The oscillators have a period of 64, while the spaceships have a velocity of 2c/5, and the period of the adjustable ships is based on the LCM of those periods. Each oscillator's phase is shifted 10 generations back after it is hit by the spaceship, while each spaceship's phase is shifted 2 generations ahead after the spaceship hits both oscillators. This means that a adjustable spaceship made of these reactions must have a period of 64n-10=5m+2, where n and m are integers.B468S02357 wrote: June 3rd, 2026, 12:40 am Speaking of hwich, what forhmula do you use to make a viable asdljoupseship?
For the 2d adjustable spaceship, each oscillator's phase is shifted 20 generations back after it is hit by two spaceships.
Each spaceship's phase is still shifted 2 generations ahead, after the spaceship hits two oscillators. This means that a 2d adjustable spaceship made of these reactions must have a period of 64n-20=5m+2, where n and m are integers.
Assuming that the displacements work, finding a period that satisfies those equations can be used to figure out about how far apart the oscillators need to be to get a functioning spaceship. Afterwards, I adjusted the position of the components until they successfully returned to their original position (relative to the overall velocity).
My process was something like this:
1. Start with the 4c/182:
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x = 15, y = 53, rule = B35e/S2-i36cHistory
.3A5.3A2$A3.A3.A3.A$A3.A3.A3.A$2A.2A3.2A.2A$2.A7.A2$2.A7.A$2A.2A3.2A.
2A$A3.A3.A3.A$A3.A3.A3.A2$.3A5.3A17$12.3A$12.3A$12.3A$13.A$13.A5$.A7.A
$3A5.3A4$A.A5.A.A$.A7.A2$.A7.A$A.A5.A.A4$3A5.3A$.A7.A!
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x = 74, y = 54, rule = B35e/S2-i36cHistory
60.3A5.3A2$59.A3.A3.A3.A$59.A3.A3.A3.A$59.2A.2A3.2A.2A$61.A7.A2$61.A7.
A$59.2A.2A3.2A.2A$59.A3.A3.A3.A$59.A3.A3.A3.A2$.A.A56.3A5.3A$A2.2A$.A.
A15$71.3A$71.3A$71.3A$72.A$72.A5$60.A7.A$59.3A5.3A4$59.A.A5.A.A$60.A7.
A2$60.A7.A$59.A.A5.A.A4$16.2A41.3A5.3A$16.3A41.A7.A$16.2A!
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x = 196, y = 54, rule = B35e/S2-i36cHistory
157.3A5.3A14.3A5.3A2$156.A3.A3.A3.A12.A3.A3.A3.A$156.A3.A3.A3.A12.A3.A
3.A3.A$156.2A.2A3.2A.2A12.2A.2A3.2A.2A$158.A7.A16.A7.A2$158.A7.A16.A7.
A$156.2A.2A3.2A.2A12.2A.2A3.2A.2A$9.D.D144.A3.A3.A3.A12.A3.A3.A3.A$8.
2D2.D143.A3.A3.A3.A12.A3.A3.A3.A$9.D.D$98.A.A56.3A5.3A14.3A5.3A$97.A2.
2A$98.A.A15$168.3A22.3A$168.3A22.3A$168.3A22.3A$169.A24.A$169.A24.A5$
157.A7.A16.A7.A$156.3A5.3A14.3A5.3A4$156.A.A5.A.A14.A.A5.A.A$157.A7.A
16.A7.A2$157.A7.A16.A7.A$156.A.A5.A.A14.A.A5.A.A$.2D$3D$.2D$113.2A41.
3A5.3A14.3A5.3A$113.3A41.A7.A16.A7.A$113.2A!
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x = 193, y = 56, rule = B35e/S2-i36cHistory
4.A5.A$4.2A3.2A$2.A2.2A.2A2.A166.3A5.3A$A.A2.2A.2A2.A.A$2.A2.2A.2A2.A
165.A3.A3.A3.A$4.2A3.2A167.A3.A3.A3.A$4.A5.A167.2A.2A3.2A.2A$180.A7.A$
4.A5.A$4.2A3.2A169.A7.A$2.A2.2A.2A2.A165.2A.2A3.2A.2A$A.A2.2A.2A2.A.A
16.C.C144.A3.A3.A3.A$2.A2.2A.2A2.A17.2C2.C143.A3.A3.A3.A$4.2A3.2A20.C.
C$4.A5.A109.A.A56.3A5.3A$119.A2.2A$120.A.A15$190.3A$190.3A$190.3A$191.
A$191.A5$179.A7.A$178.3A5.3A4$178.A.A5.A.A$179.A7.A2$179.A7.A$178.A.A
5.A.A$23.2D$22.3D$23.2D$135.2A41.3A5.3A$135.3A41.A7.A$135.2A!
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x = 194, y = 57, rule = B35e/S2-i36cHistory
8.2B5.2B$5.A.4BA2.4B$4.B2A3B2A6B$2.BA2B2AB2A2BA6B160.3A5.3A$BABA2B2AB
2A2BABA5B$B.BA2B2AB2A2BA7B158.A3.A3.A3.A$4.B2A3B2A8B159.A3.A3.A3.A$5.
A5BA2.5B160.2A.2A3.2A.2A$15.3B163.A7.A$5.A5BA2.5B$4.B2A3B2A8B161.A7.A
$B.BA2B2AB2A2BA7B158.2A.2A3.2A.2A$BABA2B2AB2A2BABA5B11.C.C144.A3.A3.A
3.A$2.BA2B2AB2A2BA7B10.2C2.C143.A3.A3.A3.A$4.B2A3B2A9B11.C.C$5.A.4BA2.
8B99.A.A56.3A5.3A$8.2B5.7B98.A2.2A$14.8B99.A.A$15.BA5B$14.2BA4B$15.3A
4B$15.3A3B$15.3A4B$18.3B$17.5B$18.3B$17.5B$18.3B$17.5B$18.3B$17.5B$18.
3B$17.5B169.3A$18.3B170.3A$19.B171.3A$19.B172.A$192.A3$7.2B5.2B$6.4B3.
4B$6.BA3B.3BAB163.A7.A$4.2BABA2B.2BABA2B160.3A5.3A$3.2BABABAB.BABABA2B
$3.2B2AB2AB.B2AB2A2B$4.7B.7B$5.5B3.5B161.A.A5.A.A$180.A7.A$5.5B3.5B$4.
7B.7B161.A7.A$3.2B2AB2AB.B2AB2A2B159.A.A5.A.A$3.2BABABAB.BABABA2B4.2C
$4.2BABA2B.2BABA2B4.3C$6.BA3B.3BAB7.2C$6.4B3.4B119.2A41.3A5.3A$7.2B5.
2B120.3A41.A7.A$136.2A!
Code: Select all
x = 194, y = 57, rule = B35e/S2-i36cHistory
8.2B5.2B$5.A.4BA2.4B$4.B2A3B2A6B$2.BA2B2AB2A2BA6B160.3A5.3A$BABA2B2AB
2A2BABA5B$B.BA2B2AB2A2BA7B158.A3.A3.A3.A$4.B2A3B2A8B159.A3.A3.A3.A$5.A
5BA2.5B160.2A.2A3.2A.2A$15.3B163.A7.A$5.A5BA2.5B$4.B2A3B2A8B161.A7.A$B
.BA2B2AB2A2BA7B158.2A.2A3.2A.2A$BABA2B2AB2A2BABA5B158.A3.A3.A3.A$2.BA
2B2AB2A2BA7B158.A3.A3.A3.A$4.B2A3B2A9B$5.A.4BA2.8B99.A.A56.3A5.3A$8.2B
5.7B98.A2.2A$14.8B99.A.A$15.BA5B$14.2BA4B$15.3A4B$15.3A3B$15.3A4B$18.
3B$17.5B$18.3B$17.5B$18.3B$17.5B$18.3B$17.5B$18.3B$17.5B169.3A$18.3B
170.3A$19.B171.3A$19.B172.A$192.A3$7.2B5.2B$6.4B3.4B$6.BA3B.3BAB163.A
7.A$4.2BABA2B.2BABA2B160.3A5.3A$3.2BABABAB.BABABA2B$3.2B2AB2AB.B2AB2A
2B$4.7B.7B$5.5B3.5B161.A.A5.A.A$180.A7.A$5.5B3.5B$4.7B.7B161.A7.A$3.2B
2AB2AB.B2AB2A2B159.A.A5.A.A$3.2BABABAB.BABABA2B$4.2BABA2B.2BABA2B$6.BA
3B.3BAB$6.4B3.4B119.2A41.3A5.3A$7.2B5.2B120.3A41.A7.A$136.2A!
Code: Select all
x = 183, y = 59, rule = B35e/S2-i36cHistory
$2.B2.2B.3B.2B2.2B$BA7BA9B147.2B2.2B.2B2.2B$3A5B3A8B146.B3A3B3A5B$21B
144.2A7B2A4B$22B141.5BA3BA9B$22B140.3B3A5B3A7B$ABA5BABA10B141.6BA3BA
10B$BA7BA10B143.2B2A7B2A6B$12.3B.3B145.2B3A3B3A6B$BA7BA10B157.3B$ABA5B
ABA10B143.17B$22B141.19B$22B140.2B3D16B$22B139.3B5D14B$3A5B3A11B90.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.6B3D16B$BA7BA13B87.73B$2.B
2.2B.3B.11B86.74B$11.12B87.58B2.2B.2B2.6B$12.11B89.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B12.7B$11.11B155.6B$12.BA9B153.7B$11.2BA
8B155.6B$12.3A8B153.7B$12.3A7B155.6B$12.3A8B153.7B$15.7B155.6B$14.9B
153.7B$15.7B155.6B$14.9B153.7B$15.7B155.6B$14.9B153.7B$15.7B155.6B$14.
9B153.7B$15.7B155.6B$14.5B.B155.7B$15.6B156.A2B.B$14.5B157.ABA3B$15.5B
149.B5.A3BA$14.5B149.3B5.BA3B$4.2B2.2B.2B2.3B148.ABABABA2.5B$3.16B146.
A2BABA2BA2.3B$3.ABA5BABA4B147.BABABABAB.5B$.19B146.7B.5B$2B5A3B5A6B
145.7B.7B$B2ABAB2AB2ABAB2A5B144.8B.8B$.A5BABA5BA4B145.8B.8B$2.A3BA3BA
3BA4B147.7B.7B$15.3B147.BABABABAB.5B$2.A3BA3BA3BA4B146.A2BABA2BA2.2B$.
A5BABA5BA4B146.ABABABA2.5B$B2ABAB2AB2ABAB2A5B137.B.B.B.B.7B.7B$2B5A3B
5A6B135.DBD23B$.19B136.2DBD22B$3.ABA5BABA4B109.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.BDBD22B$3.15B107.48B.5B$4.2B2.2B.2B2.2B107.48B3.4B$125.46B5.2B$
127.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B!
the postition of the red ships and their phase relative to the oscillators,
until the ships return just in time to collide in the right way. This can be
done by running the simulation 5n generations (in this case 140, based what looked right):
Code: Select all
x = 185, y = 59, rule = B35e/S2-i36cHistory
$3.B2.2B.3B.2B2.2B$.BA7BA9B147.2B2.2B.2B2.2B$.3A5B3A8B146.B3A3B3A5B$
22B144.2A7B2A4B$23B141.5BA3BA9B$23B140.3B3A5B3A7B$.ABA5BABA10B141.6BA
3BA10B$.BA7BA10B143.2B2A7B2A6B$13.3B.3B145.2B3A3B3A6B$.BA7BA10B157.3B$
.ABA5BABA10B143.17B$23B141.19B$23B140.2B3A16B$23B139.3B5A14B$.3A5B3A
11B90.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.6B3A16B$.BA7BA13B
87.73B$3.B2.2B.3B.11B86.75B$12.12B87.58B2.2B.2B2.7B$13.11B89.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B12.8B$12.11B155.7B$13.BA9B
153.7B$12.2BA8B155.7B$13.3A8B153.7B$13.3A7B155.7B$13.3A8B153.7B$16.7B
155.7B$15.9B153.7B$16.7B155.7B$15.9B153.7B$16.7B155.7B$15.9B153.7B$16.
7B155.7B$15.9B153.7B$16.7B155.7B$15.5B.B155.7B$16.6B156.A2B.B$15.5B
157.ABA3B$16.5B149.B5.A3BA$15.5B149.3B5.BA3B$5.2B2.2B.2B2.3B148.ABABAB
A2.5B$4.16B146.A2BABA2BA2.3B$4.ABA5BABA4B147.BABABABAB.5B$2.19B146.7B.
5B$.2B5A3B5A6B145.7B.7B$.B2ABAB2AB2ABAB2A5B144.8B.8B$2.A5BABA5BA4B145.
8B.8B$3.A3BA3BA3BA4B147.7B.7B$16.3B147.BABABABAB.5B$3.A3BA3BA3BA4B146.
A2BABA2BA2.2B$2.A5BABA5BA4B146.ABABABA2.5B$.B2ABAB2AB2ABAB2A5B137.B.B.
B.B.7B.7B$.2B5A3B5A6B135.ABA23B$2.19B136.2ABA22B$4.ABA5BABA4B109.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.BABA22B$4.15B107.48B.5B$5.2B2.2B.2B2.2B107.48B
3.4B$126.46B5.2B$128.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B!Code: Select all
x = 194, y = 82, rule = B35e/S2-i36cHistory
89.105F$89.F103.F$89.F103.F$89.F103.F$89.F103.F$89.F103.F$89.F103.F$
89.F103.F$89.F103.F$89.F103.F$89.F75.2B2.2B.2B2.2B15.F$89.F74.15B14.F$
89.F74.15B14.F$4.2B2.2B.3B.2B2.2B68.F73.ABABA3BABABA5B12.F$3.19B67.F
72.2ABAB2AB2ABAB2A5B11.F$3.19B67.F72.A2BA2BABA2BA2BA6B10.F$.23B65.F72.
ABABABABABABABA6B10.F$4BA7BA12B64.F73.22B8.F$3BABA5BABA11B64.F75.21B7.
F$.3BA7BA11B65.F73.23B7.F$2.B3A5B3A9B66.F72.ABABABABABABABA8B8.F$15.3B
.3B67.F72.A2BA2BABA2BA2BA7B9.F$2.B3A17B66.F72.2ABAB2AB2ABAB2A6B10.F$.
3BA19B65.F73.ABABA3BABABA8B9.F$3BABA19B64.F24.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.21B8.F$4BA20B64.F21.3A53B3D16B7.F$.24B64.F
21.5A51B5D14B7.F$3.22B64.F21.3A53B3D16B7.F$3.13B2A8B63.F23.73B7.F$4.2B
2.2B.3BA2BA8B63.F22.75B6.F$12.A13B63.F23.58B2.2B.11B6.F$13.AB2A9B63.F
25.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B8.12B6.F$14.A10B
64.F86.11B6.F$13.13B63.F85.11B7.F$14.11B64.F86.11B6.F$13.13B63.F85.11B
7.F$14.11B64.F86.11B6.F$13.13B63.F85.11B7.F$14.11B64.F86.11B6.F$13.13B
63.F85.11B7.F$14.11B64.F86.11B6.F$13.13B63.F85.11B7.F$14.11B64.F86.BA
9B6.F$13.13B63.F85.BABA7B7.F$14.11B64.F86.11B6.F$13.13B63.F86.3A7B7.F$
14.11B64.F87.A9B6.F$13.9B.B65.F89.7B7.F$14.10B65.F88.5B.B8.F$13.9B67.F
78.2B5.2B2.6B8.F$14.9B66.F77.4B.B.9B10.F$13.9B67.F77.B2A5B2AB.5B9.F$3.
2B2.2B.3B.3B.3B68.F75.2BAB2A3B2ABA5B10.F$2.20B67.F74.2B3ABA3BAB3A3B11.
F$2.19B68.F74.3BAB2A3B2ABA5B10.F$4BA5BA12B66.F75.3B2A5B2A5B11.F$3B2ABA
BAB2A12B65.F76.18B9.F$4BA5BA13B65.F78.8B.8B8.F$23B66.F76.19B8.F$.21B
67.F75.3B2A5B2A7B9.F$14.3B.3B68.F74.3BAB2A3B2ABA5B10.F$.21B67.F74.2B3A
BA3BAB3A2B12.F$23B66.F75.2BAB2A3B2ABA5B10.F$4BA5BA13B65.F15.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B2A5B2A7B9.F$3B2AB
ABAB2A12B65.F13.ABA53BDBD23B8.F$4BA5BA12B66.F13.2ABA52B2DBD22B8.F$2.
19B68.F13.ABA53BDBD22B9.F$2.19B68.F15.B.B.B.B.B.B.B.B.B.B.B.49B.5B11.F
$3.2B2.2B.3B.2B2.2B69.F37.48B3.4B11.F$89.F38.46B5.2B12.F$89.F40.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B23.F$89.F103.F$89.F103.F$89.F103.F$89.
F103.F$89.F103.F$89.F103.F$89.F103.F$89.F103.F$89.F103.F$89.F103.F$89.
105F!
Code: Select all
x = 244, y = 61, rule = B35e/S2-i36cHistory
222.15B$222.15B$6.2B2.2B.3B.2B2.2B198.ABABA3BABABA5B$5.19B196.2ABAB2AB
2ABAB2A5B$5.19B196.A2BA2BABA2BA2BA6B$3.23B194.ABABABABABABABA6B$2.4BA
7BA12B194.22B$2.3BABA5BABA11B196.21B$3.3BA7BA11B195.23B$4.B3A5B3A9B
195.ABABABABABABABA8B$17.3B.3B196.A2BA2BABA2BA2BA7B$4.B3A17B195.2ABAB
2AB2ABAB2A6B$3.3BA19B195.ABABA3BABABA8B$2.3BABA19B145.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.21B$2.4BA20B142.3C53B3D16B$3.24B142.
5C51B5D14B$5.22B142.3C53B3D16B$5.13B2A8B143.73B$6.2B2.2B.3BA2BA8B142.
74B$14.A13B143.58B2.2B.10B$15.AB2A9B145.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.4B8.11B$16.A10B207.10B$15.13B205.11B$16.11B207.10B$
15.13B205.11B$16.11B207.10B$15.13B205.11B$16.11B207.10B$15.13B205.11B$
16.11B207.10B$15.13B205.11B$16.11B207.BA8B$15.13B205.BABA7B$16.11B207.
10B$15.13B206.3A7B$16.11B208.A8B$15.9B.B211.7B$16.10B210.5B.B$15.9B
202.2B5.2B2.6B$16.9B200.4B.B.9B$15.9B201.B2A5B2AB.5B$5.2B2.2B.3B.3B.3B
200.2BAB2A3B2ABA5B$4.20B198.2B3ABA3BAB3A3B$4.19B199.3BAB2A3B2ABA5B$2.
4BA5BA12B198.3B2A5B2A5B$.4B2ABABAB2A12B198.18B$.5BA5BA13B200.8B.8B$2.
23B199.19B$3.21B199.3B2A5B2A7B$16.3B.3B199.3BAB2A3B2ABA5B$3.21B198.2B
3ABA3BAB3A2B$2.23B198.2BAB2A3B2ABA5B$.5BA5BA13B137.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B2A5B2A7B$.4B2ABABAB2A12B
135.CBC53BDBD23B$2.4BA5BA12B136.2CBC52B2DBD22B$4.19B138.CBC53BDBD22B$
4.19B140.B.B.B.B.B.B.B.B.B.B.B.49B.5B$5.2B2.2B.3B.2B2.2B163.48B3.4B$
186.46B5.2B$188.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.4B!
In this case, step 8 needs to be repeated for another 5 generations to get the working spaceship:
Code: Select all
x = 244, y = 58, rule = B35e/S2-i36cHistory
4.B2.2B.3B.2B2.2B199.ABA9BABA4B$2.BA7BA9B197.AB2A9B2ABA4B$2.3A5B3A8B
197.BABA9BABA6B$.22B196.21B$24B196.22B$.23B198.21B$2.ABA5BABA10B197.
23B$2.BA7BA10B197.23B$14.3B.3B197.BABA9BABA7B$2.BA7BA10B196.AB2A9B2ABA
5B$2.ABA5BABA10B196.ABA9BABA7B$.23B145.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.21B$24B142.2AC2D53B3D16B$.23B142.2A3C2D51B5D14B$
2.3A5B3A11B142.2AC2D53B3D16B$2.BA7BA13B144.74B$4.B2.2B.3B.11B86.B57.
75B$13.12B145.58B2.2B.11B$14.11B147.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.4B8.12B$13.11B209.11B$14.BA9B207.11B$13.2BA8B209.11B$14.
3A8B207.11B$14.3A7B209.11B$14.3A8B207.11B$17.7B209.11B$16.9B207.11B$
17.7B209.11B$16.9B207.11B$17.7B209.11B$16.9B207.11B$17.7B209.BA9B$16.
9B207.BABA7B$17.7B209.11B$16.5B.B210.3A7B$17.6B211.A5B.B$16.5B204.BA5.
AB2.6B$17.5B202.3AB.B.B3A5B$16.5B203.2ABA3BAB2A.5B$6.2B2.2B.2B2.3B202.
18B$5.16B200.5B2A3B2A6B$5.ABA5BABA4B201.19B$3.19B200.2B2ABA3BAB2A4B$2.
2B5A3B5A6B200.B3A5B3A6B$2.B2ABAB2AB2ABAB2A5B202.8B.8B$3.A5BABA5BA4B
201.B3A5B3A7B$4.A3BA3BA3BA4B201.2B2ABA3BAB2A6B$17.3B201.19B$4.A3BA3BA
3BA4B200.5B2A3B2A5B$3.A5BABA5BA4B200.18B$2.B2ABAB2AB2ABAB2A5B137.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.2ABA3BAB2A
6B$2.2B5A3B5A6B135.ABCBD53BDBD5B3A5B3A7B$3.19B136.2ADCBD52B2DBD6BA5BA
9B$5.ABA5BABA4B138.ABCBD53BDBD22B$5.15B140.B.B.B.B.B.B.B.B.B.B.B.B.49B
.5B$6.2B2.2B.2B2.2B165.48B3.4B$185.46B5.2B$187.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.4B!
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