From: Dieter Leithner
Date: Mon, 28 Apr 1997 08:48:46 +0200
Subject: New Stable Glider Reflector (90 degrees)
Two blocks reflect a glider by 90 degrees and produce an r-pentomino:
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....O.
.....O
...OOO
......
OO....
OO..OO
....OO
The following device makes the reaction usable in Herschel technology:
]#C Two-stage Herschel device
#C Stage 1 - Herschel departure (left): A conduit by Dave Buckingham
#C transforms the r-pentomino created by the collision of a
#C glider with two blocks to a Herschel, indicated by (1).
#C Stage 2 - Herschel arrival (right): The stage, based in part on a
#C Herschel-to-pi conduit by Paul Callahan, restores the
#C two blocks which were destroyed by the glider in stage 1.
#C The arriving Herschel is indicated by (2).
#C Dieter Leithner, 26 Apr 1997
............................................O.......................
...........................................O.O......................
.....................OO....................O.O......OO..............
.....................O....................OO.OOO....OO..............
......................O.........................O...................
.....................OO...................OO.OOO....................
..........................................OO.O......................
....................................................................
..................................................................OO
..................................................................O.
.....................................O..........................O.O.
..1...............OO..................O.........................OO..
1.1...............OO................OOO.............................
111.................................................................
1................................OO.................................
.................................OO..OO.............................
.....................................OO.............................
....................................................................
.........................OO......................................2..
..........................O............OO......................2.2..
.......................OOO......O......OO......................222..
.......................O.......O.O.............................2....
................................O...................................
....................................................OO..............
................................................OO..OO..............
...............................................O.O..................
...............................................O....................
..............................................OO....................
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#C RLE equivalent of the above
x = 68, y = 28, rule = B3/S23
44bo$43bobo$21b2o20bobo6b2o$21bo20b2ob3o4b2o$22bo25bo$21b2o19b2ob3o$
42b2obo2$66b2o$66bo$37bo26bobo$2bo15b2o18bo25b2o$2bo15b2o16b3o$3o$o32b
2o$33b2o2b2o$37b2o2$25b2o38bo$26bo12b2o22bobo$23b3o6bo6b2o22b3o$23bo7b
obo29bo$32bo$52b2o$48b2o2b2o$47bobo$47bo$46b2o!
Ironically, the glider reflected 90 degrees by the two blocks in stage 1
has to be discarded to make stage 2 work. (That glider was the reason why I
included the two-block/glider reaction in my stable reflector candidate
list several years ago in the first place). However, as gliders are
abundant and virtually free in Herschel technology, loosing one glider here
fortunately does not defeat the purpose.
The departure and arrival gates of the above core device can be linked by
seven of Dave's and Paul's Herschel stages to form a closed loop:
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#C Stable glider reflector
#C The device uses the following Herschel stages by David Buckingham
#C (B) and Paul Callahan (C): 64 (B), 190 (B), 153 (C), 153, 64, 64
#C and 117 (B) steps.
#C Dieter Leithner, 27 Apr 1997
x = 159, y = 62
23b2o$16b2o5b2o50bo$16b2o56bobo$52b2o20bobo6b2o$52bo20b2ob3o4b2o$18b2o
33bo25bo$18b2o32b2o19b2ob3o$12b2o59b2obo$12b2o$97b2o$97bo17b2o$68bo26b
obo17bo$49b2o18bo25b2o19bo11bo$49b2o16b3o45b2o9b3o$125bo$64b2o59b2o10b
2o$64b2o2b2o67bo$68b2o65bobo$135b2o13b2o$56b2o54b2o36b2o$39b2o16bo12b
2o40b2o$39bo14b3o6bo6b2o$40b3o11bo7bobo91b2o$5b2o35bo20bo92b2o$6bo76b
2o67b2o$6bobo70b2o2b2o67b2o$4b2ob2o69bobo$3bobo72bo23b2o$3bobo71b2o23b
o18b2o$b3ob2o20b2o74b3o16bo34b2o$o26bo77bo13b3o35b2o$b3ob2o18bobo91bo$
3bob2o18b2o4$25b2o$25bobo$27bo15bo9bo53b2o14bo$27b3o13b3o5b3o28b2o24bo
14b3o$30bo15bo3bo13b2o17bo13b2o6b3o18bo$29b2o14b2o3b2o13bo17bobo11b2o
6bo19b2o$64bo19b2o$64b2o5$19b2o94b2o$19b2o46b2o46b2o$67b2o$10b2o$11bo$
8b3o141b2o$8bo143b2o$16b2o94b2o32b2o$16bo19b2o74bo33b2o$17bo17bobo11b
2o6bo35b2o3b2o13bo$16b2o17bo13b2o6b3o34bo3bo13b2o$34b2o24bo30b3o5b3o
46b2o$59b2o30bo9bo39b2o5b2o$141b2o!
The above reflector uses a different method than Paul's historic first
stable glider reflector (15 Oct 1996) and its successors. At first, the two
blocks are completely destroyed by the glider, then they remain absent for
a long time, but finally are restored after the Herschel has completed the
loop. No undesirable debris, no clean up.
In the conclusion of their paper "Tight bounds on periodic cell
configurations in Life" Dave Buckingham and Paul Callahan ask:
- Is there a smaller, faster stable reflector (or glider-to-Herschel
conduit), particularly one that does not use a glider to clean up
debris?
With a minimum separation between successive gliders of 1024 (= 2^10)
generations the new reflector is slower (and larger) than the current
record holder, Dean's "Jumbo Jet" (747). However, I found the closing loop
by hand after examining only a few candidate cases. A program which would
test a large number of combinations of the ten known Herschel stages might
improve on my solution for loop closure. Paul, don't you have a program to
solve such problems?
Finally, I believe that much smaller "direct" stable reflectors (without
Herschel loops) than are currently known are waiting out there in the vast
reaches of unexplored Life space. Here, I offer a $100 prize for the first
person to find a stable glider reflector (90 or 180 degrees) with a
bounding box where no side exceeds 50 cells. Please join the search!
Dieter
