## State of the OR and XOR gates

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### State of the OR and XOR gates

I've recently been interested in classic logic gates (i.e. those that just perform computation, not also construction). AND gates, OR gates, flip-flops, memory cells, the like. For these purposes I don't need patterns to be spartan or even stable – the only requirement is that the logical constructs work on any period a multiple of 8, both for Hashlife and for the existence of small p8 reflectors (both colour-preserving and colour-changing).

It is trivial to implement an ANDNOT gate with an eater, which allows building NOT gates with a suitable gun. I already have Goucher's small AND gate:

Code: Select all

``````x = 20, y = 24, rule = B3/S23
17b2o\$17bo\$15bobo\$14bobo\$5bo4b2o3bo\$6bo3b2o\$4b3o11\$16b2o\$11b2o3bo\$11b
2o4b3o\$19bo\$3o\$2bo\$bo!``````
Already this is a universal set, but it would be nice to have a small XOR or OR gate too, rather than having to build them from AND/ANDNOT gates. The problem of OR gates was raised back in 2014, before the discovery of the syringe. Now that we have that G-to-H and several other Herschel conduits, what is the smallest known OR gate that can work at any multiple-of-8 period, and similarly for XOR gates? Remember, I do not require things to be spartan or stable.

Edit: as it turns out there was already a stable XOR gate:

Code: Select all

``````x = 138, y = 193, rule = B3/S23
136bo\$135bo\$135b3o88\$34b2o\$35bo\$35bobo\$36b2o4\$30bob2o\$30b2obo\$25b2o\$
26bo\$26bobo17b2obo\$27b2o17bob2o3\$13bo\$13b3o\$16bo\$15b2o2\$9b2o\$9bo36b2o\$
10b3o33bo\$12bo31bobo\$35bo8b2o\$34bobo2bo\$35bo3b3o\$6b2o3b2o29bo\$6bobobob
o24b4ob3o\$8bobo26bo2bo4bo\$7b2ob2o15b2o13b3o\$27bobo11b2o\$29bo\$29b2o7\$
22b2o\$5bo16bo\$4bo18b3o\$4b3o18bo4\$6b2o\$5bobo\$5bo\$4b2o\$3bo\$3b3o\$6bo\$5b2o
6\$3b2o\$3b2o\$27b2o\$27bobo\$29bo\$29b2o4\$3b2o\$2bo2bo2b2o\$3b2o2bobo\$5b2o\$5b
o\$2b2obo2bo\$2bob2obobo\$6bobo\$3b2o2bo\$b3ob2o\$o\$b3ob2o\$3bob2o2\$13b2o\$13b
2o7b2o\$22bo\$20bobo\$20b2o4\$2o\$2o5\$16bo7b2o\$15bobo6bobo\$15bobo6bo\$16bo\$
17b3o\$19bo!``````
It's still quite large though.

Edit 2: This is an OR gate made from ANDNOT gates, working at p120:

Code: Select all

``````x = 200, y = 86, rule = LifeHistory
9.A49.A49.A49.A\$9.3A47.3A47.3A47.3A\$12.A49.A49.A49.A\$11.2A48.2A48.2A
48.2A\$11.4B46.4B46.4B46.4B\$13.3B47.3B47.3B47.3B\$.B2AB2.B.B2A.4B34.B2A
B2.B.B2A.4B34.B2AB2.B.B2A.4B34.B2AB2.B.B2A.4B\$.4A.3B5A10B27.4A.3B5A
10B27.4A.3B5A10B27.4A.3B5A10B\$ABABA4BA4BA10B25.ABABA4BA4BA10B25.ABABA
4BA4BA10B25.ABABA4BA4BA10B\$2AB3A3B3A2BA10B25.2AB3A3B3A2BA10B25.2AB3A
3B3A2BA10B25.2AB3A3B3A2BA10B\$.B.2ABA3BA2B2A10B26.B.2ABA3BA2B2A10B26.B
.2ABA3BA2B2A10B26.B.2ABA3BA2B2A10B\$3.2ABA4B2A14B26.2ABA4B2A14B26.2ABA
4B2A14B26.2ABA4B2A14B\$4.BA7B2.13B26.BA7B2.13B26.BA7B2.13B26.BA7B2.13B
\$4.8B6.10B26.8B6.10B26.8B6.10B26.8B6.10B\$6.7B7.7B29.7B7.7B29.7B7.7B
29.7B7.7B\$5.10B6.8B26.10B6.8B26.10B6.8B26.10B6.8B\$5.13B2.7B2A26.13B2.
7B2A26.13B2.7B2A26.13B2.7B2A\$6.21B2AB26.21B2AB26.21B2AB26.21B2AB\$8.
22B.B26.22B.B26.22B.B26.22B.B\$8.16B2A5B2A25.16B2A5B2A25.16B2A5B2A25.
16B2A5B2A\$8.16B2A5B2A25.16B2A5B2A25.16B2A5B2A25.16B2A5B2A\$9.18B.4B27.
18B.4B27.18B.4B27.18B.4B\$16.3BA.3B.B2.4B34.3BA.3B.B2.4B34.3BA.3B.B2.
4B34.3BA.3B.B2.4B\$17.3BA46.3BA46.3BA46.3BA\$18.3AB46.3AB46.3AB46.3AB\$
19.4B46.4B46.4B46.4B\$20.4B46.4B46.4B46.4B\$19.6B44.6B44.6B44.6B\$19.2B.
4B43.2B.4B43.2B.4B43.2B.4B\$18.4B.4B41.4B.4B41.4B.4B41.4B.4B\$17.3DB3.
4B39.3DB3.4B39.3CB3.4B39.3CB3.4B\$17.2BD5.4B8.2A28.2BD5.4B8.2A28.2BC5.
4B8.2A28.2BC5.4B8.2A\$18.D7.4B7.A30.D7.4B7.A30.C7.4B7.A30.C7.4B7.A\$27.
4B3.BA.A39.4B3.BA.A39.4B3.BA.A39.4B3.BA.A\$28.4B2.B2A10.3D28.4B2.B2A
10.3D28.4B2.B2A10.3D28.4B2.B2A10.3D\$29.6B11.3BD29.6B11.3BD29.6B11.3BD
29.6B11.3BD\$30.5B10.3BD31.5B10.3BD31.5B10.3BD31.5B10.3BD\$29.6B9.4B31.
6B9.4B31.6B9.4B31.6B9.4B\$29.7B7.4B32.7B7.4B32.7B7.4B32.7B7.4B\$28.4B.
4B5.4B32.4B.4B5.4B32.4B.4B5.4B32.4B.4B5.4B\$27.4B3.4B3.4B32.4B3.4B3.4B
32.4B3.4B3.4B32.4B3.4B3.4B\$26.4B5.4B.4B32.4B5.4B.4B32.4B5.4B.4B32.4B
5.4B.4B\$25.4B7.2B.4B32.4B7.2B.4B32.4B7.2B.4B32.4B7.2B.4B\$24.4B8.6B32.
4B8.6B32.4B8.6B32.4B8.6B\$23.4B10.4B32.4B10.4B32.4B10.4B32.4B10.4B\$22.
4B10.4B32.4B10.4B32.4B10.4B32.4B10.4B\$21.4B10.4B32.4B10.4B32.4B10.4B
32.4B10.4B\$20.4B10.4B32.4B10.4B32.4B10.4B32.4B10.4B\$19.4B10.4B32.4B
10.4B32.4B10.4B32.4B10.4B\$18.4B10.4B32.4B10.4B32.4B10.4B32.4B10.4B\$
17.3DB10.4B32.3CB10.4B32.3DB10.4B32.3CB10.4B\$17.2BD10.4B33.2BC10.4B
33.2BD10.4B33.2BC10.4B\$18.D10.4B35.C10.4B35.D10.4B35.C10.4B\$28.4B46.
4B46.4B46.4B\$27.4B46.4B46.4B46.4B\$26.4B46.4B46.4B46.4B\$25.4B46.4B46.
4B46.4B\$24.4B46.4B46.4B46.4B\$23.4B46.4B46.4B46.4B\$22.4B46.4B46.4B46.
4B\$21.4B46.4B46.4B46.4B\$20.4B46.4B46.4B46.4B\$19.3AB46.3AB46.3AB46.3AB
\$18.3BA.3B.B2.4B34.3BA.3B.B2.4B34.3BA.3B.B2.4B34.3BA.3B.B2.4B\$11.9BA
8B.4B27.9BA8B.4B27.9BA8B.4B27.9BA8B.4B\$10.16B2A5B2A25.16B2A5B2A25.16B
2A5B2A25.16B2A5B2A\$10.16B2A5B2A25.16B2A5B2A25.16B2A5B2A25.16B2A5B2A\$
10.22B.B26.22B.B26.22B.B26.22B.B\$8.21B2AB26.21B2AB26.21B2AB26.21B2AB\$
7.13B2.7B2A26.13B2.7B2A26.13B2.7B2A26.13B2.7B2A\$7.10B6.8B26.10B6.8B
26.10B6.8B26.10B6.8B\$8.7B7.7B29.7B7.7B29.7B7.7B29.7B7.7B\$6.8B6.10B26.
8B6.10B26.8B6.10B26.8B6.10B\$6.9B2.13B26.9B2.13B26.9B2.13B26.9B2.13B\$
5.2B2A20B26.2B2A20B26.2B2A20B26.2B2A20B\$3.B.BABA3B3A12B26.B.BABA3B3A
12B26.B.BABA3B3A12B26.B.BABA3B3A12B\$2.2A2BA7BA12B25.2A2BA7BA12B25.2A
2BA7BA12B25.2A2BA7BA12B\$2.2A2B2A4BABA12B25.2A2B2A4BABA12B25.2A2B2A4BA
BA12B25.2A2B2A4BABA12B\$3.4B.4B2A12B27.4B.4B2A12B27.4B.4B2A12B27.4B.4B
2A12B\$3.4B2.B.3B.4B34.4B2.B.3B.4B34.4B2.B.3B.4B34.4B2.B.3B.4B\$15.3B
47.3B47.3B47.3B\$13.4B46.4B46.4B46.4B\$13.2A48.2A48.2A48.2A\$14.A49.A49.
A49.A\$11.3A47.3A47.3A47.3A\$11.A49.A49.A49.A!``````
Princess of Science, Parcly Taxel

Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### Re: State of the OR and XOR gates

A smaller XOR gate, using HSW28T1784:

Code: Select all

``````x = 107, y = 71, rule = LifeHistory
106.C\$104.2C\$105.2C30\$44.2A\$44.A\$41.A4.A2.2A\$41.5A.A2.A\$4.C22.2A16.B.
2A.A.2A\$5.C22.A10.4AB3AB2.A2.A\$3.3CB21.A.AB7.A2.A.A3B2A.A\$4.4B10.A10.
2AB.3B4.7B2.A.2A\$5.4B7.3A12.7B3.7B.A\$6.4B5.A15.16B.2A\$7.4B4.2A15.15B\$
2A6.9B14.16B\$.A7.6B14.18B\$.A.2A5.6B3.B2.2B2.20B\$2.A2.A4.35B3.2A\$3.2AB
3.27B.7B5.A\$4.14B2A16B2.7B4.A.2A\$5.13B2A16B2.8B4.A.A\$6.29B4.7B5.B\$6.
17B.4B10.8B2.B.3B\$7.15B2.5B9.16B\$7.15B5.A2B.2A5.17B\$8.13B5.A.A2B.A5.
18B\$10.13B2.A.AB2.A5.20B\$9.8B4.2A.A.A3.A7.19B\$9.6B6.2ABA2.4A.A5.19B\$
9.5B8.B2.A.A3.A.A5.17B\$9.B.B9.2A.2A2.A2.A.A6.11B\$10.3B9.A.A2.2A3.A11.
6B\$9.B2AB9.A.A19.6B\$10.2A11.A4.3D.3D.3D4.7B\$30.D.D3.D5.10B\$28.3D.3D.
3D2.BD2B.4B2A\$28.D5.D.D.D.2D.B4.2BAB2.2A\$28.3D.3D.3D2B2D5.A.A.A2.A\$
38.4B4.3A.A.2A\$37.4B4.A3.A.A\$36.4B5.2A2.A.A\$35.4B11.A!``````
Once we have XOR gates and AND gates we can construct OR gates as (A XOR B) XOR (A AND B). The outer XOR gate does not need to handle the both-inputs-1 case, making things easier, or a Toffoli gate may be used for the rightmost two operations.

I also found Goucher's old XOR gates and converted them to use glider inputs only:

Code: Select all

``````x = 224, y = 103, rule = LifeHistory
209.A\$209.3A\$212.A\$196.3D.3D.3D4.2A\$198.D.D3.D.D4.5B\$196.3D.3D.D.D6.
4B\$198.D.D.D.D.D4.6B\$172.A23.3D.3D.3D4.6B\$172.3A35.8B\$175.A34.10B\$
174.2A4.2B22.A6.7B2D\$139.C30.B3.8B22.3A4.6BDBD\$138.2BC27.4B4.7B12.A
11.A2.9BD.B\$138.3CB25.6B.9B12.3A8.2A3.8B.2BA\$139.4B10.A13.6B.10B14.A
7.15BA.A\$140.4B7.3A12.19B12.2A3.B5.12B.BA\$141.4B5.A14.19B13.8B2.13B\$
142.4B4.2A13.17B17.20B\$135.2A6.9B14.15B18.20B\$54.4B78.A7.6B14.17B17.
19B.B2A\$38.3D.3D.3D4.4B79.A.2A5.6B3.B2.2B2.22B13.21B.BA.A\$40.D.D.D.D.
D3.4B81.A2.A4.41B3.2B2.24B4.A\$38.3D.D.D.D.D2.D3B5.A77.2AB3.27B.39B2.B
.4B2.2A\$38.D3.D.D.D.D.B2DB5.A.A77.14B2A16B2.30B.6B7.2A\$38.3D.3D.3DBDB
DB5.A.A78.13B2A16B2.30B.8B5.A\$48.6B4.2A.3A77.29B4.33B3.2A6.3A\$46.9B4.
B4.A76.17B.4B10.33B4.A9.A\$46.9B2.B2AB3A78.15B4.3B10.16B.4B6.4B6.3A\$
45.11B.B2A.A80.15B5.A2B.2A6.12B5.3B6.4B9.A\$44.14B85.13B5.A.A2B.A6.9B
6.4B6.4B\$43.15B87.13B2.A.AB2.A6.11B5.2A7.4B\$42.15B8.2A22.C54.8B4.2A.A
.A3.A8.7B.B2A5.A6.4B\$41.16B8.A22.C2B53.6B6.2ABA2.4A.A8.4B2.BA.A.3A6.
4B\$40.4B2.12B4.BA.A21.B3C53.5B8.B2.A.A3.A.A6.B2A2B5.A.A7.4B\$39.4B3.
15B.B2A10.A10.4B54.B.B9.2A.2A2.A2.A.A7.2A7.2A7.4B\$38.4B4.17B12.3A7.4B
56.3B9.A.A2.2A3.A25.4B\$37.4B5.17B15.A5.4B56.B2AB9.A.A32.4B\$36.4B3.B.
17B15.2A4.4B58.2A11.A32.4B\$35.4B3.2A19B14.9B6.2A96.4B\$34.4B4.2AB.19B
14.6B7.A96.4B\$33.4B6.B4.20B2.2B2.B3.6B5.2A.A95.4B\$32.4B12.36B4.A2.A
95.4B\$31.4B13.9B.27B3.B2A95.4B\$30.4B15.7B2.16B2A14B95.4B\$29.4B16.7B2.
16B2A13B95.4B\$28.4B17.6B4.29B95.4B\$27.4B18.7B10.2B.B.17B94.4B\$26.4B
19.6B10.3B4.15B94.4B\$25.4B19.7B6.2A.2BA5.15B93.4B\$24.4B21.6B6.A.2BA.A
5.13B93.4B\$23.4B23.5B7.A2.BA.A2.13B94.4B\$22.4B24.6B7.A3.A.A.2A4.8B92.
4B\$21.4B27.4B5.A.4A2.AB2A6.6B91.4B\$20.4B27.B2A2B4.A.A3.A.A2.B8.5B90.
4B\$19.4B29.2A6.A.A2.A2.2A.2A9.B.B89.4B\$18.4B39.A3.2A2.A.A9.3B89.4B\$
17.4B48.A.A9.B2AB87.4B\$16.4B50.A11.2A87.4B\$15.4B151.4B\$14.4B151.4B\$
13.4B151.4B\$12.4B151.4B\$11.4B151.4B\$10.4B151.4B\$9.4B151.4B\$8.4B151.4B
\$7.4B151.4B\$6.4B151.4B\$5.4B151.4B\$4.4B151.4B\$3.4B151.4B\$2.4B151.4B\$.C
3B151.4B\$B2CB151.4B\$CBC151.4B\$153.4B\$152.4B\$151.4B\$150.4B\$149.4B\$148.
4B\$147.4B\$146.4B\$145.4B\$144.4B\$143.4B\$142.4B\$141.4B\$140.4B\$139.4B\$
138.4B\$137.4B\$136.4B\$135.4B\$134.4B\$133.4B\$132.4B\$131.4B\$130.4B\$129.4B
\$128.2C2B\$127.CBCB\$128.BC!``````
A possible idea for an elementary OR gate would be to use two conduits that release gliders, one of which (B) has a transparent output lane. Ideally, both should be edge shooters, but this is not strictly necessary for the first conduit (A). After receiving a Herschel, B has smoke that splits into the output glider and more smoke – and this smoke must annihilate the smoke that A produces on the way to producing its same-time-same-lane glider.

The search space is too large for me right now.
Princess of Science, Parcly Taxel

Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### Re: State of the OR and XOR gates

Code: Select all

``````x = 256, y = 146, rule = LifeHistory
43.2A\$43.A.A120.2A3.2A\$45.A4.2A112.3A.A2.2A\$41.4A.2A2.A2BA109.A4.A2.
2B\$41.A2.A.A.A.A.2A109.A2.2A.4A\$43.BABABA.A111.2A.A.A.A2.A\$44.B2ABA.A
112.A.ABABAB\$45.2B.BA113.A.AB2AB\$44.3B117.AB.2B\$35.2A6.4B120.3B\$36.A
6.B2A3B118.4B6.2A\$36.A.AB3.B2A3B116.3B2AB6.A\$37.2AB.10B114.3B2AB3.BA.
A\$39.13B111.10B.B2A\$39.14B109.13B\$39.15B107.14B\$41.8B2.4B105.15B\$41.
6B5.4B89.A13.4B2.8B33.A11.2A\$40.9B4.4B88.3A10.4B5.6B32.A.A9.B2AB\$39.
4B4.2A5.4B90.A8.4B4.9B23.A3.2A2.A.A9.3B\$26.2A10.4B5.A7.4B88.2A7.4B5.
2A4.4B13.2A6.A.A2.A2.2A.2A9.B.B\$26.BA9.4B7.3A5.4B87.5B3.4B7.A5.4B11.B
2A2B4.A.A3.A.A2.B8.5B\$25.AB9.4B10.A6.4B88.3B2.4B5.3A7.4B10.5B5.A.4A2.
AB2A6.6B\$25.5A5.4B5.2A12.4B74.2AB2A7.9B6.A10.4B8.6B7.A3.A.A.2A4.8B\$
30.A4.4B5.A14.4B73.2ABA8.8B19.4B7.5B7.A2.BA.A2.13B\$27.3AB2.7B.BA.A15.
4B75.A.B3.10B21.4B5.6B6.A.2BA.A5.13B\$26.A.2B3.7B.B2A17.4B74.3AB.2B2A
7B22.4B3.7B6.2A.2BA5.15B\$26.4A12B20.4B71.2A2.BA3B2A7B23.4B3.6B10.3B4.
15B\$24.2A2.BA3B2A7B21.4B69.A2.4A12B24.4B2.7B10.4B.17B\$23.A2.3AB.2B2A
7B22.4B68.2A.A.2B3.7B.B2A23.4B.6B4.29B\$23.2A.A.B3.10B23.4B50.A11.2A4.
A2.3AB2.7B.BA.A23.11B2.16B2A13B\$26.A8.8B23.4B48.A.A9.B2AB3.A5.A4.4B5.
A6.A17.10B2.16B2A14B\$26.2A7.9B23.4B39.A3.2A2.A.A9.3B5.5A5.4B5.2A3.3A
18.10B.27B3.B2A\$36.3B2.4B23.4B29.2A6.A.A2.A2.2A.2A9.B.B6.A8.4B8.A17.A
B3.36B4.A2.A\$34.5B3.4B23.4B27.B2A2B4.A.A3.A.A2.B8.5B16.4B7.2A15.A.AB
2.20B2.2B2.B3.6B5.2A.A\$34.2A7.4B23.4B27.4B5.A.4A2.AB2A6.6B17.4B3.5B
16.A21B14.6B7.A\$35.A8.4B23.4B24.6B7.A3.A.A.2A4.8B18.4B2.3B19.B.17B14.
9B6.2A\$32.3A10.4B23.4B23.5B7.A2.BA.A2.13B20.9B7.2AB2A7.17B15.2A4.4B\$
32.A13.4B23.4B21.6B6.A.2BA.A5.13B19.8B8.AB2A8.17B15.A5.4B\$47.4B23.4B
19.7B6.2A.2BA5.15B19.10B3.B.A11.17B12.3A7.4B\$48.4B23.4B19.6B10.3B4.
15B19.7B2A2B.B3A12.14B.B2A10.A10.4B\$49.4B23.4B18.7B10.2B.B.17B18.7B2A
3BAB2.2A11.10B4.BA.A21.4B\$50.4B23.4B17.6B4.29B18.12B4A2.A2.A7.8B9.A
22.4B\$51.4B23.4B16.7B2.16B2A13B15.2AB.7B3.2B.A.2A2.3A5.9B8.2A22.4B\$
52.4B23.4B15.7B2.16B2A14B13.A.AB.7B2.B3A2.A6.A4.9B33.4B\$53.4B23.4B13.
9B.27B3.B2A12.A5.4B4.A5.A5.A2.11B5.A29.4B\$54.4B23.4B12.36B4.A2.A10.2A
5.4B5.5A6.2A12B3.3A30.4B\$55.4B23.4B6.B4.20B2.2B2.B3.6B5.2A.A15.4B8.A
10.A10B3.A34.4B\$56.4B23.4B4.2AB.19B14.6B7.A14.4B18.2A.10B3.2A34.4B\$
57.4B23.4B3.2A19B14.9B6.2A12.4B19.A3.B.6B.5B35.4B\$58.4B23.4B3.B.17B
15.2A4.4B18.4B18.A.A5.6B.3B38.4B\$59.4B23.4B5.17B15.A5.4B16.4B19.2A7.
10B7.2AB2A26.4B\$60.4B23.4B4.17B12.3A7.4B14.4B31.8B8.AB2A27.4B\$61.4B
23.4B3.15B.B2A10.A10.4B12.4B33.10B3.B.A31.4B\$62.4B23.4B2.12B4.BA.A21.
4B10.4B34.7B2A2B.B3A32.4B\$63.4B23.16B8.A22.4B8.4B35.7B2A3BAB2.2A31.4B
\$64.4B23.15B8.2A22.4B6.4B36.12B4A2.A31.4B\$65.4B23.15B32.4B4.4B35.2AB.
7B3.2B.A.2A32.4B\$66.4B23.14B33.4B2.4B35.A.AB.7B2.B3A2.A34.4B\$67.4B23.
11B.B2A.A30.8B36.A5.4B4.A5.A35.4B\$68.4B23.9B2.B2AB3A29.6B36.2A5.4B5.
5A37.4B\$69.4B22.9B4.B4.A29.4B43.4B8.A40.4B\$70.4B23.6B4.2A.3A12.B16.6B
41.4B51.4B\$71.4B23.5B5.A.A13.3B14.8B39.4B53.4B\$72.4B23.4B5.A.A3.2A6.
3B2A13.4B2.4B37.4B55.4B\$73.4B23.4B5.A5.A6.3BA.AB10.4B4.4B35.4B57.4B\$
74.4B23.4B10.A.AB2.4B.2A2B8.4B6.4B33.4B59.4B\$75.4B23.4B10.2AB2.3B.4B
8.4B8.4B31.4B61.4B\$76.4B23.4B10.11B8.4B10.4B29.4B63.4B\$77.4B23.4B10.
10B7.4B12.4B27.4B65.2B2D\$78.4B23.4B9.8B8.4B14.4B25.4B67.BDBD\$79.4B23.
4B8.7B8.4B16.4B23.4B69.DB\$77.7B23.4B6.8B7.4B18.4B21.4B\$75.10B23.4B3.B
.8B6.4B20.4B19.4B\$74.12B23.16B5.4B22.4B6.A10.4B\$75.13B22.17B2.4B6.A
17.4B5.3A7.4B\$75.14B21.17B.5B4.3A18.4B7.A5.4B\$74.16B20.25B.A22.4B5.2A
4.4B\$73.17B20.25BA.A22.4B4.9B\$73.18B19.23B.2BAB23.4B5.6B\$72.19B20.21B
3.2B25.4B2.8B\$52.A19.20B19.20B3.2B27.15B\$50.3A20.20B18.19B3.B2AB27.
14B\$37.A11.A21.21B18.21B3.2A29.13B\$37.3A9.2A20.21B18.22B34.10B.B2A\$
40.A9.B20.19B20.21B37.3B2AB3.BA.A\$4.D22.2A10.2A9.3B19.17B16.2A3.19B
39.3B2AB6.A\$3.2BD22.A10.5B5.6B16.18B17.A3.18B42.4B6.2A\$3.3DB21.A.AB9.
4B3.10B11.20B17.A.2A17B43.3B\$4.4B10.A10.2AB.3B4.6B2.11B3.2B2.22B13.A
2.2A.A.A18B39.AB.2B\$5.4B7.3A12.7B.13B2A34B13.4A2.A4.17B37.A.AB2AB\$6.
4B5.A15.21B2A32B13.2A5.2A5.17B36.A.ABABAB\$7.4B4.2A15.53B13.A2.A2.2A6.
12B3.4B34.2A.A.A.A2.A\$2A6.9B14.54B13.3A2.A.A5.8B.4B4.4B34.A2.2A.4A\$.A
7.6B14.56B16.2A.B5.8B11.4B33.A4.A2.2B\$.A.2A5.6B3.B2.2B2.19B.B3.13B.4B
4.13B13.2A.A2.2B3.8B13.4B33.3A.A2.2A\$2.A2.A4.33B7.7B.B5.3B4.4B4.6B14.
A.A.BA2B.8B15.4B34.2A3.2A\$3.2AB3.27B.6B19.4B4.4B5.7B13.A.A.A.A9B17.4B
\$4.14B2A16B2.B.5B17.2A5.4B6.6B15.2A.2A.8B19.4B\$5.13B2A16B7.2A18.A4.4B
6.6B24.5B21.3BD\$6.29B8.A9.A6.3A4.4B7.6B24.4B23.3BD\$6.17B.4B16.3A6.3A
4.A5.4B7.8B22.4B25.3D\$7.15B2.5B17.A9.A8.4B9.6B22.4B\$7.15B5.A2B.2A22.
2A7.4B10.7B20.4B\$8.13B5.A.A2B.A22.5B3.4B9.11B17.4B\$10.13B2.A.AB2.A25.
3B2.4B8.B.2B2A9B14.4B\$9.8B4.2A.A.A3.A16.2A7.9B8.2A3B2A9B13.4B\$9.6B6.
2ABA2.4A.A14.A8.8B9.2A14B12.4B\$9.5B8.B2.A.A3.A.A10.2A.A.B3.10B11.14B
12.4B\$9.B.B9.2A.2A2.A2.A.A10.A2.3AB.2B2A7B9.5B2.B2.2B.3B11.4B\$10.3B9.
A.A2.2A3.A12.2A2.BA3B2A7B9.2A4.3B5.2A10.4B\$9.B2AB9.A.A22.4A12B10.A3.B
2AB5.A10.4B\$10.2A11.A23.A.2B3.7B.B2A5.3A5.2A7.3A6.4B\$48.3AB2.7B.BA.A
4.A18.A5.4B\$51.A4.4B5.A28.4B\$46.5A5.4B5.2A26.4B\$46.AB9.4B31.4B\$47.BA
9.4B29.4B\$47.2A10.4B27.4B\$60.4B25.4B\$61.4B23.4B\$62.4B21.4B\$63.4B19.4B
\$64.4B10.A6.4B\$65.4B7.3A5.4B\$66.4B5.A7.4B\$67.4B4.2A5.4B\$68.9B4.4B\$69.
6B5.4B\$69.8B2.4B\$67.15B\$67.14B\$67.13B\$65.2AB.10B\$64.A.AB3.B2A3B\$64.A
6.B2A3B\$63.2A6.4B\$72.3B\$73.2B.BA\$72.B2ABA.A\$71.BABABA.A\$69.A2.A.A.A.A
.2A\$69.4A.2A2.A2BA\$73.A4.2A\$71.A.A\$71.2A!``````
Princess of Science, Parcly Taxel

Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### Re: State of the OR and XOR gates

Smaller OR gate, which still fits the conditions I set:

Code: Select all

``````x = 166, y = 89, rule = LifeHistory
148.2A\$148.A\$145.A4.A2.2A\$145.5A.A2.A\$131.2A16.B.2A.A.2A\$116.A15.A10.
4AB3AB2.A2.A\$94.2A18.3A15.A.AB7.A2.A.A3B2A.A\$95.A17.A19.2AB.3B4.7B2.A
.2A\$95.A.AB14.2A20.7B3.7B.A\$96.2AB.2A12.B20.16B.2A\$98.2B2AB11.3B19.
15B\$97.3B2.B2.2B6.6B16.16B\$98.10B4.10B11.18B\$97.13B2.11B3.2B2.20B\$72.
A24.15BD3B2A15BD15B3.2A\$70.3A24.15B2D2B2A15BDBD4B.7B5.A\$57.A11.A26.
17B2D18B3D4B2.7B4.A.2A\$57.3A9.2A25.17BD21BD4B2.8B4.A.A8.B\$60.A9.B25.
16BD26B4.7B5.B8.2B\$23.C23.2A10.2A9.3B19.B3.17B.13B.B.2B10.8B2.B.3B6.
3B\$24.2C22.A10.5B5.6B11.4B2.B.27B.B19.8B.7B4.4B\$23.2C.B21.A.AB9.4B3.
10B6.9B.22B26.17B2.4B\$24.4B10.A10.2AB.3B4.6B2.11B3.34B9.2A15.22B\$25.
4B7.3A12.7B.9BD3B2A15BD27B7.A.A14.22B\$26.4B5.A15.17B2D2B2A15BDBD26B6.
A17.20B\$27.4B4.2A15.17B2D18B3DB2A23B5.2A17.19B\$20.2A6.9B14.18BD21BDB
2A21B27.13B2D2B\$21.A7.6B14.19BD48B27.11BDBDB\$21.A.2A5.6B3.B2.2B2.19B.
B3.13B.B5.26B32.9BD\$22.A2.A4.19BD13B7.7B.B13.B2.19B10.3D5.D3.3D9.9B\$
23.2AB3.20BDBD4B.6B28.2B.19B10.D3.D3.2D2.D3.D7.9B.D\$24.14B2A9B3D4B2.B
.5B28.21B9.D6.D.D2.D3.D8.7B.3D\$25.13B2A11BD4B7.2A28.8B.12B9.4D2.D2.D
2.D3.D9.5B.D.D.D\$26.29B8.A14.2A5.2A4.4B.5B.12B9.D3.D.5D.D3.D9.5B3.D\$
26.17B.B.2B16.3A12.A5.2A2B.4B2.4B3.9B.B2A7.D3.D4.D2.D3.D8.5B4.D\$27.
15B4.3B17.A12.A.A4.7B13.6B.BA.A7.3D5.D3.3D8.8B\$2.C24.15B5.A2B.2A27.2A
2.8B14.6B4.A29.4B3.2A\$C.C25.13B5.A.A2B.A31.2A5B15.5B5.2A27.4B4.A\$.2C
27.13B2.A.AB2.A31.ABA5B16.3B34.4B6.3A\$29.8B4.2A.A.A3.A33.A7B16.2B33.
4B9.A\$29.6B6.2ABA2.4A.A27.A4.8B14.4B31.4B\$29.5B8.B2.A.A3.A.A25.3A2.B.
B3.4B12.B2AB31.4B\$29.B.B9.2A.2A2.A2.A.A24.A.3A8.4B12.2A31.4B\$30.3B9.A
.A2.2A3.A24.A3.A10.4B43.4B\$29.B2AB9.A.A31.A3.A12.4B41.4B\$30.2A11.A31.
3A.A14.4B39.4B\$55.2A19.3A4.2A10.4B37.4B\$55.A.A19.A5.A.A10.4B35.4B\$57.
A4.2A21.A4.2A5.4B33.4B\$53.4A.2A2.A2.A15.4A.2A2.A2.A4.4B31.4B\$53.A2.A.
A.A.A.2A15.A2.A.A.A.A.2A5.4B29.4B\$55.BABABA.A20.BABABA.A9.4B27.4B\$56.
B2ABA.A21.B2ABA.A10.4B25.4B\$57.2B.BA23.2B.BA12.4B23.4B\$56.3B25.3B16.
4B21.4B\$47.2A6.4B16.2A6.4B17.4B19.4B\$48.A6.B2A3B15.A6.B2A3B16.4B17.4B
\$48.A.AB3.B2A3B15.A.AB3.B2A3B17.4B15.4B\$49.2AB.10B14.2AB.10B16.4B13.
4B\$51.13B15.13B16.4B11.4B\$51.14B14.14B16.4B9.4B\$51.15B10.A2.15B16.4B
7.4B\$53.8B2.4B7.3A4.8B2.4B16.4B5.4B\$53.6B5.4B5.A7.6B5.4B16.4B3.4B\$30.
B21.9B4.4B4.2A5.9B4.4B16.4B.4B\$28.4B19.4B4.2A5.9B4.4B4.2A5.4B16.7B\$
29.4B10.A6.4B5.A7.6B5.4B5.A7.4B10.A5.5B\$30.4B7.3A5.4B7.3A4.8B2.4B7.3A
5.4B7.3A4.6B\$31.4B5.A7.4B10.A2.15B10.A6.4B5.A7.6B\$32.4B4.2A5.4B14.14B
19.4B4.2A5.4B2.B2A\$33.9B4.4B15.13B21.9B4.4B3.BA.A\$34.6B5.4B14.2AB.10B
23.6B5.4B7.A\$34.8B2.4B14.A.AB3.B2A3B25.8B2.4B8.2A\$32.15B15.A6.B2A3B
23.15B\$32.14B15.2A6.4B25.14B\$32.13B25.3B25.13B\$30.2AB.10B27.2B.BA20.
2AB.10B\$29.A.AB3.B2A3B28.B2ABA.A18.A.AB3.B2A4B\$29.A6.B2A3B27.BABABA.A
18.A6.B2A3B\$28.2A6.4B27.A2.A.A.A.A.2A14.2A6.5B\$37.3B27.4A.2A2.A2.A22.
4B\$38.2B.BA28.A4.2A23.5B.BA\$37.B2ABA.A25.A.A31.B2ABA.A\$36.BABABA.A25.
2A32.ABABA.A\$34.A2.A.A.A.A.2A53.A2.A.A.A.A.2A\$34.4A.2A2.A2.A53.4A.2A
2.A2.A\$38.A4.2A59.A4.2A\$36.A.A63.A.A\$36.2A64.2A!``````
If you can find a smaller one (even if it involves p8 tech), please post it here.
Princess of Science, Parcly Taxel

chris_c
Posts: 907
Joined: June 28th, 2014, 7:15 am

### Re: State of the OR and XOR gates

Freywa wrote:Smaller OR gate, which still fits the conditions I set:

Code: Select all

``rle``
If you can find a smaller one (even if it involves p8 tech), please post it here.
Aha. When I see the need for a fast glider in the same direction as a Herschel I always think of this conduit. Hence I came up with this:

Code: Select all

``````x = 104, y = 124, rule = B3/S23
2bo\$obo\$b2o62\$76b2o\$76bo\$74bobo\$74b2o13\$44b2o\$45bo\$44bo\$44b2o2b2o\$47bo
bo\$42b4obo\$42bo2bob2o5\$11bo22b2o\$12bo22bo20b2o18bo\$10b3o22bobo18bo19b
3o\$25bo10b2o16bobo22bo7b2o\$23b3o28b2o10b2o10b2o7b2o\$22bo44bo\$22b2o43bo
bo\$7b2o59b2o\$8bo\$8bob2o\$9bo2bo\$10b2o\$25b2o\$25b2o3\$57b2o\$57b2o23b2o\$33b
o3b2o43bo13bobobobo\$32bobo3bo44b3o9bob2ob2obo\$28b2obobo3bo47bo9bo3bo3b
o\$28b2obo4bo57b2o3bob2o\$32b5obo22b2o37bo\$24b2obob2obo4bobo22bo35bobo\$
24bob2obo2bob2o2bo20b3o36b2o\$17b2o12b2obob2o8b2ob2o8bo\$17b2o26bobobobo
\$43b3o3bobo2bo\$42bo4bobob4o\$42b2ob2ob2o\$46bo3b3o\$46bob2o2bo\$47bobo!
``````

Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### Re: State of the OR and XOR gates

chris_c wrote:Aha. When I see the need for a fast glider in the same direction as a Herschel I always think of this conduit. Hence I came up with this:
Well, I admit defeat there. Congratulations.

Because it is a variant of F131 that liberates an extra glider, I didn't see it in the H-to-H collection (which only lists the standard F131). The variant should be added on the next update.

Speaking of conduits, Sokwe mentioned that F131 can be split into a H-to-R and R-to-H, but I don't see either of those components in the elementary conduits collection. These should also be added soon.
Princess of Science, Parcly Taxel

dvgrn
Moderator
Posts: 5878
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: State of the OR and XOR gates

Freywa wrote:Because it is a variant of F131 that liberates an extra glider, I didn't see it in the H-to-H collection (which only lists the standard F131). The variant should be added on the next update.
I added a note in the ECC thread. Am still hoping someone else will take over the maintenance on that collection, and maybe add repeat-time ratings for all the conduits... probably wishful thinking, but in the meantime I'm at least as competent a procrastinator as the next Lifenthusiast.

That F131 would have been really exciting a decade or two ago, since the crossing output gliders allow for a fairly reasonable Herschel splitter, just a bit too slow for gmc_nxtman's collection:

Code: Select all

``````x = 62, y = 102, rule = LifeHistory
27.7B\$27.3B3DB2.2A\$27.4BD2B.B2AB\$27.2B3D2B2.2B\$28.6B3.2B\$28.7B.2BAB\$
28.9BA.A\$29.8B.A\$29.7B3.3A\$28.8B5.A\$28.7B\$29.6B\$29.6B\$29.7B2.2B\$29.
13B\$27.16B\$27.16B\$26.17B\$26.17B\$25.19B\$24.19B\$24.6BD12B\$23.6B3D11B\$
23.8BD11B\$23.20B\$22.13BA7B\$22.12BABA6B\$21.13BA2BA2B\$21.14B2A3B\$19.17B
\$18.15B\$18.15B\$14.2B.17B\$13.2A20B\$13.2A20B\$14.2B.2AB.15B\$17.2AB2.15B\$
21.10B2A5B\$21.10B2A5B\$21.18B\$20.20B\$20.20B\$21.B.18B\$22.12BA7B.B\$23.
10BABA5B.B2A\$21.12BABA7B2A\$21.2A.10BA6B.2B\$22.A3.15B\$19.3A5.14B\$19.A
4.2B.8B.6B\$23.2A9B3.6B\$23.2AB.7B4.6B\$24.B.9B4.6B\$14.2A11.7B6.6B\$15.A
12.6B7.6B\$14.A12.4B.B9.6B\$14.2A2.2A6.4B13.6B\$17.A.A5.4B17.4B\$12.4A.A
6.4B19.4B\$12.A2.A.2A4.4B21.4B\$15.5B2.4B20.7B\$16.9B19.9B\$16.8B19.11B\$
15.8B21.13B\$4.2A9.7B22.14B\$5.A10.6B4.2A15.16B\$5.A.AB7.6B4.A15.17B\$6.
2AB.3B3.6B.BA.A15.18B\$8.14B.B2A15.19B\$8.16B17.20B\$9.15B10.A7.20B\$8.
16B10.3A3.21B\$6.18B13.A2.21B\$4.19B13.2A2.19B\$4.2BC16B18.17B\$3.3BCBC4B
.9B17.18B\$4.2B3C4B.10B14.20B\$3.5BC4B.11B.2B3.2B2.22B\$2.22B.13BD18B\$.
4B6.27BDBD14B\$4B7.16B2A9B3D13B\$3B9.15B2A11BD13B\$2B10.11B.30B\$B12.10B
3.2B.3B.4B4.13B\$14.7B12.3B4.4B4.6B\$14.7B10.4B4.4B5.7B\$15.5B11.2A5.4B
6.6B\$16.3B13.A4.4B6.6B\$17.4B8.3A4.4B7.6B\$16.2A.2A8.A5.4B7.8B\$15.ABABA
BA12.4B9.6B\$13.3A.B.A.A2.A22.7B\$12.A4.A.A.4A20.14B\$12.2A.2A.2A23.B.2B
2A11BD\$16.A3.3A19.2A3B2A9B3DB\$16.A.2A2.A19.2A14BDBD\$17.A.A23.15BD\$41.
5B2.B2.2B2.2B\$41.2A4.3B\$42.A3.B2AB\$39.3A5.2A\$39.A!``````

Freywa
Posts: 589
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

### Re: State of the OR and XOR gates

With the relatively small OR gate, it is easy to build an RS flip-flop:

Code: Select all

``````x = 155, y = 118, rule = LifeHistory
151.4B\$150.4B\$149.4B\$148.4B\$108.2A11.A25.4B\$107.B2AB9.A.A23.4B\$108.3B
9.A.A2.2A3.A3.A10.4B\$107.B.B9.2A.2A2.A2.A.A2.3A7.4B\$107.5B8.B2.A.A3.A
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108.13B2.A.AB2.A8.6B4.D3.D\$106.13B5.A.A2B.A7.5B5.D3.D\$105.15B5.A2B.2A
6.7B4.D3.D\$40.A.A62.15B4.3B10.6B5.D2.D\$39.A.2A2.A58.17B.B.2B10.7B6.2D
.D\$39.A3.3A58.29B4.6B\$35.2A.2A.2A60.13B2A16B2.7B\$35.A4.A.A.4A54.14B2A
16B2.7B\$36.3A.B.A.A2.A53.2AB3.27B.9B\$10.2A26.ABABABA55.A2.A4.36B\$9.B
2AB11.2A.A.2A8.2A.2A8.A46.A.2A5.6B3.B2.2B2.20B4.B\$10.3B4.A.2A.A2.A.2A
2.A8.4B8.3A36.2A6.A7.6B14.19B.B2A\$9.B.B5.2A.A.2A.A4.A.A6.3B13.A35.A.A
4.2A6.9B14.19B2A\$9.5B8.B2.5A.A6.5B11.2A37.A11.4B4.2A15.17B.B\$9.6B6.2A
BA4.A7.7B10.4B29.2A3.A.2A8.4B5.A15.17B\$9.8B4.2A.A.AB2.A6.7B12.3B19.A
9.A3.A3.A6.4B7.3A12.17B\$10.13B2.A.A2B.A4.10B3.2B.3B.4B16.3A9.A.2A.2A.
A5.4B10.A10.2AB.15B\$8.13B5.A2B.2A3.11B.20B8.A13.A.A.A.A5.4B21.A.AB4.
12B\$7.15B3.3B7.15B2A16B7.2A14.4B5.4B22.A9.11B\$7.15B3.2B7.16B2A16B2.B.
5B13.4B5.4B22.2A8.13B\$6.17B.4B6.34B.6B4.3B6.7B3.4B33.12B\$6.41B.27B2.
6B2.2B.8B.4B35.10B\$5.13B2A16B.11B.2B3.2B2.25B.16B37.9B\$4.14B2A16B.10B
14.38B38.9B\$3.2AB3.27B.9B17.35B39.9B\$2.A2.A4.36B18.33B41.5B\$.A.2A5.6B
3.B2.2B2.20B17.33B42.4B\$.A7.6B14.18B16.7B.24B43.4B\$2A6.9B14.16B14.2AB
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10.5B2.14B43.4B\$5.4B7.3A12.14B.B2A10.2A10.2A4.3B2A9B43.4B\$4.4B10.A10.
2AB.3B3.6B.BA.A22.A4.3B2A8B43.4B\$3.3DB21.A.AB7.6B4.A19.3A6.11B43.4B\$
3.2BD22.A10.6B4.2A18.A11.2B.4B43.4B\$4.D5.3D14.2A9.7B38.4B43.4B\$9.D3.D
24.8B36.4B43.4B\$9.D29.8B34.4B43.4B\$10.3D26.9B32.4B43.4B\$13.D24.5B2.4B
30.4B43.4B\$9.D3.D21.A2.A.2A4.4B28.4B43.4B\$10.3D22.4A.A6.4B26.4B43.4B\$
40.A.A5.4B24.4B43.4B\$37.2A2.2A6.4B22.4B43.4B\$37.A12.4B20.4B43.4B\$38.A
12.4B18.4B43.4B\$37.2A13.4B16.4B43.4B\$53.4B14.4B43.4B\$54.4B12.4B43.4B\$
55.4B10.4B43.4B\$56.4B8.4B43.4B\$57.4B6.4B43.4B\$58.4B4.4B43.4B\$59.4B2.
4B43.4B\$60.8B43.4B\$61.6B43.4B\$62.4B43.4B\$61.6B41.4B\$60.7B40.4B\$59.4B
3.B2A26.2A9.4B\$58.4B4.BA.A26.A8.4B\$57.4B8.A26.A.AB4.4B\$56.4B9.2A26.2A
B3.4B5.4D\$55.4B40.7B6.D3.D\$54.4B41.6B7.D3.D\$53.4B43.6B6.4D\$40.2A10.4B
43.8B5.D.D\$41.A9.4B43.8B6.D2.D\$39.A10.4B43.4B.5B5.D3.D\$39.5A5.4B5.2A
36.4B4.4B\$44.A4.4B5.A36.4B6.B3D\$41.3AB2.7B.BA.A35.4B8.D2B\$40.A.2B3.7B
.B2A35.4B10.D\$40.4A12B36.4B\$38.2A2.BA3B2A7B35.4B\$37.A2.3AB.2B2A7B34.
4B\$37.2A.A.B3.10B33.4B\$40.A8.8B31.4B\$40.2A7.9B29.4B\$50.3B2.4B27.4B\$
48.5B3.4B25.4B\$48.2A7.4B23.4B\$49.A8.4B21.4B\$46.3A10.4B19.4B\$46.A13.4B
6.A10.4B\$61.4B5.3A7.4B\$62.4B7.A5.4B\$63.4B5.2A4.4B\$64.4B4.9B\$65.4B5.6B
\$66.4B2.8B\$67.15B\$68.14B\$69.13B\$70.10B.B2A\$72.3B2AB3.BA.A\$72.3B2AB6.A
\$74.4B6.2A\$74.3B\$71.AB.2B\$70.A.AB2AB\$70.A.ABABAB\$67.2A.A.A.A.A2.A\$67.
A2.A2.2A.4A\$69.2A4.A\$75.A.A\$76.2A!``````
The ANDNOT gate (R input) can be moved to any suitable place along the loop. It should be easy to use different syringe+H-to-2G combinations to achieve all residues for the loop period modulo 8; the arrangement shown has period 787.
Princess of Science, Parcly Taxel