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« Early MWSS gun in Golly 1.3 | Main | Some New Oscillators »

2007 December 17

Discovery
New 180-degree glider reflector, period 4 and up

2007-12-16-reflector-pN.rle
p6, p7, p8, and p22 versions of Noam Elkies'
spark-assisted glider reflection reaction,
with a previously-known p15 'kickback simulator'
included at the far right for timing comparisons.
From patterns by Jason Summers, 5-6 October 2007.
Noam Elkies responded to the challenge of finding a period-4 glider reflector by designing a new type of 180-degree reflector based on a spark-assisted block reconstruction. Jason Summers built a faster version at p22 (upper right), which produces a glider on the same path two ticks earlier.

The original reflection reaction can work at higher periods; variants are shown at right with p6, p7, and p8 sparks. The reflection path is the same as a kickback reaction, but the timing is different. By comparison, a pentadecathlon-based kickback emulator (far right) is four ticks faster -- or four ticks slower, since timing can be adjusted mod 8 by changing the reflector's location.

2007-12-16-Lx134-p8-and-p4.rle
Lx134 conduit, p8 and p4 versions -- recovery times 172 and 292
Reflector by Noam Elkies, 15 Nov 2007, improved by David Eppstein
David Eppstein contributed a p4 oscillator that could accomplish the same catalysis as the p22 oscillator above; improved versions are shown in the period 4 and period 8 reflectors at right, cleaning up the extra debris in an Lx134 conduit.

2007-12-16-reflector-p7.rle
Noam Elkies' previous block-restoration reaction (4 October 2007)
used with a kickback reaction to suppress a p63 glider stream.
Any p63+56N should be possible. P7 mechanism by Jason Summers.
The reflection's one-half-diagonal offset is the same as that of a kickback reaction, but the timing is different. Combining this reflector with a kickback reaction or a previously-known kickback simulator makes it possible to construct a variety of glider-relay oscillators, and thin certain odd-period glider streams.

2007-12-16-glider-to-pi-use.rle
Two conduits containing successful H-to-R-to-H stages, with
p8 glider-to-pi converters helping out with the catalysis.
Based on a p15 Herschel fanout device that produces mirror-image
R-pentominoes at generation 262 -- remove the eater near the
input glider path to see the mirror-image Rs.
The reaction can also be modified to produce pi heptominoes instead of output gliders, as shown in this example where glider-assisted p8 oscillators use a pi heptomino to solve a difficult Herschel-conduit problem in close quarters: a beehive catalyst needs to be shoved back one cell after a signal passes through the conduit. (At p15 this task can be accomplished by a pentadecathlon, which allows both output R pentominoes to be used.)

Posted by Dave Greene on 2007 December 17 02:02 |