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| A '''stable reflector''' is a [[reflector]] composed entirely of [[still life]]s. 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 [[oscillator]]s 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 [[stable reflector 1|explicit example]] until [[Paul Callahan]] did so in October [[:Category:Patterns found in 1996|1996]].
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| ==Types of stable reflectors==
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| There are several distinct categories of stable reflector:
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| * 'Create-then-remove' reflector - A reflector that temporarily creates an unwanted still-life and later destroys it.
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| * 'Destroy-then-rebuild' reflector - A reflector that temporarily destroys a necessary still-life and later reconstructs it.
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| * Direct reflector - A reflector that does not contain a Herschel track.
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| ===Repeat time===
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| 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.
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| ===Staged-recovery systems===
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| The staged-recovery 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.
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| ==History==
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| All known stable reflectors are quite slow. Callahan's original reflector has a repeat time of 4840, soon improved to 1686 and then 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 [[:Category:Patterns found in 1997|1997]] using a somewhat different method; he used a boat as the 'bait' catalyst, which is converted, on impact, directly into a Herschel, which 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. In 2009, Adam P. Goucher used a staged-recovery system to delete the beehive much quicker, lowering the repeat time to 466.
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| In April [[:Category:Patterns found in 2001|2001]], [[Dave Greene]] found a 180-degree stable glider reflector with a repeat time of only 202 known as the [[boojum reflector]]. This reflector won a $100 prize that [[Dietrich Leithner|Dieter Leithner]] had offered in April [[:Category:Patterns found in 1997|1997]] for the first stable reflector to fit in a 50×50 [[bounding box]], and an additional $100 that [[Alan Hensel]] had offered in January [[:Category:Patterns found in 1999|1999]] for the same feat.
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| In [[:Category:Patterns found in 2009|2009]], [[Adam P. Goucher]] constructed a 180-degree stable glider reflector with a repeat time of only 106, known as the [[rectifier]].
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| In April, [[:Category:patterns found in 2013|2013]] [[Mike Playle]] found a small 90-degree reflector with a repeat time of 43 generations, known as the [[snark]].
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| ===Prizes===
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| Dave Greene offered two $50 prizes for stable reflectors:
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| * Find a stable glider reflector that fits inside a 50×50 bounding box.
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| * Find a stable glider reflector that fits inside a 35×35 bounding box.
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| Matthias Merzenich offered two similar $50 prizes for stable reflectors:
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| * Find a stable glider reflector with a repeat time of 100 generations or less.
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| * Find a stable glider reflector with a repeat time of 61 generations or less.
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| Mike Playle won all four prizes with his discovery of his small stable reflector in April, 2013.
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| ==External links==
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| * {{Cite web|url=https://groups.google.com/d/msg/comp.theory.cell-automata/sHpFoieXvk4/NQRWMvcD76oJ|title=Still-life glider reflector found|author=Paul Callahan|date=November 16, 1996|accessdate=May 11, 2013}}
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| * A detailed summary of stable technology, 1996-2009. [http://www.calcyman.co.uk/life/stable.htm]
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| * A complete list of notable stable reflectors. [http://www.calcyman.co.uk/life/reflectors.htm]
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| [[Category:glossary]]
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