wildmyron wrote: May 12th, 2020, 8:47 am
muzik wrote: August 5th, 2019, 9:16 am
Have all orthogonal speeds 3c/n been proven yet?
As
mentioned by "2718281828", they're definitely possible, but I don't think anyone has posted a set covering all periods here. I vaguely recall I even had some search results aiming to achieve that result, but I never completed them or posted them here.
Here's a full set covering all periods. They all use the push-reflect + pull-reflect mechanism with a small c/2 ship and SL reflectors. They were discovered some months ago and originally posted to the ConwayLife Discord server on 2020-05-30.
(3,0)c/(4n), p(4n); n>=6 - 3c/24
Code: Select all
x = 11, y = 3, rule = B2cen3jkr4-knqty5-cein6ac78/S01c2in3ajry4-jkwyz5-acik6aik8
2o2b2o$2obobo4bo$4b2o!
(3,0)c/(4n+1), p(4n+1); n>=6 - 3c/25
Code: Select all
x = 11, y = 3, rule = B2cin3-cej4aciz5-cjry6kn7/S01e2ain3cjkr4aknr5-eikn6ak78
o2bo$ob2o6bo$3bo!
(3,0)c/(4n+2), p(4n+2); n>=4 - 3c/18 (Uses the same SL for push and pull)
Code: Select all
x = 11, y = 3, rule = B2-ak3ery4ackqr5jnqy6cek8/S01c2aei3-acr4-atwz5akqr6ckn7e8
bo2b2o4bo$2obobo3b2o$bo2b2o4bo!
(3,0)c/(4n+3), p(4n+3); n>=5 - 3c/23
Code: Select all
x = 11, y = 3, rule = B2ck3-knqr4acknw5jkq6-ek78/S1e2eik3-aejn4inqrtw5knqry6e7e
3bo$ob2o5b2o$o2bo!
These were all found with LLS. The searches didn't take too long to run - once the actual search file had been set up (which is a bit tedious). It also took a bit of trial and error to find the right reaction times for the searches to start giving results. I haven't tried to optimise for reaction speed and space so it's possible that there are 3c/p adjustable saceships for p(4n) and p(4n+1) which have lower minimum periods.
I considered extending this further, but it starts to get trickier for higher displacements because it just physically takes longer for the reaction to shift the SL the required number of cells and reform the reflected spaceship (particularly for the pull where the ship has to form a long way in front of where the reaction initially occurs). I expect 5c/N would be doable with LLS, but I'm not sure how far that idea can be pushed. A better idea IMO is to find a mechanism with adjustable displacement. It just so happens that my earlier post regarding antiphotons in a box suggests a method to find precisely such a mechanism. Expect a follow-up post on this topic in a day or two.
kiho park wrote: August 3rd, 2020, 7:16 am
After few days of LLS searching, I found new type of adjustable spaceship using c2o wickstretcher and a c2o spaceship.
If following spaceship hits the tail of the wickstretcher, then chasing spaceship is delayed and the line wickstretcher start to burning while the "fire" reach to the front of wickstretcher then wickstretcher delayed too.
<snip>
I also trying to find other adjustable spaceships advancing or shifting instead of delaying them or using other speed such as c3o, c4o, c5o, 2c5 and 2c3o or faster speeds.
Furthermore, I'll also try diagonal or oblique design if possible.
This is a very nice idea and great to see it working with such a simple design. You've prompted me to make this post which has been in draft form for some time now - all the spaceships here have been previously posted to the ConwayLife Discord server, but I never got around to posting them here.
In particular there has been a fair bit of discussion about adjustable spaceships with speeds > c/2 on the Discord server. After unsuccessful exploration of several proposed designs by A for Awesome, AforAmpere, myself and others; I found this solution where a c/2 diagonal bounces between two c/2 orthogonal ships and the phase of each is advanced with each bounce (prompted by a discussion with AforAmpere):
(n+1)c/(2n+1), p(4n+2), n>=3, 19 cells (discovered 2020-06-22)
Code: Select all
x = 8, y = 57, rule = B2ac3aekqy4ent5y6ae8/S12n3-ai4aeijn5ae6n7e
4bo$6bo$3b3o$6bo$4bo2$2bobo$4bo$o4bo2$2bo2$4bobo$o2bob3o$4bobo6$4bo$6b
o$3b3o$6bo$4bo2$2bobo$4bo$5bo5$4bobo$3bob3o$4bobo5$4bo$6bo$3b3o$6bo$4b
o2$2bobo$4bo$5bo6$4bobo$3bob3o$4bobo!
The resulting family of spaceships all have speed c/2 < v <= 4c/7. I called this reaction a bounce+nudge. Another idea I tried was a bounce shift - where the bounce reaction produces a lane shift in the orthogonal ship (no phase change). A for Awesome originally proposed this idea and found component reactions (bounce+push and bounce+pull) at c/3, but not both in a single rule. I tried the same idea at c/2 and was also able to find component reactions but the combined search was ultimately unsuccessful. I also tried the idea at 2c/3 with a p3 knightship (before I tried c/2) and managed to find a bounce+pull, but couldn't even find a bounce+push let alone both in a single rule.
Explosive, paired bounce+pull reaction at 2c/3 (discovered 2020-06-27):
Code: Select all
x = 5, y = 20, rule = B2aci3cejy4jnyz5ejq7c8/S12ci3cknqr4cikntz5aeqr6ein7c
o2bo$2b2o$bobo5$bobo$2bobo$5o$bo2bo7$bobo$2b2o$o2bo!
However, I had been able to find adjustable period 2c/3 spaceships which just require a single bounce reaction:
2c/3, p(6n), n>=3 (discovered 2020-06-23)
Code: Select all
x = 13, y = 59, rule = B2aci3cejy4ejn5ajq6aek78/S12cn3-aeiy4ikntyz5-cikq6n
12bo$10bo$9bo2bo$10bo3$9bobo$10bobo$3bo4b5o$6bo2bo2bo3$8bobo$obo4bobo
2bo$b4o3bobo$2b4o6bo5$12bo$10bo$9bo2bo$10bo3$9bobo$10bobo$8b5o$9bo2bo
4$10bo$9bo2bo$10bo$12bo5$12bo$10bo$9bo2bo$10bo3$9bobo$10bobo$8b5o$9bo
2bo5$10bo$9bo2bo$10bo$12bo!
There were several other similar results found with slight variations of this search:
Same ships, different reaction
Code: Select all
x = 5, y = 16, rule = B2aci3cejy4eijn5aj6aei7c/S12cn3-eiy4ikntz5-cjky6-ac7c8
4bo$2bo$bo2bo$2bo3$bobo$2bobo$5o$bo2bo3$2bo$bo2bo$2bo$4bo!
Different ships
Code: Select all
x = 5, y = 16, rule = B2acn3ej4ceinwyz5ikqry6acn7e/S01e2-ae3kn4eiknq5ejny6ikn7
bobo$obo$bobo4$bobo$4bo$3b2o$4bo4$bobo$obo$bobo!
One other, earlier, failed attempt at finding adjustable > c/2 spaceships was bouncing a photon between two orthogonal c/2 spaceships, nudging forward at each reflection. Here's a bounce+push reaction found 2020-06-14:
Code: Select all
x = 12, y = 16, rule = B2-in3ceik4cjkqrt5aqy6-ci7c8/S2cen3ceiny4aeiktyz5knqy6ci78
10bo$9bo$8b2obo$9bo$10bo7$10bo$2bo6bo$obo5b2obo$2bo6bo$10bo!
I'm sure that I found a corresponding bounce+pull reaction but I don't have an example to hand. I was definitely unable to find a pair of reactions which worked in a single rule.
, but here are some things to consider before deciding that I just did an LLS search:
I also imagined and tried that design using two c2 diagonal spaceships and a c1 orthogonal spaceship but I couldn't get any satisfiable result.