I have recently realized that there is a surprising amount of depth in rules that only use one death transition. What Dx means is that every survival transition is on except for x. for example D3a is equivalent to S0123-a45678. This thread is for findings in 1D rules/Interesting 1D rules and for theory about 1D rules
Possible 1D transitions:
For a 1D rules to be able to have the trailing edge of the pattern die it must have D0, D1e, D1c, D2a, D2c, D2e, D2k, D3a, D3i, D3j, D3n, or D4a. Out of those transitions only D0 has been proved to not support any ships. Out of the rest. D2a, D2k, D3a, and D4a are the only transitions with known speeds.
D2k supports c, D2a supports c, and c/2. D3a supports c, and c/4. D4a has by far the most speeds of ship.
Until recently the only speed known in D3a was c until Ampere found this beautiful extensible c/4 that does not use B1e or B2a
Code: Select all
x = 25, y = 6, rule = B3ai4ir/S0123-a45678
3ob2o$b2ob2obo$6b2ob3ob2o$10b2ob2obo$15b2ob3ob3o$19b2ob3o!There are a plethora of speeds in D4a the highest period of which being this 4c/276d
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x = 5, y = 6, rule = B2ce3en4akw5an6-ei7/S01234-a5678
bo$3o$b3o$b4o$b3o$3b2o!Here is the 1D rule with the most known speeds of ship at 5: c/3o,c/7d,c/9d,c/16d, and 2c/58d
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x = 215, y = 78, rule = B2cek4anr5ajn6ac7c/S01234-a5678
bo2bo101b3o74b4o16b4o7bo$o4bo97b6o74b4o14b5o5b3o$6o96b7o73b5o14b4o5b5o
$6o95b7o72b6o14b5o6b2o$b4o96b5o73b5o17b4o7bo$99b6o73b6o19bo$98b7o72b6o
$98b6o72b5o$96b7o72b6o$96b5o74b4o$95b6o72b6o$93b6o74b5o$92b7o72b6o$91b
6o74b5o$91b6o72b6o$89b7o72b5o$88b7o73b5o$87b7o72b6o$86b7o73b5o$86b5o
73b5o$84b7o72b6o$83b7o72b6o$82b7o72b6o$82b6o72b6o$80b7o72b6o$79b7o73b
5o$79b6o72b6o$77b7o73b5o$76b7o72b6o$75b6o73b6o$75b6o73b5o$74b6o72b5o$
72b7o72b6o$71b7o72b6o$70b7o72b6o$70b6o72b5o$69b6o72b6o$67b6o74b5o$67b
6o72b6o$65b7o72b5o$64b7o72b6o$63b7o72b5o$62b7o72b6o$62b5o74b5o$60b7o
72b6o$59b7o73b5o$58b7o72b6o$57b7o72b6o$56b7o72b6o$55b6o73b6o$54b7o73b
5o$53b6o73b5o$53b6o73b5o$51b6o73b6o$50b7o72b6o$49b6o73b5o$48b7o72b6o$
47b7o72b5o$46b7o72b6o$46b5o74b4o$44b7o72b6o$43b7o72b5o$42b7o72b6o$41b
6o73b6o$41b6o72b6o$39b7o73b4o$38b7o72b5o$37b7o72b6o$36b7o73b4o$36b6o
72b6o$34b7o73b5o$34b6o72b6o$32b7o72b5o$32b6o72b6o$30b6o74b5o$30b6o74b
4o$31b4o76bo$32b2o!
•Find 1D ships using D1c, D1e, D2c, D2e, D3i, D3j, D3n, or prove that ships are impossible in them
•Find more 1D ships
•Find a period adjustable 1D ship
•Find an speed adjustable 1D ship
•Find an omniperiodic 1D rule
•Find a Turing Complete 1D rule
•Find a 1D gun
•Find a Nonadjustable 1D ship over period 300
•Find a 1D rule with more than 5 NRSS
xp2 had created a 1D database a while ago, I have updated it and extended it with many more D4a ships, and it is attached here. If anyone finds any more 1d Ships please post them here and I will update the database. (Note I will only be storing the smallest c/3o and c/6o for D4a) but for every other speed every ship and ever other 1D transition the ship will be included so I would encourage you to post any you find.