From: Jason Summers
Date: Sat Dec 15, 2007 7:20 pm
Subject: Arbitrary speed spaceship idea
This is a concept I've been thinking about, for constructing orthogonal
caterpillar-like spaceships of more-or-less arbitrary speeds. It's just
an idea, and at this time I have no plans to actually try to construct
such a thing.
Start with the idea of a glider bouncing back and forth between two
still lifes, in such a way that the still lifes and the glider are
translated northward by a few cells by the reflection reactions. Call
this contraption a "relay". You could change its period, and thus its
speed, simply by moving the reflectors closer together or farther apart.
We don't know any way to actually do this (short of theoretical
universal-constructor arguments), but bear with me.
It's too much to ask that the same still life reappear in just the right
place, but I'll settle for a *different* still life (or constellation of
still lifes) appearing *somewhere*. Then, a little while later, a convoy
of *WSSs flies by and "fixes" the still life, turning it back into the
original still life, translated northward from its original location.
The *WSS convoys are going to have to be created and destroyed somehow,
so we need to do more than just break even. One option is to have one of
the reflection reactions produce an additional glider that escapes. (A
more ambitious possibility would be for two closely-following relays to
have sparks that can interact, in such a way that gliders can be
produced in different directions.)
This much is certainly possible. I lack the technology to do it
efficiently, but I wanted to make a working proof-of-concept:
Code: Select all
x = 176, y = 1392, rule = B3/S23
159bo$158bobo$158boo16$138boo$139boo$138bo93$30boo$30bobo$31boo9$159bo
$158bobo$158boo8$146boo$145bobo$147bo99$172b3o$171bobbo$30boo142bo$30b
obo137bo3bo$31boo141bo$171bobo$$149b3o$149bobbo15b3o$149bo17bobbo$149b
o3bo16bo$149bo16bo3bo$150bobo17bo$167bobo17$163b3o$162bobbo$165bo$161b
o3bo$165bo$162bobo4$148b3o$147bobbo$150bo$146bo3bo$146bo3bo$150bo$147b
obo6$148bo$147b3o10b3o$146boobo10bobbo$146b3o11bo$146b3o11bo3bo$146b3o
11bo$147boo12bobo19$167bo$166b3o$165boobo$165b3o$166boo6$170bo$169b3o$
168boobo$168b3o$156b3o9b3o$155bobbo10boo$158bo$154bo3bo$154bo3bo$158bo
$155bobo6$173bo$159b3o10b3o$158bobbo10boboo$161bo11b3o$157bo3bo11b3o$
161bo11b3o$158bobo12boo16$155bo$154b3o$154boboo$155b3o$155boo6$152bo$
151b3o$151boboo$152b3o$152b3o9b3o$152boo10bobbo$164bo$164bo3bo$164bo3b
o$164bo$165bobo4$149b3o$148bobbo$151bo$147bo3bo$151bo$148bobo$$166bo$
165b3o$164boobo$164b3o$164b3o$164b3o$165boo229$23bo$11b3o8b3o$11bobbo
6boobo$11bo9b3o$11bo3bo5b3o$11bo10boo$12bobo3$10bo$9b3o$8boobo$8b3o$8b
3o$9boo10$19b3o$18bobbo$21bo$17bo3bo$21bo$18bobo4$4b3o$3bobbo$6bo$bbo
3bo$bbo3bo$6bo$3bobo10$16b3o$15bobbo$18bo$14bo3bo$3o15bo$obbo11bobo$o$
o3bo$o$bobo29$29bo$28b3o$27boobo$27b3o$27b3o$28boo11$42b3o$42bobbo$42b
o$42bo$43bobo9$45bo$33b3o8b3o$32bobbo8boboo$35bo9b3o$31bo3bo9b3o$35bo
9boo$32bobo3$32bo$31b3o$31boboo$32b3o$32b3o$32boo7$43bo$29b3o10b3o$29b
obbo8boobo$29bo11b3o$29bo3bo7b3o$29bo11b3o$30bobo9boo7$28bo$27b3o$26b
oobo$26b3o$27boo6$25bo$24b3o$23boobo$23b3o$23b3o11b3o$24boo10bobbo$39b
o$35bo3bo$35bo3bo$39bo$36bobo133b3o$171bobbo$174bo$22b3o145bo3bo$21bo
bbo149bo$24bo146bobo$20bo3bo$24bo124b3o$21bobo125bobbo15b3o$149bo17bo
bbo$149bo3bo16bo$38b3o108bo16bo3bo$38bobbo108bobo17bo$38bo128bobo$38bo
3bo$38bo3bo$38bo$39bobo5$23b3o$22bobbo$25bo$21bo3bo$25bo$22bobo3$39b3o
121b3o$39bobbo119bobbo$39bo125bo$39bo3bo117bo3bo$39bo3bo121bo$39bo122b
obo$40bobo3$148b3o$147bobbo$150bo$146bo3bo$146bo3bo$150bo$147bobo6$
148bo$147b3o10b3o$146boobo10bobbo$146b3o11bo$146b3o11bo3bo$146b3o11bo$
147boo12bobo19$167bo$166b3o$165boobo$165b3o$166boo6$170bo$169b3o$168b
oobo$168b3o$156b3o9b3o$155bobbo10boo$158bo$154bo3bo$154bo3bo$158bo$
155bobo6$173bo$159b3o10b3o$158bobbo10boboo$161bo11b3o$157bo3bo11b3o$
161bo11b3o$158bobo12boo16$155bo$154b3o$154boboo$155b3o$155boo6$152bo$
151b3o$151boboo$152b3o$152b3o9b3o$152boo10bobbo$164bo$164bo3bo$164bo3b
o$164bo$165bobo4$149b3o$148bobbo$151bo$147bo3bo$151bo$148bobo$$166bo$
165b3o$164boobo$164b3o$164b3o$164b3o$165boo229$23bo$11b3o8b3o$11bobbo
6boobo$11bo9b3o$11bo3bo5b3o$11bo10boo$12bobo3$10bo$9b3o$8boobo$8b3o$8b
3o$9boo10$19b3o$18bobbo$21bo$17bo3bo$21bo$18bobo4$4b3o$3bobbo$6bo$bbo
3bo$bbo3bo$6bo$3bobo10$16b3o$15bobbo$18bo$14bo3bo$3o15bo$obbo11bobo$o$
o3bo$o$bobo29$29bo$28b3o$27boobo$27b3o$27b3o$28boo11$42b3o$42bobbo$42b
o$42bo$43bobo9$45bo$33b3o8b3o$32bobbo8boboo$35bo9b3o$31bo3bo9b3o$35bo
9boo$32bobo3$32bo$31b3o$31boboo$32b3o$32b3o$32boo7$43bo$29b3o10b3o$29b
obbo8boobo$29bo11b3o$29bo3bo7b3o$29bo11b3o$30bobo9boo7$28bo$27b3o$26b
oobo$26b3o$27boo6$25bo$24b3o$23boobo$23b3o$23b3o11b3o$24boo10bobbo$39b
o$35bo3bo$35bo3bo$39bo$36bobo3$22b3o$21bobbo$24bo$20bo3bo$24bo$21bobo
3$38b3o$38bobbo$38bo$38bo3bo$38bo3bo$38bo$39bobo5$23b3o$22bobbo$25bo$
21bo3bo$25bo$22bobo3$39b3o$39bobbo$39bo$39bo3bo$39bo3bo$39bo$40bobo!
There are two relays in my example pattern, for illustrative purposes.
What happens here is that a glider collides with a boat, reflecting the
glider 180 degrees, and producing an extra southeastward glider in the
process. A constellation of still lifes remains, which is later turned
back into a boat 10 cells north of wherever the original boat was.
At the other end, a ship reflects a glider, and is turned into a block.
The block is later turned back into a ship 10 cells north of the
original. These two reflections combine to translate the glider a total
of 10 cells north.
The key point is that there is a great deal of flexibility in the
position and timing of these relays. Their location would form the DNA
of the spaceship. They can be shifted vertically by any multiple of 2
cells, and advanced by any number of generations -- all provided you
avoid a window where the passing *WSSs would interfere. This window can
be made relatively small by increasing the period (though there might
also be drawbacks to a large period).
I don't have a specific plan for how to create and delete the *WSSs.
Constructing convoys of *WSSs is certainly harder than constructing the
blinkers needed by the 17c/45 spaceship. But the slower speed of the
spaceship may compensate for that. If, as in my example, relays can only
emit gliders in a single direction, then we need at least two tracks of
relays, which would fire gliders at each other.
Further thoughts:
The relays don't necessarily have to be based on still lifes.
Oscillators such as blinkers could work too, though they may make life
more difficult.
The *WSSs could move in the same direction or the opposite direction of
the spaceship itself. For technical reasons, I think it will be easier
to construct them at the back of the spaceship, so they should probably
move in the same direction.
In my example pattern, the spaceship would move at 10c/1140. This is
probably not good. I suspect that, ideally, the displacement, period,
and the period of a *WSS (4) would all be relatively prime. So, the
displacement and period should be odd numbers with no common factor.
A displacement of 10 might be about the right magnitude, though. I don't
think you want it to be too small, or objects you create at generation N
could interfere with objects created at generation N+(the period).
It's hard to estimate how serious the interference problems are. We have
to deal with the windows where relays can't be placed, and likely the
task of firing gliders safely through tracks of relays. Instinctively, I
don't think those issues would make such a spaceship impossible, but
they could turn out to be a big problem in practice.
--
Jason Summers