Conway's Life: Glider reflector?
Bill Taylor
It wasn't a staatic reflector, but had some period, and the gliders had
to arrive at those cycle times.
Can someone post it again please?
Also - at the time it was said that the static glider reflector was
the "holy grail" of Life experts. Is that still so? Is none known?
Thnx IA
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Bill Taylor W.Ta...@math.canterbury.ac.nz
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May the source be with you.
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Dean Hickerson
> A year or two ago someone posted a glider reflector here.
>
> It wasn't a staatic reflector, but had some period, and the gliders had
> to arrive at those cycle times.
>
> Can someone post it again please?
Large period reflectors have been known for a long time, like this p30
"buckaroo", found by David Buckingham in the early 1970s:
.o.....................
..o....................
ooo....................
.........o.............
........o.o............
......oo...o...........
......oo...o...........
......oo...o...........
..oo....o.o........oo..
.o.o.....o.........o.o.
.o...................o.
oo...................oo
And this p46 reflector (one of several); I'm not sure who found this one:
.o...............................
..o..............................
ooo..............................
.................................
.....oo...oo........o............
....o..o.o..o.......o..oo........
...o.........o.....o.....o.....oo
..oo.........oo.....o.o..oo....oo
...o.........o......o...oo.......
....o..o.o..o.........ooo........
.....oo...oo.....................
......................ooo........
....................o...oo.......
....oo..............o.o..oo....oo
....oo.............o.....o.....oo
....................o..oo........
....................o............
In September 1998, Noam Elkies found a mechanism for building low period
reflectors. Each one needs a spark from an oscillator of the desired
period. Here are the period 8 and 6 versions, using a p8 "figure 8" and
a p6 "pipsquirt":
......oo.....oo.. .......oo.....oo
o.o...oo.....o... .o.o...oo.....o.
.oo........o.o... ..oo........o.o.
.o.........oo.... ..o.........oo..
.......oo........ ........oo......
.......o.o....... ........o.o.....
........o........ .........o......
................. ................
...........ooo... ................
...........ooo... ........ooo.....
...........ooo... ................
..............ooo .......o.o.o....
..............ooo .....ooo.o.ooo..
..............ooo ....o.....o...o.
...o.o.oo..oo.o.
...o.oo..oo..o..
..oo....o..oo...
o..o.o.o..o.....
oo..oo.oooo.....
......o.........
......o.o.......
.......oo.......
Period 5 requires some more work:
..........o.........oo...oo...
.........o.o.oo......o....o...
.........o.o.o.o.....o.ooo....
..........o.o..o....oo.o......
............o.o.oo............
...........o..o.o.o.oo..o.....
...........oo.o...o..o..o.....
......oo.....o.o...o.o.o.oo...
o.o...oo..........oo..o.o.o...
.oo........oo.......o.o.o.ooo.
.o.........oo.......o..o.o...o
.......oo...ooo....oo....o..oo
.......o.o...o.......oooo.....
........o....o.ooooo..........
.................oo.o.ooo.....
...............o...o.oo..o....
................o.o.....o.....
..............o.o.o.oooo......
.....ooooooo..oo...o.o........
....o.o.oo.ooo................
..ooo...o.....oo..............
.o...oooo.oo..o.o.............
o..o....o..o...o..............
.oooooooo.o...................
......o.o..ooo................
...oo...oo.o..o...............
...o..o....o.o................
.....oo.o.o.o.................
........o.o...................
........o.o...................
.....oo.o.oo..................
.....o..o.....................
.......oo.....................
In August 1999, Noam found a p7 oscillator that produced the necessary
spark, giving this p7 reflector:
......oo.....oo...........
o.o...oo.....o............
.oo........o.o............
.o.........oo.............
.......oo.................
.......o.o................
........o.................
..........................
..........................
.................o........
..............o..ooo...oo.
....oo.oo.oo..ooo...o..o..
....o.oo...ooo....oo.o.o..
.........o....oooo.o.o..oo
.....oooo.oo.o...o...oo.o.
.....o..o.o.oo..oo.oo.o.o.
..........o.o....ooo.o..oo
..........o.oooo......o.o.
...........o....oooooo..o.
.............o..o..o....oo
............oo............
> Also - at the time it was said that the static glider reflector was
> the "holy grail" of Life experts. Is that still so? Is none known?
Paul Callahan found one in October 1996. It's been improved several times
since then, both in size and in repeat time (the time between successive
reflections). I believe the best so far is one found by Stephen Silver in
November 1998. (See the "reflector" entry in Stephen's Life Lexicon at
http://www.cs.jhu.edu/~callahan/lexicon.htm
for more about the history of such reflectors.)
Here it is in RLE format, which can be read by several widely-used Life
programs, including Andrew Trevorrow's Macintosh program LifeLab and
Johan Bontes's IBM PC program Life32:
#C Stable reflector with repeat time of 497.
x = 81, y = 62
74b2o$74bo$72bobo$30bo37b2o2b2o$4bo9bo15b3o35b2o$4b3o5b3o18bo$o6bo3bo
20b2o11b2o$b2o3b2o3b2o32b2o$2o7$20b2o52b2o$20b2o34b2o16bobo$8b2o45bobo
18bo$7bo2bo44bo20b2o$2b2o4b2o44b2o4b2o$bobo54bo2bo$bo56b2o$2o65b2o$10b
2o33b2o20b2o$10bo34bo$11b3o32b3o$13bo34bo11$57bo$57b3o$60bo$59b2o10$
79b2o$79b2o9$64b2o$64b2o!
Dean Hickerson
de...@math.ucdavis.edu
Mirek Wojtowicz
Taylor) wrote:
>A year or two ago someone posted a glider reflector here.
>(...)
>Can someone post it again please?
I don't know the original post, here are two reflectors I extracted
from some guns. There exist really many of them, with different
periods. Look at large libraries of Life patterns, you can find links
to them for example on my page.
1. 180 degrees
...*
....*
..***
.
..............********
..............*.****.*
..............********
.
.
.
.
........***
.......*...*
......*.....*
......**.*.**
.
.
.........*
........*.*
........*.*
.........*
.
.........**
.........**
2. 90 degrees
.....................................*
....................................*
....................................***
.
.
.
.
.
.
.
..**............****.....***
..**............*.**.......*
................*.......*.**
.................**.....**
.
.................**.....**
................*.......*.**
..**............*.**.......****
..**............****.....******
> Also - at the time it was said that the static glider reflector was
> the "holy grail" of Life experts. Is that still so? Is none known?
It exists since a long time. The one I know comes from Dean Hickerson.
Except for the reflected glider some other gliders escape from it,
they can be easily captured using eaters.
x = 66, y = 120
31bo20bo$32bo17b3o$30b3o16bo$49boo6$59bo$57b3o$56bo$56boo$34boo$34boo
6$46boo$46boo$60boo$60boo$64boo$14boo48boo$14boo11$28boo$28bobo$30bo9b
oo$30boo8bobo$41bo5$9boo$10bo$7b3o26boboo$7bo28boobo$$45boo$45boo$25b
oo$25bobo$oo25bo$bo25boo$bobo15boo$bboo15boo9$35boo$36bo$36bobo$20boo
15boo$20bobo$22bo$22boo6$28booboo$29bobo$29bobbo$10boo15bobo3bo4boo15b
oo$10boo15boo3boo4boo15bobo$31bo25bo$31bo25boo$30boobo$29bobboo$29boo
17bo$46b3o$45bo$45boo4$9boo$8bobo$8bo$7boo4$52boo$52boo4$47boo$47boo$
51boo$51boo$10boo$10boo$16boo27boo$16boo27boo3$14boo$14boo5boo$21boo!
Stable glider reflector
This uses Paul Callahan's catalysis of a glider into a Herschel
and a glider, followed by David Buckingham's 77, 64, 64, 77, and
77 gen Herschel moves. Incoming gliders can be as close as 747
gens apart.
Dean Hickerson, 11/8/96
Hope this helps,
Mirek Wojtowicz
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mailto: mir...@homemail.com
http://www.mirwoj.opus.chelm.pl
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