.A$96.B.A
.4A.A17.A.A.A.2A.A$96.2AB.A.A2.A18.A.A.A3.A.A$103.A.A21.A.4A$106.A$
106.B$107.B$108.A!Code: Select all
x = 16, y = 9, rule = R2,C3,S100-342,B9-13,50-55,NW31073100000701010700310100013100070101070000310731H
2$5.B$3.ABAB.A$4.A3.2BA$3.A.A.A$4.A.2A!Code: Select all
x = 62, y = 123, rule = R2,C3,S147-342,B56,NW31073100000701010700310100013100070101070000310731H
10$13.A.A2$13.A.A.A2$15.A.A3.B$19.A.B$23.A.A$21.A$23.A.A.A2$25.A.A$
21.2A2$22.2B21$26.A.A$33.2A$22.A.A.A.A.A.A$32.A.2B$22.A.A3.A.A2$24.A.
A.A.A2$28.A.A5$39.2A2$40.2B10$45.2A2$46.2B2.A.A2$50.A.A.A2$45.B2.B3.A
.A.A$48.B$43.A5.B4.A.A$42.B3.A$45.B.A3.A2.B$40.A5.B3.B$39.B3.A$42.B.A
3.A$37.A5.B3.B$36.B3.A$39.B.A3.A$34.A5.B3.B$33.B3.A$36.B.A3.A$31.A5.B
3.B$30.B3.A$33.B.A3.A$28.A5.B3.B$27.B3.A$30.B.A3.A$25.A5.B3.B$24.B3.A
$27.B.A3.A$22.A5.B3.B$21.B3.A$24.B.A3.A$19.A5.B3.B$16.A.A3.A$21.B.A3.
A$16.A.A.A.B3.B$19.A.A$18.A.A3.A$17.A.A.A.A2$21.A.A$20.B!Code: Select all
x = 155, y = 82, rule = R2,C3,S1,3-7,B9,50-51,NW31073100000701010700310100013100070101070000310731H
8$24.A$20.2A2.B3.3A$19.A3B.B$21.2A2.B3.3A$26.A$22.A.A$21.A4BA$23.A.A$
35.AB$27.2A3.AB$26.A3BA2.BAB$28.2A12.A$16.B24.AB$13.B28.B$20.B22.B$
118.A$119.BA$44.B74.ABA$23.B96.AB$42.A74.B4.A$13.B26.B.B.A$44.A$44.A$
118.B$16.B$23.B96.B8.A$20.B103.2A4.BA$130.AB$128.BA2.BA$128.AB2.AB$
130.BA2.A$128.A.AB$127.AB$128.BA$127.AB2.AB$128.BA2.BA$128.A2.AB$132.
BA$132.A!Code: Select all
x = 7, y = 8, rule = R2,C0,S1,B50-51,NW31073100000701010700310100013100070101070000310731H
2$3bo$3bo2$3bo!Code: Select all
x = 33, y = 34, rule = R2,C0,S64,113,120,127,B3,5,54,57,99,103,106,148,155,NW31073100000701010700310100013100070101070000310731H
3$24bo$23bobo$22bob2o$21bob2o$22b2o2$18bo$17bobo$18b2o$17bo$14bobobo$
13bobob2o$14b2o2$10bo$9bobo12bo$10b2o11b2o$22bo$21b2o3$18bo$17b2o!
Code: Select all
x = 25, y = 28, rule = R2,C0,S0,6,64-66,113,120,127,B3,5,14,54,57,99,103,106,148,155,NW31073100000701010700310100013100070101070000310731H
8$8bo2$12bo$8bo2$12bo!