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2007 December 17

New 180-degree glider reflector, period 4 and up

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.

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.

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.

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.)

Engineered Objects
Early MWSS gun in Golly 1.3

Bill Gosper's original p1100 MWSS gun, circa 1984
Bill Gosper's original four-barrelled p1100 MWSS gun, circa 1984
-- perhaps only the 3rd gun pattern constructed in Conway's Life.
The bounding box is over 12,000 cells on a side.
Golly 1.3 was released last month, with a number of useful improvements to editing functionality: unlimited undo/redo support, configurable keyboard shortcuts for scripts and edit operations, and scripting support in Perl as well as Python.

An early LWSS gun by Bill Gosper, constructed around 1984, serves as the Rosetta Stone for the two scripting languages. This is a very large, sparse pattern of centinal reflectors, with a central column of signal splitters that produce the gliders needed to maintain eight p1100 LWSS streams.

The pattern takes up about 60K as RLE, or about 750K as a flat file; it can be reduced to about 5K of Python or Perl script (see Golly 1.3's Scripts collection). The Perl version is somewhat larger, but appears to be able to recreate the pattern slightly faster.

p1100 pure-period MWSS gun (centinals and Herschels)
Dave Greene, 28 September 2007
For comparison purposes, here's a p1100 MWSS gun incorporating Herschel technology, which first became available more than a decade after Gosper's MWSS gun was constructed. This new gun would fit comfortably between most of the adjacent glider trails in the original MWSS gun:

2007 December 16

Wicks & Fuses
Frozen LWSS fuse / rake

Sideways LWSS rake based on a glider+constellation->LWSS reaction.
This puffer produces a row of still-life constellations, each
of which can output an LWSS and two gliders when hit by a glider.
The result is a repeating sideways LWSS generating reaction
at the back, progressively thawing the "frozen LWSS" string.
David Bell, 4 November 2007.
David Bell has constructed a two-stage sideways LWSS rake, where the first stage builds "frozen LWSSs" -- a chain of repeated still-life constellations -- and the second "thawing" stage consists of a glider that follows the chain (at a much slower speed) and liberates the stored LWSSs.

Here are a few more patterns experimenting with the "frozen spaceship" idea:

glider-to-LWSS still life in X-shaped pattern, using 2LWSS->2G
David Bell, 30 October 2007

Three fuses built from variants of an MWSS-to-MWSS still life
conversion reaction from Jason Summers, 29 October 2007,
David Bell, 9 November 2007

modified version of a glider-to-MWSS still life from Jason Summers
(29 October 2007) allows an MWSS input trigger instead of a glider.
David Bell, 30 October 2007

Four fuses using different variants of a glider-constructible
still life that produces an MWSS when annihilated by a glider.
Still lifes in the fuses on the right also output an extra glider.
David Bell, 11 November 2007

2007 December 15

Engineered Objects
Prime Number Calculators

Four prime-number calculators:
-- 1st quadrant (upper right):
Original sieve by Dean Hickerson, 1 November 1991
-- 2nd quadrant (upper left): new sieve #1
Uses every glider relay, p60 instead of p40 LWSS rake.
-- 3rd quadrant (lower left): new sieve #2
Vertical guns replaced with an equivalent reflector.
-- 4th quadrant (lower right): new sieve #3
Contains no glider guns, only pentadecathlon reflectors.

New sieves by Jason Summers, 15 October 2005.
A few years ago Jason Summers constructed three new versions of Dean Hickerson's 1991 Life prime-number calculator. These all produce the same strings of spaceships: an LWSS appears at time 60N if and only if N is prime. This is twice as fast as the original 1991 pattern, which is included for comparison (upper right quadrant).

In the pattern at right, the LWSS streams from the two bottom quadrants are set up to annihilate each other. The top two streams -- one at 60N and one at 120N -- are reflected upward along the central axis for comparison purposes. The spaceships representing 2, the first number in each series, are exactly in alignment.

Detail of four-primers pattern
Detail of four-primers pattern after 100,000 ticks.
All four quadrants use the same basic structure of reflected gliders to perform the prime-sieving operation. After running 100,000 generations in Golly (which seems fairly quick, in spite of the lack of regularity in the northbound output) the center of the above pattern looks like this:

2007 December 09

Update: smaller Garden of Eden previously known

72-bit 12x11 Garden of Eden
Achim Flammenkamp's 12x11 Garden of Eden --
black cells ON, blue-gray cells must be OFF
Achim Flammenkamp, 23 June 2004
Paul Kwiatkowski has pointed out that Nicolay Beluchenko's 12x12 pattern, based on a 12x13 Garden of Eden pattern from June 14, 2004, is not the smallest known "orphan". Achim Flammenkamp discovered a 12x11 GoE a week later, on June 23, 2004:

It is still an open question whether 11x11 or smaller Garden of Eden patterns exist.