Stable reflector

A stable reflector is a reflector composed entirely of still lifes. That is, it is a collection of still lifes that can reflect some type of spaceship (usually a glider) without suffering permanent damage. Stable reflectors are special in that, if they satisfy certain conditions, they can be used to construct oscillators of all sufficiently large periods. It was known for some time that stable reflectors were possible (see universal constructor), but no one was able to construct an explicit example until Paul Callahan did so in October 1996 (see History).

Types of stable reflectors

There are several distinct categories of stable reflector:

• 'Create-then-remove' reflector - A reflector that temporarily creates an unwanted still-life and later destroys it.
• 'Destroy-then-rebuild' reflector - A reflector that temporarily destroys a necessary still-life (bait) and later reconstructs it.
• Direct reflector - A reflector that does not contain a Herschel track.

Repeat time

The repeat time, also called the recovery time or compression of a stable reflector is the number of generations after the acceptance of one spaceship required for the reflector to be able to reflect the next spaceship.

Staged-recovery systems

Staged recovery is a construction method that attains reduced repeat time at the cost of complexity. The first such system was invented by Dave Greene, when he incorporated it into his highway robber and stable Heisenburp patterns. In 2009, Adam P. Goucher built two 'Create-then-remove' reflectors using a staged-recovery system.

History

Before 2013, all known stable reflectors were quite slow. Callahan's original reflector starting with Herschel receiver has a repeat time of 4840, soon improved to 1686, 894 and then 850. In November 1996, Dean Hickerson managed to reduce the repeat time to 747 using a specialised Herschel-to-glider conduit. David Buckingham reduced it to 672 in May 1997 using a somewhat different method; he used a boat as the 'bait' catalyst, which is converted directly into a Herschel on impact, that rebuilds the initial boat. In October 1997, Stephen Silver reduced the time to 623 by a method closer to the original; instead of using a boat and conduit 1 to convert the R-pentomino into a Herschel, Silver used a loaf. In November 1998, Callahan reduced this to 575 with a new initial reaction based on a beehive, rather than a block. A small modification by Silver a few days later brought this down to 497. A brief summary of these can be found on the forums.

In April 2001, Dave Greene found a 180-degree stable glider reflector with a repeat time of only 202 known as the boojum reflector. In 2009, Adam P. Goucher constructed an improved version with a repeat time of only 106, known as the rectifier.

Also in 2009, Adam P. Goucher used staged-recovery systems to delete the beehive much quicker, lowering the repeat time to 487 and then 466. In 2012 Sergey Petrov (Guam) reduced the repeat time further, to 444, with a new conduit. When the Snark was discovered, it became possible to cut down the repeat time to 386 ticks.

In April, 2013 Mike Playle found a small 90-degree reflector known as the Snark. The Snark is currently the smallest known stable reflector, with a recovery time of 43.

As of the end of 2017, the following splitter is among the smallest known 90-degree colour-changing reflectors. The top output can be blocked by eater 1 if needed.

x = 56, y = 44, rule = B3/S23 16b2o11bo6b2o$16b2o10bobo4bo2bo$28bobo3bob3o2b2o$27b2ob2obobo6bo$31bob o3b2o3bobo$27b2obo2b4obo4b2o$27b2obobo3bo$31bobo3bo$32bobo3bo$33bo3b2o 14bo$52bobo$53bo2$24b2o$24b2o$9b2o$8bo2bo$7bob2o42b2o$7bo45b2o$6b2o$ 21b2o$21bo$22b3o$24bo5b2o$29bobo$29bo$28b2o3$36bo15b2o$35bobo14bobo$ 35bobo16bo$36bo17b2o$3o37b2o$2bo37bobo$bo40bo$42b2o5$35bobo$36b2o$36bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 2 HEIGHT 400 THEME 6 GPS 60 LOOP 340 X 5 ZOOM 8 AUTOSTART ]]

(click above to open LifeViewer) RLE: here Plaintext: here

In 2020, Entity Valkyrie constructed a 0-degree stable reflector based on a reaction by Martin Grant. This "reflector" changes the color of the glider, and is the first color-changing stable reflector with repeat time lower than that of the syringe. This reflector is known as the Bandersnatch.

Prizes

Also see: Problem

In 2001, Dave Greene's discovery of the boojum reflector won two long-standing prize offers of $100 each from Alan Hensel and Dietrich Leithner, for a stable reflector fitting inside a 50×50 bounding box. Greene offered two follow-up $50 prizes for stable reflectors:

• Find a stable 90-degree glider reflector that fits inside a 50×50 bounding box.
• Find a stable 90-degree glider reflector that fits inside a 35×35 bounding box.

Matthias Merzenich offered two similar $50 prizes for stable reflectors:

• Find a stable glider reflector with a repeat time of 100 generations or less.
• Find a stable glider reflector with a repeat time of 61 generations or less.

Mike Playle won all four prizes with his discovery of his small stable reflector in April, 2013. Playle then offered a new prize of $100 USD for a similarly small and fast stable reflector that changes the glider's color (since the Snark is a color-preserving reflector):

• Find a color-changing stable glider reflector that's at most 25×25, with a repeat time of 50 generations or less.

External links

• Paul Callahan (November 16, 1996). "Still-life glider reflector found". Retrieved on May 11, 2013.
• A detailed summary of stable technology, 1996-2009. [1]
• A complete list of notable stable reflectors. [2]