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Pipes (03-qy456/2ak/3)
Posted: March 30th, 2022, 12:00 am
by Yoel
This rule is closely related to Fireworld and is a priori known to be Turing-complete, because it supports Fireworld's Rule110 units. It is notable for common natural rakes that generate the
ruler function sequence and heavy puffers and breeders that I call pipes, quite similar to Star Wars' bases. It is omniperiodic (except p2, like all Generations rules).
The ruler function generator:
Code: Select all
x = 30, y = 27, rule = 03-qy456/2ak/3
13$17.2A$17.AB.A$15.2A.A2.A$15.ABA.A.B$16.A.A.A.B$19.B$19.A$20.2B$20.
2A!
Some common pipes:
Code: Select all
x = 47, y = 42, rule = 03-qy456/2ak/3
3$21.A6.A$20.3A.A.5A$21.10A2$21.10A$20.3A.A.5A$21.A6.A10$7.B.A3.A2.A
3.A.A2.A2.A.A$8.7A.7A.5AB3A$7.8A.7A.5AB3A$9.A3.A2.A3.A.A2.A2.A.A12$
25.A4.A$24.3A.5A$25.8A$24.B2.A.A.A!
Guns with periods >=10 can be constructed from splitter loops. I didn't find a p7 gun yet.
Code: Select all
x = 385, y = 331, rule = 03-qy456/2ak/3
29$66.B2.BA.BA.BA.BA.BA.BA.BA.BA.A$67.4A.BA.BA.BA.BA.BA.BA.BA$66.3A$
67.A9$67.A.A.B$67.B3A.BA.BA.BA.BA.BA.BA.BA.BA.BA.BA2.A$65.A.B2.A.BA.B
A.BA.BA.BA.BA.BA.BA.BA.BA8$67.BA$66.2A$65.4A$66.2A$66.2A$66.2A$66.A.B
A2.BA2.BA2.BA2.BA2.BA$66.A.BA2.BA2.BA2.BA2.BA2.BA2.A$66.2A$66.2A$66.
2A$65.4A$66.2A$67.BA9$66.A2.A.B$69.2B.BA3.BA3.BA3.BA3.BA3.A$68.B.A.BA
3.BA3.BA3.BA3.BA7$65.A.A$64.3AB$65.2A$66.2A$65.B$66.2B$65.A.A3.BA4.BA
4.BA4.BA4.BA4.BA5.A$65.A5.BA4.BA4.BA4.BA4.BA4.BA$64.3A$65.3A$66.A10$
60.A2.A5.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA3.A$59.7A3.BA
4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA$60.A2.2A.A$64.2AB$65.A$
65.A$64.3A$65.A7$67.A$65.4A$64.B2.A$63.A$62.3A$63.A3.BA6.BA6.BA6.BA2.
A$63.A3.BA6.BA6.BA6.BA$62.3A$63.A$64.B2.A$65.4A$67.A16$68.A2$66.B$67.
2A$66.2A$67.AB$67.2A2$66.B.A7.BA7.BA7.BA7.BA6.A$64.A.A.A7.BA7.BA7.BA
7.BA$63.4AB$64.A3.B6$65.A2$67.B$65.2A$66.2A$65.BA$65.2A2$212.A$58.AB
7.BA7.BA7.BA7.BA7.BA$53.A4.AB4.A2.BA7.BA7.BA7.BA7.BA5.A101.2A$212.2B$
64.2BA$65.A$65.2A$64.BA$64.2A2$64.A2$212.2A$212.2B5$61.A$67.BA7.BA7.B
A$67.BA7.BA7.BA8.A$63.2A$62.A2B147.2A$63.A148.2B$62.2A$63.AB$63.2A2$
64.A4$212.2A$212.2B4$64.A151.A.A2$62.B152.2A6.A$63.BA149.A2B5.3A$62.A
B148.AB.2A6.A$64.B144.A2.AB7.A.A$62.2B154.2B.2B$61.A.A7.BA8.BA$61.A9.
BA8.BA4.A107.A20.A.A$60.3A131.4A$61.A133.A2.B8.AB3.2BA.A$64.A132.AB8.
AB3.6A$63.3A150.A$64.A133.B$192.A5.B.A$203.A17.2A$192.A.ABA3.A.3A16.
2B$194.ABA6.A23.A$195.A6.2A$157.AB8.AB8.AB8.AB7.2B4.BA$155.A.AB8.AB8.
AB8.AB7.2A4.BA17.AB4.2A7.BA8.BA8.BA8.BA.A$221.AB4.2B7.BA8.BA8.BA8.BA$
64.A156.2A6.A$63.3A131.A23.A6.ABA$64.A137.2B16.3A.A3.ABA.A$64.2AB135.
2A17.A$64.2A158.A.B5.A$226.B$64.3A141.A$64.2A5.BA9.BA9.BA3.A108.6A3.B
A8.BA$64.2A5.BA9.BA9.BA113.A.A2B3.BA8.B2.A$64.3A160.4A$63.B.A.A138.A.
A20.A$67.B.A.A$60.A2.A.A.5A130.2B.2B$59.10A.3A128.A.A7.BA2.A$60.A.A.A
.A.B2.A129.A6.2A.BA$200.3A5.2BA$201.A6.2A2$206.A.A4$211.2B$211.2A9$
211.2B$211.2A9$211.2B$211.2A9$211.2B$211.2A2$212.A!
A rake gun based on a photon-to-rake transformer:
Code: Select all
x = 87, y = 43, rule = 03-qy456/2ak/3
12$17.A$74.A$73.3A$11.A2.B.A3.A2.B.A48.A$11.B2AB4.AB2AB$9.A.B2.A4.AB
2.A3$16.A11.BA18.BA18.BA$13.A2.A.A9.BA18.BA18.BA8.A$17.2B58.3A$78.A2$
10.A.B2.A4.AB2.A$12.B2AB4.AB2AB$12.A2.B.A3.A2.B.A2$10.A$18.A!
Reflectors:
Code: Select all
x = 108, y = 68, rule = 03-qy456/2ak/3
9$41.A5$41.2A$41.2B32.A4$41.2A$18.A.B2.A17.2BA$20.B2ABA3.BA3.BA3.BA4.
A$20.A2.BA3.BA3.BA3.BA3.3A$42.3A$43.A7$15.A2$75.2A$9.A2.B.A3.A2.B.A
51.2B$9.B2AB4.AB2AB$7.A.B2.A4.AB2.A3$14.A11.BA18.BA18.BA$11.A2.A.A9.B
A18.BA18.BA$15.2B$76.A$75.3A$8.A.B2.A4.AB2.A53.A$10.B2AB4.AB2AB$10.A
2.B.A3.A2.B.A2$8.A$16.A!
Splitters:
Code: Select all
x = 303, y = 151, rule = 03-qy456/2ak/3
30$92.A$91.3A$92.A$30.A2$53.A8.AB18.AB15.BA18.BA13.A$24.A2.BA4.A2.B.A
23.AB18.AB15.BA18.BA$24.B2ABA3.AB2AB$22.A.B2.A2.A.AB2.A16.A5.AB18.AB
21.BA18.BA10.A$59.AB18.AB21.BA18.BA2$46.BA18.BA18.BA$26.A4.A14.BA18.B
A18.BA3.A$90.3A$91.A2$23.A.B2.A2.A.AB2.A$25.B2ABA3.AB2AB$25.A2.BA4.A
2.B.A2$23.A$31.A19$93.A$92.3A101.A$93.A$27.A$85.A$84.3A10.BA8.BA15.A$
27.A57.A11.BA8.BA44.A$29.A55.2AB2.2A$85.B.A2.2B8.BA$84.B7.A7.BA22.A$
28.2B62.B$24.A2.A.A4.BA8.BA8.BA8.BA8.BA8.BA5.B.B58.2A42.2A$27.A6.BA8.
BA8.BA8.BA8.BA8.BA6.A59.2B42.2B$91.3A$92.A$27.A$29.A3$29.A2$152.2A42.
2A$152.2B42.2B3$189.A3$189.2A7.B$186.A2.2B6.B$191.A4.2A$152.2A36.ABA
4.A$152.2B32.A3.ABA.A.3A$197.A$188.B5.A$186.A.B2$158.A27.A10.BA8.BA8.
BA8.BA$189.2A6.BA8.BA8.BA8.BA4.A$189.2B$158.AB.BA8.BA8.BA8.A$96.A55.
2A4.AB.BA8.BA8.BA8.A$151.B38.3A$96.2BA53.A38.A$97.A53.3A.A7.A$97.A54.
A$96.A2B56.A2.2A3.A$97.2A59.2B$160.A$93.A7.BA8.BA8.BA8.BA8.BA8.BA6.AB
A$96.A4.BA8.BA8.BA8.BA8.BA8.BA7.A$159.3A$96.2BA61.A$97.A$97.A$96.A2B
2$98.A!
AND-NOT:
Code: Select all
x = 150, y = 149, rule = 03-qy456/2ak/3
14$32.A3$24.A2.A.B3.A.B2.A$27.2B.BA3.B2AB20.A$26.B.A.BA3.A2.B.A17.3A$
59.A2$29.A.A2B3.BA8.BA8.BA$28.6A3.BA8.BA8.BA5.A$29.A33.3A$64.A$54.A3.
2B$53.4A$54.A.A2B3$29.A$28.6A3.BA8.BA8.BA$29.A.A2B3.BA8.BA8.BA$57.2A$
58.A$26.B.A.BA3.A2.B.A16.3A$27.2B.BA3.B2AB19.A$24.A2.A.B3.A.B2.A3$32.
A10$63.A36$39.A2$39.2A$31.A2.A4.2B2.A$34.2A30.A$35.A3.A4.A2.A17.3A31.
A$66.A$65.2A$36.A.A7.BA8.BA8.A$35.4AB6.BA8.BA8.BA$36.A3.B2$62.A9.A$
61.3A7.3A$62.A7.3A$71.A$36.A3.B$35.4AB6.BA8.BA8.BA$36.A.A7.BA8.BA8.A$
65.2A$66.A$35.A3.A4.A2.A17.3A$34.2A30.A$31.A2.A4.2B2.A$39.2A2$39.A!
Spacefiller:
Code: Select all
x = 20, y = 12, rule = 03-qy456/2ak/3
2$7.2A.2A$7.2B.2B$5.AB5.BA$3.AB2.2A.2A2.BA$3.AB2.2A.2A2.BA$5.AB5.BA$
7.2B.2B$7.2A.2A!
Re: Pipes (03-qy456/2ak/3)
Posted: March 30th, 2022, 10:13 am
by breaker's glider gun
Ooh! a failedrep messy breeder!
Code: Select all
x = 330, y = 318, rule = 03-qy456/2ak/3
152$173.2A$173.ABA$172.B.A$173.A.A$171.AB.B.BA$169.2A3.A.A.BA$167.AB6.
A2.BA$167.AB$180.2A$170.B.BA6.2B$169.B.2A9.BA$170.A2.B6.2B2.BA$170.AB
A7.2A2.BA$169.B.A$160.2A15.2B7.2A$160.2B15.2A7.2B2$157.2A$157.2B2$154.
2A6.AB7.BA$154.2B6.AB7.BA2$151.2A12.AB.BA$151.2B12.AB.BA$167.B$167.A9.
2B19.2A$168.2B2.A4.2A19.2B$168.2A$145.2A25.A28.2A$145.2B54.2B2$142.2A
6.AB31.BA19.2A$142.2B6.AB31.BA19.2B2$139.2A12.AB25.BA25.2A$139.2B12.A
B25.BA25.2B$166.2B33.BA$136.2A18.AB8.2A9.BA22.BA7.2A$136.2B18.AB19.BA
31.2B$198.BA$133.2A5.AB17.AB9.A27.BA13.2A$133.2B5.AB17.AB52.2B$195.BA
$130.2A30.AB6.A24.BA19.2A$130.2B30.AB52.2B$151.2B39.BA$127.2A22.2A12.
AB.BA22.BA25.2A$127.2B36.AB.BA49.2B$154.2B11.B2.AB17.BA$124.2A6.AB20.
2A11.A3.B17.BA31.2A$124.2B6.AB34.2BA51.2B$157.2B9.2A3.AB11.BA$121.2A12.
AB20.2A14.AB11.BA37.2A$121.2B12.AB88.2B$160.2B14.AB5.BA$118.2A18.AB20.
2A14.AB5.BA43.2A$118.2B18.AB32.A55.2B$163.2B14.ABA$115.2A24.AB20.2A7.
A6.ABA49.2A$115.2B24.AB37.A50.2B$178.2B$112.2A6.AB22.AB32.2A33.BA19.2A
$112.2B6.AB22.AB67.BA19.2B2$109.2A12.AB22.AB38.B22.BA25.2A$109.2B12.A
B22.AB37.B23.BA25.2B$231.BA$106.2A18.AB22.AB16.A38.BA22.BA7.2A$106.2B
18.AB22.AB55.BA31.2B$187.BA39.BA$103.2A5.AB17.AB56.BA39.BA13.2A$103.2B
5.AB17.AB112.2B$225.BA$100.2A30.AB36.A54.BA19.2A$100.2B30.AB112.2B$222.
BA$97.2A36.AB33.A51.BA25.2A$97.2B36.AB112.2B$219.BA$94.2A6.AB34.AB30.
A48.BA31.2A$94.2B6.AB34.AB112.2B$177.A38.BA$91.2A12.AB34.AB41.BA30.BA
37.2A$91.2B12.AB34.AB27.A13.BA69.2B$213.BA$88.2A18.AB34.AB67.BA43.2A$
88.2B18.AB34.AB112.2B$190.BA18.BA$85.2A24.AB34.AB41.BA18.BA49.2A$85.2B
24.AB34.AB112.2B$207.BA$82.2A6.AB22.AB34.AB18.A36.BA34.BA19.2A$82.2B6.
AB22.AB34.AB91.BA19.2B$204.BA$79.2A12.AB22.AB48.A36.BA10.BA22.BA25.2A
$79.2B12.AB22.AB97.BA22.BA25.2B$201.BA58.BA$76.2A18.AB22.AB79.BA34.BA
22.BA7.2A$76.2B18.AB22.AB115.BA31.2B$198.BA17.BA39.BA$73.2A5.AB17.AB97.
BA17.BA39.BA13.2A$73.2B5.AB17.AB172.2B$195.BA58.BA$70.2A30.AB66.A24.B
A58.BA19.2A$70.2B30.AB172.2B$192.BA58.BA$67.2A36.AB63.A21.BA58.BA25.2A
$67.2B36.AB172.2B$179.A9.BA58.BA$64.2A6.AB34.AB79.BA58.BA31.2A$64.2B6.
AB34.AB172.2B$171.A2.BA70.BA$61.2A12.AB34.AB53.AB6.BA38.BA30.BA37.2A$
61.2B12.AB34.AB53.AB2.A43.BA69.2B$243.BA$58.2A18.AB34.AB127.BA43.2A$58.
2B18.AB34.AB172.2B$163.2B55.BA18.BA$55.2A24.AB34.AB44.2A55.BA18.BA49.
2A$55.2B24.AB34.AB172.2B$237.BA$52.2A6.AB22.AB34.AB48.A66.BA34.BA19.2A
$52.2B6.AB22.AB34.AB151.BA19.2B$234.BA$49.2A12.AB22.AB78.A66.BA34.BA25.
2A$49.2B12.AB22.AB181.BA25.2B$231.BA58.BA$46.2A18.AB22.AB139.BA34.BA22.
BA7.2A$46.2B18.AB22.AB175.BA31.2B$228.BA17.BA39.BA$43.2A5.AB17.AB157.
BA17.BA39.BA13.2A$43.2B5.AB17.AB232.2B$225.BA58.BA$40.2A30.AB96.A54.B
A58.BA19.2A$40.2B30.AB232.2B$222.BA58.BA$37.2A36.AB93.A51.BA58.BA25.2A
$37.2B36.AB232.2B$179.A39.BA58.BA$34.2A6.AB34.AB139.BA58.BA31.2A$34.2B
6.AB34.AB232.2B$171.A2.BA3.BA3.BA3.BA3.BA3.BA3.BA70.BA$31.2A12.AB34.A
B53.AB3.AB3.AB3.AB3.AB3.AB3.AB6.BA3.BA3.BA3.BA3.BA3.BA3.BA38.BA30.BA37.
2A$31.2B12.AB34.AB53.AB3.AB3.AB3.AB3.AB3.AB3.AB2.A73.BA69.2B$273.BA$28.
2A18.AB34.AB187.BA43.2A$28.2B18.AB34.AB232.2B$250.BA18.BA$25.2A24.AB34.
AB161.BA18.BA49.2A$25.2B24.AB34.AB232.2B$267.BA$22.2A6.AB22.AB34.AB78.
A96.BA34.BA19.2A$22.2B6.AB22.AB34.AB211.BA19.2B$264.BA$19.2A12.AB22.A
B108.A96.BA10.BA22.BA25.2A$19.2B12.AB22.AB217.BA22.BA25.2B$261.BA58.B
A$16.2A18.AB22.AB199.BA34.BA22.BA$16.2B18.AB22.AB235.BA$258.BA17.BA39.
BA$13.2A5.AB17.AB217.BA17.BA39.BA$13.2B5.AB17.AB$255.BA58.BA$10.2A30.
AB126.A84.BA58.BA$10.2B30.AB!
Re: Pipes (03-qy456/2ak/3)
Posted: March 30th, 2022, 10:41 pm
by Ohhhhhhhhh
breaker's glider gun wrote: March 30th, 2022, 10:13 am
Ooh! a failedrep messy breeder!
Code: Select all
x = 330, y = 318, rule = 03-qy456/2ak/3
152$173.2A$173.ABA$172.B.A$173.A.A$171.AB.B.BA$169.2A3.A.A.BA$167.AB6.
A2.BA$167.AB$180.2A$170.B.BA6.2B$169.B.2A9.BA$170.A2.B6.2B2.BA$170.AB
A7.2A2.BA$169.B.A$160.2A15.2B7.2A$160.2B15.2A7.2B2$157.2A$157.2B2$154.
2A6.AB7.BA$154.2B6.AB7.BA2$151.2A12.AB.BA$151.2B12.AB.BA$167.B$167.A9.
2B19.2A$168.2B2.A4.2A19.2B$168.2A$145.2A25.A28.2A$145.2B54.2B2$142.2A
6.AB31.BA19.2A$142.2B6.AB31.BA19.2B2$139.2A12.AB25.BA25.2A$139.2B12.A
B25.BA25.2B$166.2B33.BA$136.2A18.AB8.2A9.BA22.BA7.2A$136.2B18.AB19.BA
31.2B$198.BA$133.2A5.AB17.AB9.A27.BA13.2A$133.2B5.AB17.AB52.2B$195.BA
$130.2A30.AB6.A24.BA19.2A$130.2B30.AB52.2B$151.2B39.BA$127.2A22.2A12.
AB.BA22.BA25.2A$127.2B36.AB.BA49.2B$154.2B11.B2.AB17.BA$124.2A6.AB20.
2A11.A3.B17.BA31.2A$124.2B6.AB34.2BA51.2B$157.2B9.2A3.AB11.BA$121.2A12.
AB20.2A14.AB11.BA37.2A$121.2B12.AB88.2B$160.2B14.AB5.BA$118.2A18.AB20.
2A14.AB5.BA43.2A$118.2B18.AB32.A55.2B$163.2B14.ABA$115.2A24.AB20.2A7.
A6.ABA49.2A$115.2B24.AB37.A50.2B$178.2B$112.2A6.AB22.AB32.2A33.BA19.2A
$112.2B6.AB22.AB67.BA19.2B2$109.2A12.AB22.AB38.B22.BA25.2A$109.2B12.A
B22.AB37.B23.BA25.2B$231.BA$106.2A18.AB22.AB16.A38.BA22.BA7.2A$106.2B
18.AB22.AB55.BA31.2B$187.BA39.BA$103.2A5.AB17.AB56.BA39.BA13.2A$103.2B
5.AB17.AB112.2B$225.BA$100.2A30.AB36.A54.BA19.2A$100.2B30.AB112.2B$222.
BA$97.2A36.AB33.A51.BA25.2A$97.2B36.AB112.2B$219.BA$94.2A6.AB34.AB30.
A48.BA31.2A$94.2B6.AB34.AB112.2B$177.A38.BA$91.2A12.AB34.AB41.BA30.BA
37.2A$91.2B12.AB34.AB27.A13.BA69.2B$213.BA$88.2A18.AB34.AB67.BA43.2A$
88.2B18.AB34.AB112.2B$190.BA18.BA$85.2A24.AB34.AB41.BA18.BA49.2A$85.2B
24.AB34.AB112.2B$207.BA$82.2A6.AB22.AB34.AB18.A36.BA34.BA19.2A$82.2B6.
AB22.AB34.AB91.BA19.2B$204.BA$79.2A12.AB22.AB48.A36.BA10.BA22.BA25.2A
$79.2B12.AB22.AB97.BA22.BA25.2B$201.BA58.BA$76.2A18.AB22.AB79.BA34.BA
22.BA7.2A$76.2B18.AB22.AB115.BA31.2B$198.BA17.BA39.BA$73.2A5.AB17.AB97.
BA17.BA39.BA13.2A$73.2B5.AB17.AB172.2B$195.BA58.BA$70.2A30.AB66.A24.B
A58.BA19.2A$70.2B30.AB172.2B$192.BA58.BA$67.2A36.AB63.A21.BA58.BA25.2A
$67.2B36.AB172.2B$179.A9.BA58.BA$64.2A6.AB34.AB79.BA58.BA31.2A$64.2B6.
AB34.AB172.2B$171.A2.BA70.BA$61.2A12.AB34.AB53.AB6.BA38.BA30.BA37.2A$
61.2B12.AB34.AB53.AB2.A43.BA69.2B$243.BA$58.2A18.AB34.AB127.BA43.2A$58.
2B18.AB34.AB172.2B$163.2B55.BA18.BA$55.2A24.AB34.AB44.2A55.BA18.BA49.
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AB126.A84.BA58.BA$10.2B30.AB!
Are you calling me or just Oohing?
Re: Pipes (03-qy456/2ak/3)
Posted: March 31st, 2022, 9:04 am
by breaker's glider gun
Ohhhhhhhhh wrote: March 30th, 2022, 10:41 pm
Are you calling me or just Oohing?
just Oohing.
Sorry, did not think
Re: Pipes (03-qy456/2ak/3)
Posted: March 31st, 2022, 10:47 pm
by Ohhhhhhhhh
Yoel wrote: March 30th, 2022, 12:00 am
AND-NOT:
Code: Select all
x = 150, y = 149, rule = 03-qy456/2ak/3
14$32.A3$24.A2.A.B3.A.B2.A$27.2B.BA3.B2AB20.A$26.B.A.BA3.A2.B.A17.3A$
59.A2$29.A.A2B3.BA8.BA8.BA$28.6A3.BA8.BA8.BA5.A$29.A33.3A$64.A$54.A3.
2B$53.4A$54.A.A2B3$29.A$28.6A3.BA8.BA8.BA$29.A.A2B3.BA8.BA8.BA$57.2A$
58.A$26.B.A.BA3.A2.B.A16.3A$27.2B.BA3.B2AB19.A$24.A2.A.B3.A.B2.A3$32.
A10$63.A36$39.A2$39.2A$31.A2.A4.2B2.A$34.2A30.A$35.A3.A4.A2.A17.3A31.
A$66.A$65.2A$36.A.A7.BA8.BA8.A$35.4AB6.BA8.BA8.BA$36.A3.B2$62.A9.A$
61.3A7.3A$62.A7.3A$71.A$36.A3.B$35.4AB6.BA8.BA8.BA$36.A.A7.BA8.BA8.A$
65.2A$66.A$35.A3.A4.A2.A17.3A$34.2A30.A$31.A2.A4.2B2.A$39.2A2$39.A!
Your and-not doesn’t seems to be as useful - it looks like only one side giving an input signal will give an output, which is called “not-and” (my English is not good so I’m not sure) probably. But, generally, it’s also proof of Turing-completeness.
Edit #1:
New splitter, probably better:
Code: Select all
#CXRLE Pos=-3,-12
x = 11, y = 12, rule = 03-qy456/2ak/3
9.A$8.3A$9.A3$2.A3$BA$BA5.A$6.3A$7.A!
Edit #2: It’s period is 10 and 12, 13, etc. (10, 12+)
I think it will be worth to create a universal constructor.
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 5:49 am
by Yoel
Not really a proof, but a strong indication of being Turing-complete. A rigid proof requires an explicit construction of infinitely extendable Rule110 units or another known universal computation model with an infinite tape. Strictly speaking, even a "rosary" is a not a formal proof in mathematical sense. In my experience, the main problem with circuitry is synchronization issues. While a rule may have splitters and logic gates, putting everything in place requires some mechanisms that allow to delay a photon or whatever signal agent by a certain number of gens, or to move, or to phase-shift it in a specific way. For example, I've almost built a Rule110 unit for Bugs (a well known Larger than Life rule), but I can no yet figure out how to synchronize the units by shifting the bugs (spaceships) to a very specific position. Brian's Brain, although it's badly explosive, was surprisingly easier to handle.
People on this forum usually call this gate "AND-NOT". If you mean NAND, I have one, but it is embarrassingly bulky. If I come up with something neat, I'll post it. Anyhow, this rule
is Turing-complete, because it is largely compatible with Fireworld. See below Rule110 copied from Fireworld.
Thanks for the splitter, it is clearly the best so far!
Still looking for a p7 gun.
Code: Select all
x = 1568, y = 311, rule = 03-qy456/2ak/3:T1568,0
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15.A14.BA3.2A10.AB62.A15.A14.BA3.2A10.AB$29.A2B12.B17.2A7.A2.A5.A2.A
57.A2B12.B17.2A7.A2.A5.A2.A57.A2B12.B17.2A7.A2.A5.A2.A57.A2B12.B17.2A
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75.2A7.2A101.2A7.2A101.2A7.2A101.2A7.2A101.2A7.2A101.2A7.2A101.2A7.2A
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A$61.A18.A92.A18.A92.A18.A92.A18.A92.A18.A92.A18.A92.A18.A92.A18.A92.
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81.A29.A81.A29.A81.A29.A81.A29.A81.A29.A81.A29.A81.A29.A81.A29.A$56.B
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5.A22.A65.2BA10.B2ABA5.A22.A65.2BA10.B2ABA5.A22.A65.2BA10.B2ABA5.A22.
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A10.B2ABA5.A22.A65.2BA10.B2ABA5.A22.A65.2BA10.B2ABA5.A22.A65.2BA10.B
2ABA5.A22.A$64.A11.A2.BA95.A11.A2.BA95.A11.A2.BA95.A11.A2.BA95.A11.A
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53.A2B44.BA3.B2.A2.A53.A2B44.BA3.B2.A2.A53.A2B44.BA$79.AB23.A2.A2.BA
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BA$59.A5.A13.AB2.A2.A84.A5.A13.AB2.A2.A84.A5.A13.AB2.A2.A84.A5.A13.AB
2.A2.A84.A5.A13.AB2.A2.A84.A5.A13.AB2.A2.A84.A5.A13.AB2.A2.A84.A5.A
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5.A13.AB2.A2.A84.A5.A13.AB2.A2.A84.A5.A13.AB2.A2.A$5.2A110.2A110.2A
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25.AB9.AB43.A2.A.B3.A2.A.B11.A2.BA25.AB$6.2A46.2B.BA4.2B12.B2ABA5.A
18.BA10.2A46.2B.BA4.2B12.B2ABA5.A18.BA10.2A46.2B.BA4.2B12.B2ABA5.A18.
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BA4.2B12.B2ABA5.A18.BA$53.B.A.BA3.B.A2.A7.A.B2.A2.A22.2A57.B.A.BA3.B.
A2.A7.A.B2.A2.A22.2A57.B.A.BA3.B.A2.A7.A.B2.A2.A22.2A57.B.A.BA3.B.A2.
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2A$7.A80.A2.A27.A80.A2.A27.A80.A2.A27.A80.A2.A27.A80.A2.A27.A80.A2.A
27.A80.A2.A27.A80.A2.A27.A80.A2.A27.A80.A2.A27.A80.A2.A27.A80.A2.A27.
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A111.A111.A111.A111.A$83.A111.A111.A111.A111.A111.A111.A111.A111.A
111.A111.A111.A111.A111.A$59.2B110.2B110.2B110.2B110.2B110.2B110.2B
110.2B110.2B110.2B110.2B110.2B110.2B110.2B$59.2A110.2A110.2A110.2A
110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A6$71.A
111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A$36.
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33.A73.A3.A33.A$70.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A
110.2A110.2A110.2A110.2A110.2A$59.2B9.2B99.2B9.2B99.2B9.2B99.2B9.2B
99.2B9.2B99.2B9.2B99.2B9.2B99.2B9.2B99.2B9.2B99.2B9.2B99.2B9.2B99.2B
9.2B99.2B9.2B99.2B9.2B$59.2A110.2A110.2A110.2A110.2A110.2A110.2A110.
2A110.2A110.2A110.2A110.2A110.2A110.2A$40.2A110.2A110.2A110.2A110.2A
110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A$39.2A19.A90.2A
19.A90.2A19.A90.2A19.A90.2A19.A90.2A19.A90.2A19.A90.2A19.A90.2A19.A
90.2A19.A90.2A19.A90.2A19.A90.2A19.A90.2A19.A$64.B.A.BA3.B.A2.A97.B.A
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3.B.A2.A$65.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B101.2B.BA
4.2B101.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B
101.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B101.2B.BA4.2B$39.A22.A2.A.B3.A
2.A.B74.A22.A2.A.B3.A2.A.B74.A22.A2.A.B3.A2.A.B74.A22.A2.A.B3.A2.A.B
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67.A33.A5.A$51.B.A2.A106.B.A2.A106.B.A2.A106.B.A2.A106.B.A2.A106.B.A
2.A106.B.A2.A106.B.A2.A106.B.A2.A106.B.A2.A106.B.A2.A106.B.A2.A106.B.
A2.A106.B.A2.A$48.A.B.2B106.A.B.2B106.A.B.2B106.A.B.2B106.A.B.2B106.A
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A.B.2B106.A.B.2B$50.B.A.B35.A71.B.A.B35.A71.B.A.B35.A71.B.A.B35.A71.B
.A.B35.A71.B.A.B35.A71.B.A.B35.A71.B.A.B35.A71.B.A.B35.A71.B.A.B35.A
71.B.A.B35.A71.B.A.B35.A71.B.A.B35.A71.B.A.B35.A$93.A9.2A100.A9.2A
100.A9.2A100.A9.2A100.A9.2A100.A9.2A100.A9.2A100.A9.2A100.A9.2A100.A
9.2A100.A9.2A100.A9.2A100.A9.2A100.A9.2A$103.2B110.2B110.2B110.2B110.
2B110.2B110.2B110.2B110.2B110.2B110.2B110.2B110.2B110.2B$93.2A110.2A
110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A110.2A
110.2A$A.A28.A2.A13.A43.A2B15.A.A.A28.A2.A13.A43.A2B15.A.A.A28.A2.A
13.A43.A2B15.A.A.A28.A2.A13.A43.A2B15.A.A.A28.A2.A13.A43.A2B15.A.A.A
28.A2.A13.A43.A2B15.A.A.A28.A2.A13.A43.A2B15.A.A.A28.A2.A13.A43.A2B
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2.A13.A43.A2B15.A$39.A53.A57.A53.A57.A53.A57.A53.A57.A53.A57.A53.A57.
A53.A57.A53.A57.A53.A57.A53.A57.A53.A57.A53.A57.A53.A57.A53.A$35.A57.
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57.A53.A57.A53.A57.A53.A57.A53.A57.A$92.2BA109.2BA109.2BA109.2BA109.
2BA109.2BA109.2BA109.2BA109.2BA109.2BA109.2BA109.2BA109.2BA109.2BA2$
31.A60.A50.A60.A50.A60.A50.A60.A50.A60.A50.A60.A50.A60.A50.A60.A50.A
60.A50.A60.A50.A60.A50.A60.A50.A60.A50.A60.A$39.A111.A111.A111.A111.A
111.A111.A111.A111.A111.A111.A111.A111.A111.A$30.2B71.2A37.2B71.2A37.
2B71.2A37.2B71.2A37.2B71.2A37.2B71.2A37.2B71.2A37.2B71.2A37.2B71.2A
37.2B71.2A37.2B71.2A37.2B71.2A37.2B71.2A37.2B71.2A$27.BA7.BA.A63.2B
34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA
7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.
A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.2B34.BA7.BA.A63.
2B$25.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.
4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A99.4A5.4A$23.A.AB
4.A2.AB8.A4.A10.A4.A10.A4.A10.A4.A37.A.AB4.A2.AB8.A4.A10.A4.A10.A4.A
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10.A4.A10.A4.A10.A4.A2$43.2A110.2A110.2A110.2A110.2A110.2A110.2A110.
2A110.2A110.2A110.2A110.2A110.2A110.2A$30.A5.BA5.2B4.A16.A14.A16.A43.
A5.BA5.2B4.A16.A14.A16.A43.A5.BA5.2B4.A16.A14.A16.A43.A5.BA5.2B4.A16.
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14.A16.A43.A5.BA5.2B4.A16.A14.A16.A43.A5.BA5.2B4.A16.A14.A16.A43.A5.B
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A16.A$27.A8.BA69.A31.A8.BA69.A31.A8.BA69.A31.A8.BA69.A31.A8.BA69.A31.
A8.BA69.A31.A8.BA69.A31.A8.BA69.A31.A8.BA69.A31.A8.BA69.A31.A8.BA69.A
31.A8.BA69.A31.A8.BA69.A31.A8.BA69.A$48.2B11.B2.2A94.2B11.B2.2A94.2B
11.B2.2A94.2B11.B2.2A94.2B11.B2.2A94.2B11.B2.2A94.2B11.B2.2A94.2B11.B
2.2A94.2B11.B2.2A94.2B11.B2.2A94.2B11.B2.2A94.2B11.B2.2A94.2B11.B2.2A
94.2B11.B2.2A$60.B4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B
4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B
4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B
4.2A8.2A20.2A73.B4.2A8.2A20.2A73.B4.2A8.2A20.2A$75.2B20.2B4.2A82.2B
20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A82.
2B20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A
82.2B20.2B4.2A82.2B20.2B4.2A82.2B20.2B4.2A$24.A.AB4.A2.AB28.2B13.2A
21.2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.A
B4.A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.
2B13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.
2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.AB4.
A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.2B31.A.AB4.A2.AB28.2B
13.2A21.2B31.A.AB4.A2.AB28.2B13.2A21.2B$26.4A5.4A9.2A30.2B10.2A44.4A
5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A
5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A
5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A
5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A5.4A9.2A30.2B10.2A44.4A
5.4A9.2A30.2B10.2A$28.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA31.B9.2B
46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA31.B
9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA
31.B9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.
2BA31.B9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.A7.2BA31.B9.2B46.BA7.BA.
A7.2BA31.B9.2B$31.2B16.A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.
A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.
A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.
A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.
A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A44.2B16.A15.A14.AB15.2A$43.2A4.
A17.A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A
17.A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.
A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.A
13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.A13.BA15.2A55.2A4.A17.A13.
BA15.2A55.2A4.A17.A13.BA15.2A$32.A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.
A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.A10.2B3.A2B29.B
63.A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.A10.2B3.A2B
29.B63.A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.A10.2B3.A2B29.B63.A10.2B3.
A2B29.B2$50.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.
A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A
16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A
5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A62.A9.2A5.A14.A16.A$
60.2B13.2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B13.
2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B13.2A95.2B
13.2A$75.2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A82.
2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A82.2B26.2A
82.2B26.2A$36.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A
4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A
2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A
2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.
AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A
8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B
.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB
2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.
A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A
2.2B43.A2.A4.AB2.A7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B43.A2.A4.AB2.A
7.BA7.BA.A2.A8.A5.A2.BA.A2.A2.B.A2.2B$45.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB
2AB58.B8.4A5.4A4.2A7.2A4.B2ABA3.AB2AB$40.A2.2A4.A2.A.AB5.A.AB7.A2.A5.
A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.A2.
2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.
A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.
A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.
A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A
53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.A
B7.A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB
2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.
A.AB7.A2.A5.A2.A.B2.A4.AB2.A53.A2.2A4.A2.A.AB5.A.AB7.A2.A5.A2.A.B2.A
4.AB2.A3$44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A
44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.
A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.B
A4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A44.A
15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.
A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A2.A44.A15.A15.A15.A6.A2.BA4.A
2.A$102.B111.B111.B111.B111.B111.B111.B111.B111.B111.B111.B111.B111.B
111.B$95.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A
4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.
A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A99.A2.A4.2A2.A3$
103.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.A111.
A!
Ohhhhhhhhh wrote: March 31st, 2022, 10:47 pm
Yoel wrote: March 30th, 2022, 12:00 am
AND-NOT:
Code: Select all
x = 150, y = 149, rule = 03-qy456/2ak/3
14$32.A3$24.A2.A.B3.A.B2.A$27.2B.BA3.B2AB20.A$26.B.A.BA3.A2.B.A17.3A$
59.A2$29.A.A2B3.BA8.BA8.BA$28.6A3.BA8.BA8.BA5.A$29.A33.3A$64.A$54.A3.
2B$53.4A$54.A.A2B3$29.A$28.6A3.BA8.BA8.BA$29.A.A2B3.BA8.BA8.BA$57.2A$
58.A$26.B.A.BA3.A2.B.A16.3A$27.2B.BA3.B2AB19.A$24.A2.A.B3.A.B2.A3$32.
A10$63.A36$39.A2$39.2A$31.A2.A4.2B2.A$34.2A30.A$35.A3.A4.A2.A17.3A31.
A$66.A$65.2A$36.A.A7.BA8.BA8.A$35.4AB6.BA8.BA8.BA$36.A3.B2$62.A9.A$
61.3A7.3A$62.A7.3A$71.A$36.A3.B$35.4AB6.BA8.BA8.BA$36.A.A7.BA8.BA8.A$
65.2A$66.A$35.A3.A4.A2.A17.3A$34.2A30.A$31.A2.A4.2B2.A$39.2A2$39.A!
Your and-not doesn’t seems to be as useful - it looks like only one side giving an input signal will give an output, which is called “not-and” (my English is not good so I’m not sure) probably. But, generally, it’s also proof of Turing-completeness.
Edit #1:
New splitter, probably better:
Code: Select all
#CXRLE Pos=-3,-12
x = 11, y = 12, rule = 03-qy456/2ak/3
9.A$8.3A$9.A3$2.A3$BA$BA5.A$6.3A$7.A!
Edit #2: It’s period is 10 and 12, 13, etc. (10, 12+)
I think it will be worth to create a universal constructor.
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 7:56 am
by AbhpzTa
p7 gun:
Code: Select all
x = 7, y = 10, rule = 03-qy456/2ak/3
.A3.A$3A.3A$.A3.A$.A$.2A2.A$2A$.2A$2.2A$.3AB$2.A.A!
Yoel wrote: March 30th, 2022, 12:00 am...
Guns with periods >=10 can be constructed from splitter loops. I didn't find a p7 gun yet.
Code: Select all
x = 385, y = 331, rule = 03-qy456/2ak/3
29$66.B2.BA.BA.BA.BA.BA.BA.BA.BA.A$67.4A.BA.BA.BA.BA.BA.BA.BA$66.3A$
67.A9$67.A.A.B$67.B3A.BA.BA.BA.BA.BA.BA.BA.BA.BA.BA2.A$65.A.B2.A.BA.B
A.BA.BA.BA.BA.BA.BA.BA.BA8$67.BA$66.2A$65.4A$66.2A$66.2A$66.2A$66.A.B
A2.BA2.BA2.BA2.BA2.BA$66.A.BA2.BA2.BA2.BA2.BA2.BA2.A$66.2A$66.2A$66.
2A$65.4A$66.2A$67.BA9$66.A2.A.B$69.2B.BA3.BA3.BA3.BA3.BA3.A$68.B.A.BA
3.BA3.BA3.BA3.BA7$65.A.A$64.3AB$65.2A$66.2A$65.B$66.2B$65.A.A3.BA4.BA
4.BA4.BA4.BA4.BA5.A$65.A5.BA4.BA4.BA4.BA4.BA4.BA$64.3A$65.3A$66.A10$
60.A2.A5.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA3.A$59.7A3.BA
4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA$60.A2.2A.A$64.2AB$65.A$
65.A$64.3A$65.A7$67.A$65.4A$64.B2.A$63.A$62.3A$63.A3.BA6.BA6.BA6.BA2.
A$63.A3.BA6.BA6.BA6.BA$62.3A$63.A$64.B2.A$65.4A$67.A16$68.A2$66.B$67.
2A$66.2A$67.AB$67.2A2$66.B.A7.BA7.BA7.BA7.BA6.A$64.A.A.A7.BA7.BA7.BA
7.BA$63.4AB$64.A3.B6$65.A2$67.B$65.2A$66.2A$65.BA$65.2A2$212.A$58.AB
7.BA7.BA7.BA7.BA7.BA$53.A4.AB4.A2.BA7.BA7.BA7.BA7.BA5.A101.2A$212.2B$
64.2BA$65.A$65.2A$64.BA$64.2A2$64.A2$212.2A$212.2B5$61.A$67.BA7.BA7.B
A$67.BA7.BA7.BA8.A$63.2A$62.A2B147.2A$63.A148.2B$62.2A$63.AB$63.2A2$
64.A4$212.2A$212.2B4$64.A151.A.A2$62.B152.2A6.A$63.BA149.A2B5.3A$62.A
B148.AB.2A6.A$64.B144.A2.AB7.A.A$62.2B154.2B.2B$61.A.A7.BA8.BA$61.A9.
BA8.BA4.A107.A20.A.A$60.3A131.4A$61.A133.A2.B8.AB3.2BA.A$64.A132.AB8.
AB3.6A$63.3A150.A$64.A133.B$192.A5.B.A$203.A17.2A$192.A.ABA3.A.3A16.
2B$194.ABA6.A23.A$195.A6.2A$157.AB8.AB8.AB8.AB7.2B4.BA$155.A.AB8.AB8.
AB8.AB7.2A4.BA17.AB4.2A7.BA8.BA8.BA8.BA.A$221.AB4.2B7.BA8.BA8.BA8.BA$
64.A156.2A6.A$63.3A131.A23.A6.ABA$64.A137.2B16.3A.A3.ABA.A$64.2AB135.
2A17.A$64.2A158.A.B5.A$226.B$64.3A141.A$64.2A5.BA9.BA9.BA3.A108.6A3.B
A8.BA$64.2A5.BA9.BA9.BA113.A.A2B3.BA8.B2.A$64.3A160.4A$63.B.A.A138.A.
A20.A$67.B.A.A$60.A2.A.A.5A130.2B.2B$59.10A.3A128.A.A7.BA2.A$60.A.A.A
.A.B2.A129.A6.2A.BA$200.3A5.2BA$201.A6.2A2$206.A.A4$211.2B$211.2A9$
211.2B$211.2A9$211.2B$211.2A9$211.2B$211.2A2$212.A!
...
That p11 gun (left, bottommost) is pseudo-period. It should be:
Code: Select all
x = 8, y = 11, rule = 03-qy456/2ak/3
2.A2$.2A$3A$.2A$2.3A$2.A2.B$2.A3.A$.2A.4A$2.3A.A$3.A!
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 10:44 am
by ZackBuildit777
Ohhhhhhhhh wrote: March 31st, 2022, 10:47 pm
Yoel wrote: March 30th, 2022, 12:00 am
AND-NOT:
Code: Select all
x = 150, y = 149, rule = 03-qy456/2ak/3
14$32.A3$24.A2.A.B3.A.B2.A$27.2B.BA3.B2AB20.A$26.B.A.BA3.A2.B.A17.3A$
59.A2$29.A.A2B3.BA8.BA8.BA$28.6A3.BA8.BA8.BA5.A$29.A33.3A$64.A$54.A3.
2B$53.4A$54.A.A2B3$29.A$28.6A3.BA8.BA8.BA$29.A.A2B3.BA8.BA8.BA$57.2A$
58.A$26.B.A.BA3.A2.B.A16.3A$27.2B.BA3.B2AB19.A$24.A2.A.B3.A.B2.A3$32.
A10$63.A36$39.A2$39.2A$31.A2.A4.2B2.A$34.2A30.A$35.A3.A4.A2.A17.3A31.
A$66.A$65.2A$36.A.A7.BA8.BA8.A$35.4AB6.BA8.BA8.BA$36.A3.B2$62.A9.A$
61.3A7.3A$62.A7.3A$71.A$36.A3.B$35.4AB6.BA8.BA8.BA$36.A.A7.BA8.BA8.A$
65.2A$66.A$35.A3.A4.A2.A17.3A$34.2A30.A$31.A2.A4.2B2.A$39.2A2$39.A!
Your and-not doesn’t seems to be as useful - it looks like only one side giving an input signal will give an output, which is called “not-and” (my English is not good so I’m not sure) probably. But, generally, it’s also proof of Turing-completeness.
nope, its ANDNOT, NOTAND would be an inversion of an AND output, and is generally called NAND, but ANDNOT is where one input is inverted before the and gate is run, like a AND (NOT b), and if accompanied by a signal splitter, its enough to prove turing completion, whereas a NAND gate is not enough to my knowledge.
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 10:50 am
by pzq_alex
ZackBuildit777 wrote: April 1st, 2022, 10:44 am
<snip>
nope, its ANDNOT, NOTAND would be an inversion of an AND output, and is generally called NAND, but ANDNOT is where one input is inverted before the and gate is run, like a AND (NOT b), and if accompanied by a signal splitter, its enough to prove turing completion, whereas a NAND gate is not enough to my knowledge.
NAND is enough to produce universal computation. Observe that a NAND a = NOT a, and thus a AND b = NOT (a NAND b) is computable.
Finally, by a OR b = NOT ((NOT a) AND (NOT b)), or is also computable.
I'm not sure about ANDNOT.
Edit: 3^5th post
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 10:53 am
by Yoel
AbhpzTa wrote: April 1st, 2022, 7:56 am
p7 gun:
Code: Select all
x = 7, y = 10, rule = 03-qy456/2ak/3
.A3.A$3A.3A$.A3.A$.A$.2A2.A$2A$.2A$2.2A$.3AB$2.A.A!
Yoel wrote: March 30th, 2022, 12:00 am...
Guns with periods >=10 can be constructed from splitter loops. I didn't find a p7 gun yet.
Code: Select all
x = 385, y = 331, rule = 03-qy456/2ak/3
29$66.B2.BA.BA.BA.BA.BA.BA.BA.BA.A$67.4A.BA.BA.BA.BA.BA.BA.BA$66.3A$
67.A9$67.A.A.B$67.B3A.BA.BA.BA.BA.BA.BA.BA.BA.BA.BA2.A$65.A.B2.A.BA.B
A.BA.BA.BA.BA.BA.BA.BA.BA8$67.BA$66.2A$65.4A$66.2A$66.2A$66.2A$66.A.B
A2.BA2.BA2.BA2.BA2.BA$66.A.BA2.BA2.BA2.BA2.BA2.BA2.A$66.2A$66.2A$66.
2A$65.4A$66.2A$67.BA9$66.A2.A.B$69.2B.BA3.BA3.BA3.BA3.BA3.A$68.B.A.BA
3.BA3.BA3.BA3.BA7$65.A.A$64.3AB$65.2A$66.2A$65.B$66.2B$65.A.A3.BA4.BA
4.BA4.BA4.BA4.BA5.A$65.A5.BA4.BA4.BA4.BA4.BA4.BA$64.3A$65.3A$66.A10$
60.A2.A5.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA3.A$59.7A3.BA
4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA4.BA$60.A2.2A.A$64.2AB$65.A$
65.A$64.3A$65.A7$67.A$65.4A$64.B2.A$63.A$62.3A$63.A3.BA6.BA6.BA6.BA2.
A$63.A3.BA6.BA6.BA6.BA$62.3A$63.A$64.B2.A$65.4A$67.A16$68.A2$66.B$67.
2A$66.2A$67.AB$67.2A2$66.B.A7.BA7.BA7.BA7.BA6.A$64.A.A.A7.BA7.BA7.BA
7.BA$63.4AB$64.A3.B6$65.A2$67.B$65.2A$66.2A$65.BA$65.2A2$212.A$58.AB
7.BA7.BA7.BA7.BA7.BA$53.A4.AB4.A2.BA7.BA7.BA7.BA7.BA5.A101.2A$212.2B$
64.2BA$65.A$65.2A$64.BA$64.2A2$64.A2$212.2A$212.2B5$61.A$67.BA7.BA7.B
A$67.BA7.BA7.BA8.A$63.2A$62.A2B147.2A$63.A148.2B$62.2A$63.AB$63.2A2$
64.A4$212.2A$212.2B4$64.A151.A.A2$62.B152.2A6.A$63.BA149.A2B5.3A$62.A
B148.AB.2A6.A$64.B144.A2.AB7.A.A$62.2B154.2B.2B$61.A.A7.BA8.BA$61.A9.
BA8.BA4.A107.A20.A.A$60.3A131.4A$61.A133.A2.B8.AB3.2BA.A$64.A132.AB8.
AB3.6A$63.3A150.A$64.A133.B$192.A5.B.A$203.A17.2A$192.A.ABA3.A.3A16.
2B$194.ABA6.A23.A$195.A6.2A$157.AB8.AB8.AB8.AB7.2B4.BA$155.A.AB8.AB8.
AB8.AB7.2A4.BA17.AB4.2A7.BA8.BA8.BA8.BA.A$221.AB4.2B7.BA8.BA8.BA8.BA$
64.A156.2A6.A$63.3A131.A23.A6.ABA$64.A137.2B16.3A.A3.ABA.A$64.2AB135.
2A17.A$64.2A158.A.B5.A$226.B$64.3A141.A$64.2A5.BA9.BA9.BA3.A108.6A3.B
A8.BA$64.2A5.BA9.BA9.BA113.A.A2B3.BA8.B2.A$64.3A160.4A$63.B.A.A138.A.
A20.A$67.B.A.A$60.A2.A.A.5A130.2B.2B$59.10A.3A128.A.A7.BA2.A$60.A.A.A
.A.B2.A129.A6.2A.BA$200.3A5.2BA$201.A6.2A2$206.A.A4$211.2B$211.2A9$
211.2B$211.2A9$211.2B$211.2A9$211.2B$211.2A2$212.A!
...
That p11 gun (left, bottommost) is pseudo-period. It should be:
Code: Select all
x = 8, y = 11, rule = 03-qy456/2ak/3
2.A2$.2A$3A$.2A$2.3A$2.A2.B$2.A3.A$.2A.4A$2.3A.A$3.A!
Great, thanks!
How did you find it? Just by playing around or by some algorithm?
pzq_alex wrote: April 1st, 2022, 10:50 am
ZackBuildit777 wrote: April 1st, 2022, 10:44 am
<snip>
nope, its ANDNOT, NOTAND would be an inversion of an AND output, and is generally called NAND, but ANDNOT is where one input is inverted before the and gate is run, like a AND (NOT b), and if accompanied by a signal splitter, its enough to prove turing completion, whereas a NAND gate is not enough to my knowledge.
NAND is enough to produce universal computation. Observe that a NAND a = NOT a, and thus a AND b = NOT (a NAND b) is computable.
Finally, by a OR b = NOT ((NOT a) AND (NOT b)), or is also computable.
I'm not sure about ANDNOT.
Of course AND-NOT is enough given a source of 1 (guns):
1∧ ¬a = ¬a (inverter)
Everything else can be built out of it, e.g. ¬ (a ∧¬(¬b)) = . ¬ (a∧b).
NOT:
Code: Select all
x = 134, y = 43, rule = 03-qy456/2ak/3
6$16.A3$8.A.B2.A3.A.AB$10.B2ABA4.4A70.A$10.A2.BA6.BA.A67.3A$93.A$16.
2B80.A$13.A2.2A2.BA8.BA8.BA8.BA8.BA8.BA8.BA8.BA5.3A29.A$12.3A5.BA8.BA
8.BA8.BA8.BA8.BA8.BA8.BA6.A$13.A$92.2B$89.A2.2A$88.3A$89.A2.2A$92.2B$
78.A.B21.A$77.3A.A8.BA9.3A$78.A2.A8.BA10.A2$93.A$75.A2.BA.A4.BA.A2.3A
$75.B2ABA4.4A5.A$73.A.B2.A5.AB3$81.A!
AND:
Code: Select all
x = 170, y = 60, rule = 03-qy456/2ak/3
9$27.A3$19.A2.A5.A2.A$22.2A80.A3.A$23.A3.2B3.A2.A67.5AB4.BA8.BA8.BA8.
BA8.BA8.BA.A$27.2A75.A.A6.BA8.BA8.BA8.BA8.BA8.BA2$24.A4.BA8.BA8.BA8.B
A8.BA8.BA8.BA8.BA$14.A8.3A3.BA8.BA8.BA8.BA8.BA8.BA8.BA8.BA2.2B$24.A
78.2A2$6.A.B2.A3.A.AB81.A4.BA3.A$8.B2ABA4.4A70.A7.3A3.BA2.3A$8.A2.BA
6.BA.A67.3A7.A7.3A$91.A17.A$14.2B80.A$11.A2.2A2.BA8.BA8.BA8.BA8.BA8.B
A8.BA8.BA5.3A$10.3A5.BA8.BA8.BA8.BA8.BA8.BA8.BA8.BA6.A$11.A$90.2B12.A
$87.A2.2A11.3A$86.3A15.A$87.A2.2A$90.2B$76.A.B21.A$75.3A.A8.BA9.3A$
76.A2.A8.BA10.A2$91.A$73.A2.BA.A4.BA.A2.3A$73.B2ABA4.4A5.A$71.A.B2.A
5.AB3$79.A!
NAND:
Code: Select all
x = 187, y = 51, rule = 03-qy456/2ak/3
7$27.A$130.A$27.2B100.3A$19.A.AB8.A98.A$21.4A6.2A71.A24.2A$23.BA2.A4.
A2.A67.3A3.BA8.BA8.BA$104.A4.BA8.BA8.BA$103.2A$24.A.BA7.BA8.BA8.BA8.B
A8.BA8.BA8.BA7.B2.2A$14.A8.3AB8.BA8.BA8.BA8.BA8.BA8.BA8.BA8.B.2B17.A.
B$24.A.A98.3A$126.A.B49.A$6.A2.A.B4.AB2.A79.A.BA6.A$9.2B.B3.AB2AB70.A
7.3AB6.3A3.A$8.B.A.B.A2.A2.B.A67.3A7.A.A5.3A3.3A2.BA8.BA$91.A17.A5.A
3.BA8.BA$92.B3.A32.2A$11.A2.BA8.BA8.BA8.BA8.BA8.BA8.BA8.BA4.2A3.3A32.
A$10.3A.BA8.BA8.BA8.BA8.BA8.BA8.BA8.BA10.A17.A3.2A.B.A2.A2.3A$11.A
108.B.2B6.A$104.A5.A2.A5.AB.A.B$87.A15.3A$86.3A15.A$87.A30.A2$76.A23.
A$75.6A3.BA13.3A$76.A.A2B3.BA4.2A8.A$92.B$91.A$73.B.A.BA3.A2.B.A2.3A$
74.2B.BA3.B2AB5.A$71.A2.A.B3.A.B2.A3$79.A!
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 11:59 am
by Sarah
wheee
Code: Select all
x = 19, y = 12, rule = 03-qy456/2ak/3
6.A.B$6.2B$10.B.AB.A.A$7.2B.B.AB.4A$7.2A5.B.2A$16.2A$14.A.2A$13.ABA.A
$2.B.A.A3.A.A2.2A$.2A.5A.5A.A$6A.5A.3A.B$.A.A.A.A.A.A.A2.B!
Re: Pipes (03-qy456/2ak/3)
Posted: April 1st, 2022, 12:16 pm
by ZackBuildit777
pzq_alex wrote: April 1st, 2022, 10:50 am
ZackBuildit777 wrote: April 1st, 2022, 10:44 am
<snip>
nope, its ANDNOT, NOTAND would be an inversion of an AND output, and is generally called NAND, but ANDNOT is where one input is inverted before the and gate is run, like a AND (NOT b), and if accompanied by a signal splitter, its enough to prove turing completion, whereas a NAND gate is not enough to my knowledge.
NAND is enough to produce universal computation. Observe that a NAND a = NOT a, and thus a AND b = NOT (a NAND b) is computable.
Finally, by a OR b = NOT ((NOT a) AND (NOT b)), or is also computable.
I'm not sure about ANDNOT.
ANDNOT is the most common single gate universal set used, you can do a NOT gate by doing (1 ANDNOT a), do AND by doing (a ANDNOT (a ANDNOT b)), and do OR via combining those
Re: Pipes (03-qy456/2ak/3)
Posted: April 2nd, 2022, 5:10 am
by Ohhhhhhhhh
ZackBuildit777 wrote: April 1st, 2022, 12:16 pm
pzq_alex wrote: April 1st, 2022, 10:50 am
ZackBuildit777 wrote: April 1st, 2022, 10:44 am
<snip>
nope, its ANDNOT, NOTAND would be an inversion of an AND output, and is generally called NAND, but ANDNOT is where one input is inverted before the and gate is run, like a AND (NOT b), and if accompanied by a signal splitter, its enough to prove turing completion, whereas a NAND gate is not enough to my knowledge.
NAND is enough to produce universal computation. Observe that a NAND a = NOT a, and thus a AND b = NOT (a NAND b) is computable.
Finally, by a OR b = NOT ((NOT a) AND (NOT b)), or is also computable.
I'm not sure about ANDNOT.
ANDNOT is the most common single gate universal set used, you can do a NOT gate by doing (1 ANDNOT a), do AND by doing (a ANDNOT (a ANDNOT b)), and do OR via combining those
Uh…
Whatever, I’m certainly bad at English. I mean, I thought NAND is same as ANDNOT, but now I see that they are not the same.
Thank for the help!
Re: Pipes (03-qy456/2ak/3)
Posted: April 2nd, 2022, 6:08 pm
by Yoel
Since this rule is partially compatible with Fireworld (03ajkr/2ak/3), ANDNOT, as it is used in my Rule110 units, is simply a collision of 2 photons. I just wanted to post a version specific to this particular rule, using stable reflectors. The basic ANDNOT is just one of these:
Code: Select all
x = 52, y = 22, rule = 03-qy456/2ak/3
7$19.2B20.2B$19.2A20.2A6$12.BA18.BA$12.BA18.BA!
For example. this 32-bit register from Fireworld, which relies on ANDNOT gates, works in this rule as well:
Code: Select all
x = 1029, y = 224, rule = 03-qy456/2ak/3
93$587.A$762.A2$580.A2.A.B.2A2.A.B$583.2B.B4.2B162.A2.A.B.2A2.A.B$
582.B.A.BA2.B.A2.A162.2B.B4.2B$757.B.A.BA2.B.A2.A3$587.2B$587.2A173.
2B$762.2A3$588.A$763.A5$584.A6.A$759.A6.A$584.A6.A$759.A6.A$452.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A6.A2.A2.A
.A.A$627.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.
A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.
A2.A6.A2.A2.A.A.A$596.2B$452.A.A2.A.B.2A2.A.B127.B5.A169.2B$457.2B.B
4.2B129.BA29.A.A2.A.B.2A2.A.B127.B5.A$456.B.A.BA2.B.A2.A125.AB35.2B.B
4.2B129.BA$452.A144.B3.A29.B.A.BA2.B.A2.A125.AB$595.2B30.A144.B3.A$
595.A.A3.A168.2B$452.A8.2B134.A172.A.A3.A27.A.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A$461.2A164.A8.2B134.A$595.B40.2A166.A10.A$452.A12.A
130.BA3.A168.B212.A$595.AB30.A12.A130.BA3.A40.A$452.A144.B172.AB32.A$
465.2A134.A25.A144.B210.A$448.A.A.A13.2A127.A44.2A134.A27.A11.2A$485.
A.A.A5.A.A.A10.A.A.A5.A.A.A3.A.A.A.A.A8.A.A.A7.A.A5.A7.A17.2A8.A.A.A
17.A.A.A13.2A127.A44.2A$591.2B67.A.A.A5.A.A.A10.A.A.A5.A.A.A3.A.A.A.A
.A8.A.A.A7.A.A5.A7.A17.2A8.A.A.A19.A.A.A167.A10.A$461.2B.B2.A23.A9.A
8.A5.A5.A9.A12.A5.A3.A5.A3.A.A3.A.A192.2B$63.A397.2A.B5.A165.2B.B2.A
23.A9.A8.A5.A5.A9.A12.A5.A3.A5.A3.A.A3.A.A$491.A9.A8.A5.A5.A9.A12.A5.
A3.A5.A3.A3.A3.A14.A47.2A.B5.A167.AB.A5.BA8.BA8.BA8.BA8.BA8.BA8.BA8.B
A58.BA8.BA8.A10.A$666.A9.A8.A5.A5.A9.A12.A5.A3.A5.A3.A3.A3.A14.A49.AB
7.BA8.BA8.BA8.BA8.BA8.BA8.BA8.BA58.BA8.BA13.A$448.A.A.A12.2A20.A.A7.A
.A10.A.A.A7.A9.A12.A.A.A5.A.A.A.A3.A7.A398.2B3.2A$75.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A70.2A133.A.A.A17.A.A.A12.2A20.A.A7.A.A10.A.A.A7.A9.A12.A.
A.A5.A.A.A.A3.A7.A223.2A4.A2.A.A$452.A38.A3.A14.A5.A5.A9.A12.A5.A3.A
5.A3.A7.A67.2A133.A.A.A19.A.A.A.A2.A$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
231.A38.A3.A14.A5.A5.A9.A12.A5.A3.A5.A3.A7.A60.2A3.A$452.A14.A23.A3.A
14.A5.A5.A9.A12.A5.A3.A5.A3.A7.A17.2A8.A202.A5.A13.AB18.AB8.AB38.AB
18.AB8.AB38.AB7.BA.A6.A$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A195.2B34.A14.A
23.A3.A14.A5.A5.A9.A12.A5.A3.A5.A3.A7.A17.2A8.A47.AB18.AB8.AB38.AB18.
AB8.AB38.AB5.A.BA$461.2B22.A.A.A5.A.A.A.A8.A.A.A5.A.A.A7.A12.A5.A3.A
5.A3.A7.A192.2B36.A$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A56.A8.2A138.A34.2B
22.A.A.A5.A.A.A.A8.A.A.A5.A.A.A7.A12.A5.A3.A5.A3.A7.A234.A$458.A168.A
8.2A138.A27.A10.A$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A237.A337.2A$452.A3.B
144.A368.2A11.A$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A61.BA168.A3.B144.A27.
A$456.AB174.BA$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A56.A5.B142.A29.AB171.A
165.A12.A$591.2A34.A5.B142.A$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A60.A134.
2B173.2A36.A.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A.A.A2.A2.A2.A.A$452.A3.A.A142.
A29.A134.2B$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A61.2B168.A3.A.A142.A$456.B
175.2B$75.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A56.A4.BA125.A2.A.B2.AB.A.B3.A
29.B$456.AB129.2B4.B.2B30.A4.BA125.A2.A.B2.AB.A.B3.A40.A.A.A5.A.A.A
10.A.A.A5.A.A.A3.A.A.A.A.A8.A.A.A7.A.A5.A7.A$458.B127.B.A2.2A.B.A2.A.
A29.AB129.2B4.B.2B$452.A180.B127.B.A2.2A.B.A2.A.A46.A9.A8.A5.A5.A9.A
12.A5.A3.A5.A3.A.A3.A.A$456.A144.A25.A$631.A144.A46.A9.A8.A5.A5.A9.A
12.A5.A3.A5.A3.A3.A3.A$452.A3.A.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
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Ohhhhhhhhh wrote: April 2nd, 2022, 5:10 am
ZackBuildit777 wrote: April 1st, 2022, 12:16 pm
pzq_alex wrote: April 1st, 2022, 10:50 am
NAND is enough to produce universal computation. Observe that a NAND a = NOT a, and thus a AND b = NOT (a NAND b) is computable.
Finally, by a OR b = NOT ((NOT a) AND (NOT b)), or is also computable.
I'm not sure about ANDNOT.
ANDNOT is the most common single gate universal set used, you can do a NOT gate by doing (1 ANDNOT a), do AND by doing (a ANDNOT (a ANDNOT b)), and do OR via combining those
Uh…
Whatever, I’m certainly bad at English. I mean, I thought NAND is same as ANDNOT, but now I see that they are not the same.
Thank for the help!