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.

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 and later reconstructs it.
• Direct reflector - A reflector that does not contain a Herschel track.

Repeat time

The repeat time of a stable reflector is the number of generations after the acceptance of one pattern required for the reflector to be able to reflect the next pattern.

Staged-recovery systems

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.

History

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 found a variant in which the repeat time is reduced to 747. David Buckingham reduced it to 672 in May 1997 using a somewhat different method, and in October 1997 Stephen Silver reduced it to 623 by a method closer to the original. In November 1998 Callahan reduced this to 575 with a new initial reaction. A small modification by Silver a few days later brought this down to 497.

In April 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 Dieter Leithner had offered in April 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 1999 for the same feat.

In 2009, Adam P. Goucher constructed a 180-degree stable glider reflector with a repeat time of only 106, known as the rectifier. It is currently the fastest known 180-degree stable reflector.

Records

Ideally, stable reflectors should be as small and fast as possible. :

• Smallest 90° reflector: [1]
• Fastest 90° reflector: [2]
• Smallest 180° reflector: rectifier
• Fastest 180° reflector: rectifier

The third record is debatable, since the boojum reflector has a smaller bounding box across all phases; the rectifier has the smallest quiescent configuration. The terms 'active' and 'passive' bounding box should be used to avoid confusion.

Prizes

Dave Greene has offered two $50 prizes for stable reflectors:

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

External links

• A detailed summary of stable technology, 1996-2009. [3]
• A complete list of notable stable reflectors. [4]