Now, big strings of Silver reflectors and complicated 223x106 G-to-MWSS converters and so on were what was was available in 2010, when the pi and phi calculators and Osqrtlogt showed up. But looking at all this anachronistic circuitry has made me curious about what a pi calculator would look like if it were built in 2019.
I'll try posting a few "original" and "replacement" circuits, each pair in its own post, and see if anyone wants to make a move or two in the Pointless Optimization Game.
First, here's the splitter that's used to program the computer, producing a NW-traveling action signal wherever it's present on the NE/SW glider lane representing the computer's current state.
Code: Select all
x = 183, y = 176, rule = LifeHistory 174.A3B$173.BABA$172.2B2A$171.4B$170.4B$161.B7.4B$75.10B76.B6.4B$75. 3B83.B5.4B$75.4B82.B4.4B$75.5B81.B3.4B$75.B.4B80.B2.4B$75.B2.4B79.B. 4B$75.B3.4B78.5B$75.B4.4B77.4B$75.B5.4B75.11B$75.B6.4B73.4B$83.4B71. 4B$84.4B69.4B$85.4B67.4B$86.4B65.4B$87.4B63.4B$88.4B61.4B$89.4B59.4B$ 90.4B57.4B$91.4B55.4B$92.4B53.4B$93.4B51.4B$94.4B49.4B$95.4B47.4B$96. 4B45.4B$97.4B43.4B$98.4B41.4B$99.4B39.4B$100.4B37.4B$101.4B21.A13.4B$ 102.4B20.3A10.4B$103.4B22.A8.4B$104.4B20.2AB6.4B$105.4B19.5B3.4B3.2A$ 106.4B20.3B2.4B4.A$107.4B19.8B2.BA.A$108.4B16.2BA8B.B2A$109.4B13.3BAB A9B$110.4B12.3BABA10B$111.4B9.2AB.2BA10B$112.4B7.A.AB.11B.B2A$113.4B 6.A6.7B3.BA.A$114.4B4.2A5.7B7.A$115.4B11.6B7.2A$116.4B9.7B$117.4B7.8B $118.4B5.9B$119.4B3.4B.5B$120.4B.4B.7B$121.7B2.2B2A3B$122.5B4.B2A2B$ 122.5B3.6B$121.7B2.6B$120.4B.4B.7B$119.4B3.4B.6B$118.4B5.9B$117.4B7. 8B$116.4B9.8B$115.4B11.7B$48.A65.4B13.6B7.2A$46.3A64.4B14.7B6.A$20.2A 23.A66.4B15.7B3.BA.A$21.A23.2A64.4B16.8B2.B2A$21.A.AB18.4B63.4B17.11B $22.2AB.2A14.3B20.A43.4B18.11B$24.2B2AB12.4B.3B.B12.3A42.4B19.11B$24. 4B6.18B10.A44.4B21.11B$24.6B3.16B2A2B5.B3.2A42.4B22.2B.8B$25.6B2.16B 2A2B3.8B41.4B22.13B$25.7B.20B.8B21.A20.4B23.14B$24.38B12.2A5.3A19.4B 22.12B.4B9.2A$23.20B2.2B.15B10.B2AB3.A14.A6.4B21.13B3.4B8.A$22.18B8. 17B8.3B4.2A11.3A5.4B21.17B.4B4.BA.A$22.16B11.19B2.2B2.B2.5B10.A7.4B 22.18B.4B3.B2A$23.14B12.31B12.2A5.4B21.2AB.13B2A2B.7B$22.16B12.7B.21B 2A9.4B4.4B21.A.AB3.4B.6B2AB3.6B$20.2AB.14B11.25B2A3B2A8.3B5.4B22.A8.B 4.8B3.4B$19.A.AB.6B3.3B.B2A8.26B2A2B.B8.4B4.4B22.2A15.6B2.6B$19.A4.6B 7.BA.A8.8B2.19B9.4B4.4B39.7B.8B$18.2A4.7B9.A8.6B11.10B10.4B4.4B40.6B. 4B2.4B$24.8B2.2A4.2A8.5B12.9B9.4B4.4B42.9B4.4B$22.12BA.A13.4B14.9B7. 4B4.4B43.8B6.4B$22.11B3.A13.4B15.7B7.4B4.4B43.8B8.4B$22.5B2A4B3.2A10. 2AB.B17.6B6.4B4.4B35.A8.7B10.4B$22.5B2A3B15.A.AB18.6B6.4B4.4B36.3A6. 6B12.4B$22.10B15.A20.8B4.4B4.4B40.A4.7B13.4B$22.9B15.2A21.8B2.4B4.4B 19.A20.2A4.7B14.4B$22.9B38.13B4.4B.3B.B12.3A15.A4.4B.8B15.4B$23.8B38. 28B10.A18.3A4.11B16.4B$22.8B39.25B2A2B5.B3.2A20.A2.12B17.4B$23.6B40. 25B2A2B3.8B19.2A2.12B18.4B$17.2A4.6B39.30B.8B21.B3.11B20.4B$18.A4.6B 37.41B19.3B4.7B24.4B$18.A.AB.7B36.22B2.2B.15B16.6B3.8B24.4B$19.2AB2. 6B35.20B8.17B11.10B2.9B24.12B$21.8B36.21B8.19B2.2B3.23B24.4B$21.8B36. 17B.4B7.31B2A16B.B23.4B$22.8B34.19B.4B7.7B.22B2A17B2A22.5B$23.7B8.A 23.21B2.3B6.50B2A22.B.4B$24.6B6.3A23.21B3.4B3.52B23.B2.4B$24.7B4.A25. 20B7.2A4.8B2.36B2.5B21.B3.4B$24.7B4.2A25.20B6.A5.6B11.4B.13B5.5B6.2A 21.B4.4B$24.8B.4B26.19B7.3A3.5B12.3B5.B.7B3.3B.2B7.A22.B5.4B$24.11B 28.18B10.A3.4B14.4B15.2A12.3A19.B6.4B$24.12B28.17B15.3B16.2A16.A14.A 27.4B$24.12B28.16B14.4B17.A14.3A44.4B$25.11B29.14B15.2A20.3A11.A47.4B $28.7B31.13B16.A22.A60.4B$27.8B5.2A27.11B12.3A85.3B$26.8B6.A29.9B13.A 88.2B$27.8B2.BA.A29.7B105.B$26.10B.B2A31.4B$26.12B34.3B$26.12B35.4B$ 24.2AB2.9B37.2A$23.A.AB2.8B38.A$23.A6.6B40.3A$22.2A5.6B43.A$30.5B$30. 7B$30.8B2.2A$28.12BA.A$28.11B3.A$28.5B2A4B3.2A$28.5B2A3B$28.10B$28.9B $28.9B$29.8B$28.8B$29.6B$23.2A4.6B$24.A4.6B$24.A.AB.7B$25.2AB2.6B$27. 8B$27.8B$28.8B$29.7B8.A$30.6B6.3A$30.7B4.A$26.B3.7B4.2A$25.3B2.8B.4B$ 25.4B.11B$25.4B.12B$22.20B$21.9B.11B$21.10B3.9B9.B$21.22B.2B5.4B$20. 27B2.7B$19.35B2A2B$18.35BA2BAB$17.37B2AB$16.4B.31B.4B$15.4B3.30B2.2B$ 14.4B5.B2.3B.21B$13.4B9.4B3.11B4.B$12.4B10.B2AB4.8B5.3B$11.4B12.2A6. 6B6.B2AB$10.4B23.2B9.2A$9.4B23.2B$B7.4B23.B2AB$B6.4B25.2A$B5.4B$B4.4B $B3.4B$B2.4B$B.4B$5B$4B$10B!
1) the SW output lane is the same as the SW input lane, so the input glider ends up at the same place if the circuit is removed (slightly different timing is allowed);
2) the NW output lane is transparent.
The best replacement I've come up with so far is this one:
Code: Select all
x = 106, y = 99, rule = LifeHistory 99.A3B$98.BABA$97.2B2A$96.4B$95.4B$86.B7.4B$86.B6.4B$86.B5.4B$86.B4. 4B$86.B3.4B$75.A10.B2.4B$75.3A8.B.4B$78.A7.5B$77.2A7.4B$77.5B3.11B$ 79.3B2.4B$69.2A7.9B$69.A8.8B$66.2A.A.B3.10B$66.A2.3AB.2B2A7B$67.2A2.B A3B2A7B$69.4A12B$69.A.2B3.7B.B2A3.2A$70.3AB2.7B.BA.A.A.A$73.A4.4B5.A. A$68.5A5.4B5.A2.A$68.A10.4B5.A.AB$70.A9.4B5.A3B$69.2A10.4B6.4B$85.B5. 6B$85.2B4.7B$84.4B2.8B.4B.B$67.4B14.17B.B2A$86.18B2A$65.4B17.16B.2B$ 86.5BD10B$10B53.4B19.6BD8B$4B80.2AB.2B3D7B$5B56.4B18.A.AB2.11B$B.4B 77.A5.10B3.2A$B2.4B52.4B19.2A5.2B2A6B3.A$B3.4B80.3B2A6B4.A$B4.4B48.4B 28.10B3.2A$B5.4B79.8B.B2A$B6.4B25.A18.4B29.7B3.B2AB2A$B7.4B24.3A49.6B 6.B.A$9.4B26.A49.8B2.2A3.A$10.4B24.2A10.A38.8B.A2.4A$11.4B23.5B6.A.A 36.8B.A.A.A$12.4B24.4B5.A.A27.A8.7B3.A2.A.2A$13.4B10.A11.6B3.2A.3A25. 3A6.6B7.A.A$14.4B9.3A9.6B4.B4.A27.A4.2B3D2B6.2A2.A$15.4B11.A8.7B.B2AB 3A6.A20.2A4.4BD2B3.A.A2.A.A$16.4B9.2A5.2B.6B2.B2A.A6.3A15.A4.4B.4B3DB 3.2A2.A.A$17.4B8.21B7.A18.3A4.11B8.A$18.4B9.17B5.B3.2A20.A2.12B$19.4B 7.2B2A15B2.8B19.2A2.12B$20.4B5.2BA2BA22B21.B3.11B$21.4B4.3B2A23B19.3B 4.7B$22.4B.9B3.19B16.6B3.8B$23.12B4.21B11.10B2.9B$24.10B4.25B2.2B3. 23B$25.9B3.4B4.14BD15B2A3BD12B.B$26.9B.4B6.6B.4BDBD15B2A2B2D13B2A$27. 7B.4B5.5B.B2.4B3D18B2D14B2A$28.10B6.2A7.4BD21BD15B$29.8B8.A8.26BD9B2. 5B$30.6B6.3A19.B.13B5.5B6.2A$31.4B7.A27.B.7B3.3B.2B7.A$30.6B46.2A12. 3A$29.8B28.2A16.A14.A$28.4B2.4B27.A14.3A$27.4B4.4B27.3A11.A$26.4B6.4B 28.A$25.4B8.4B$24.4B10.4B$23.4B12.4B$22.4B14.4B$21.4B16.4B$20.4B18.4B $19.4B20.4B$18.4B22.4B$17.4B24.4B$9.B6.4B26.4B$9.B5.4B28.4B$9.B4.4B 30.12B$9.B3.4B32.4B$9.B2.4B34.4B$9.B.4B35.5B$9.5B36.B.4B$9.4B37.B2.4B $9.3B38.B3.4B$9.10B31.B4.4B$50.B5.4B$50.B6.4B$58.4B$59.4B$60.4B$61.3B!
... Probably a tighter packing or a faster time through the circuit won't really matter much at all, unless the next smaller power-of-two size is available. The old pi/phi circuitry was based on a spacing of 128 cells diagonally between items in the grid. It looks like it will be easy to reduce that spacing to 64 cells diagonally, and cut down the size of the computer circuitry by a factor of 4.
But unless there's a way to cut the 54 or 38 measurement all the way down to 32 somehow, it might be better to keep HashLife happier and stick with a strict 64-cell separation.