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A '''reflector''' is a [[still life|stable]] or [[oscillator|oscillating]] pattern that can reflect some specific type of [[spaceship]] (usually a [[glider]]) without suffering permanent damage. The first known reflector was the [[pentadecathlon]], which can function as a 180-degree glider reflector as in [[relay]]. Other examples include the [[buckaroo]], the [[twin bees shuttle]] and some oscillators based on the [[traffic jam]] reaction. Glider [[gun]]s can also be made into reflectors, although these are mostly rather large.
A '''reflector''' is a [[still life|stable]] or [[oscillator|oscillating]] pattern that can reflect some specific type of [[spaceship]] (usually a [[glider]]) without suffering permanent damage. The first known reflector was the [[pentadecathlon]], which can function as a 180-degree glider reflector as in [[relay]]. Other examples include the [[buckaroo]], the [[twin bees shuttle]] and some oscillators based on the [[traffic jam]] reaction. Glider [[gun]]s can also be made into reflectors, although these are mostly rather large.


In September [[:Category:Patterns found in 1998|1998]] [[Noam Elkies]] found some fast small-period glider reflectors based on an arrangement of a [[block]], [[boat]] and [[eater 1]] that can be used in conjunction with [[pipsquirter 1]], [[pipsquirter 2]], or [[figure eight]] to create a 90-degree glider reflector of period 6, 7, or 8, respectively. A more complicated construction allows a period 5 version of the reflector (which, as had been anticipated, soon led to a [[true period]] 55 gun - see [[Quetzal]]). A variant of the [[pentadecathlon]] can also be used to construct a period 15 reflector in this way.
==Bouncers and bumpers==
{{alsosee|Bumper and bouncer gallery}}
In September {{year|1998}} [[Noam Elkies]] found some fast small-period glider reflectors based on an arrangement of a [[block]], [[boat]] and [[eater 1]] that can be used in conjunction with a suitable [[sparker]] to create a 90-degree glider reflector. [[Pipsquirter 1]], [[pipsquirter 2]], and [[figure eight]] work for periods 6, 7, and 8, respectively. A more complicated construction is required for a [[p5 reflector]] (which, as had been anticipated, soon led to a [[true period]] 55 gun - see [[Quetzal]]). A variant of the [[pentadecathlon]] can also be used to construct a period 15 reflector in this way.  These [[colour-changing]] reflectors were later labeled "[[bouncer]]s", to distinguish them from the [[colour-preserving]] [[bumper]]s discovered by Tanner Jacobi in April {{year|2016}}.


==Stable reflectors==
==Stable reflectors==
{{main|Stable reflector}}
{{main|Stable reflector}}
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 [[:Category:Patterns found in 1996|1996]].
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 {{year|1996}}.  Stable reflectors were progressively reduced in size.  The record holder for many years was [[Silver's reflector]], but that has been replaced for many purposes by Mike Playle's successful hunt for the [[Snark]].
 
==Glider timing adjustment==
 
When using 2 90-degree reflectors to make a flexible 180-degree reflector, moving the reflector pair one cell outwards or inwards changes the glider's timing by 8 ticks.  This is because gliders travel at [[c/4]], and when the path length is increased, the glider has to travel one [[full diagonal]] cell farther on both the outward trip and the return trip.  If one of the 90-degree reflectors is [[colour-changing]] and one is [[colour-preserving]], it is possible to achieve a 4-tick change in timing by swapping the two reflectors: the total distance that the glider travels is then changed by just one [[half diagonal]].
 
A complete [[toolkit]] for adjusting glider timings therefore requires eight different combinations of reflectors for each color of output.  Timing changes that are multiples of 8 (often called "mod 8" adjustments) can be made just by moving reflectors.  But adjusting a glider's timing by 1, 2, 3, 4, 5, 6, or 7 ticks requires replacing one or more reflectors with new mechanisms that have the appropriate timing.  The [[period-doubler toolkit]]<ref name="post55071" /> is a recent example of this kind of [[universal]] substitution mechanism.
 
When using reflectors in period x:
<table border=2 cellspacing=0>
 
<tr><th>Period</th><th>CP1</th><th>CP2</th><th>CC</th></tr>
 
<tr>
<td  colspan=4></td>
</tr><tr>
<td >3</td>
<td >[[Snark]]</td>
<td >[[p3 bumper]]</td>
<td >Unknown</td>
</tr><tr>
<td >4</td>
<td >[[Snark]]</td>
<td >[[p4 bumper]]</td>
<td >[[p4 CC cenark]]
[[p4 bouncer]]</td>
</tr><tr>
<td >5</td>
<td >[[Snark]]</td>
<td >[[p5 bumper]]</td>
<td >[[p5 bouncer]]</td>
</tr><tr>
<td >6</td>
<td >[[Snark]]</td>
<td >[[p6 bumper]]</td>
<td >[[p6 bouncer]]</td>
</tr><tr>
<td >7</td>
<td >[[Snark]]</td>
<td >[[p7 bumper]]</td>
<td >[[p7 bouncer]]</td>
</tr><tr>
<td >8</td>
<td >[[Snark]]</td>
<td >[[p8 bumper]]</td>
<td >[[p8 bouncer]]</td>
</tr><tr>
<td >9</td>
<td >[[Snark]]</td>
<td >[[p9 bumper]]</td>
<td >[[p9 bouncer]]</td>
</tr><tr>
<td >10</td>
<td >[[Snark]]</td>
<td >[[p5 bumper]]</td>
<td >[[p5 bouncer]]</td>
</tr><tr>
<td >11</td>
<td >[[Snark]]</td>
<td >[[p11 bumper]]</td>
<td >Unknown</td>
</tr><tr>
<td >12</td>
<td >[[Snark]]</td>
<td >[[p6 bumper]]</td>
<td >[[p6 bouncer]]</td>
</tr><tr>
<td >13</td>
<td >[[Snark]]</td>
<td >Unknown</td>
<td >Unknown</td>
</tr><tr>
<td >14</td>
<td >[[Snark]]</td>
<td >[[p7 bumper]]</td>
<td >[[34P14 shuttle]]
as reflector</td>
</tr><tr>
<td >15</td>
<td >[[Snark]]</td>
<td >[[p15 bumper]]</td>
<td >[[p15 bouncer]]</td>
</tr><tr>
<td colspan=4>CP1 is the Snark.
CP2 is a CP reflector that is not the Snark (e.g. Bumper).
CC is a CC reflector (e.g. Bouncer).</td>
</tr>
</table>
By using 3 reflectors, it can basically lead a glider from one place and time to any other place and time. The Snark is used as the CP reflector, and the bouncer is used as a CC reflector. By putting one more reflector that is CP but a different timing compared to the Snark, tne glider stream will be easy to rephase in steps of 1-7.
 
==References==
<references>
<ref name="post55071">{{LinkForumThread
|f      = 2
|t      = 2316
|p      = 55071
|title  = Re: Construction practice
|format = ref
|author = Chris Cain
|date  = January 13, 2018
}}</ref>
</references>


==External links==
==External links==
{{LinkWeisstein|Reflector.html}}
{{LinkWikipedia|Reflector_(cellular_automaton)}}
{{LinkLexicon|lex_r.htm#reflector}}
{{LinkLexicon|lex_r.htm#reflector}}

Revision as of 22:23, 6 March 2020

A reflector is a stable or oscillating pattern that can reflect some specific type of spaceship (usually a glider) without suffering permanent damage. The first known reflector was the pentadecathlon, which can function as a 180-degree glider reflector as in relay. Other examples include the buckaroo, the twin bees shuttle and some oscillators based on the traffic jam reaction. Glider guns can also be made into reflectors, although these are mostly rather large.

Bouncers and bumpers

Also see: Bumper and bouncer gallery

In September 1998 Noam Elkies found some fast small-period glider reflectors based on an arrangement of a block, boat and eater 1 that can be used in conjunction with a suitable sparker to create a 90-degree glider reflector. Pipsquirter 1, pipsquirter 2, and figure eight work for periods 6, 7, and 8, respectively. A more complicated construction is required for a p5 reflector (which, as had been anticipated, soon led to a true period 55 gun - see Quetzal). A variant of the pentadecathlon can also be used to construct a period 15 reflector in this way. These colour-changing reflectors were later labeled "bouncers", to distinguish them from the colour-preserving bumpers discovered by Tanner Jacobi in April 2016.

Stable reflectors

Main article: Stable reflector

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. Stable reflectors were progressively reduced in size. The record holder for many years was Silver's reflector, but that has been replaced for many purposes by Mike Playle's successful hunt for the Snark.

Glider timing adjustment

When using 2 90-degree reflectors to make a flexible 180-degree reflector, moving the reflector pair one cell outwards or inwards changes the glider's timing by 8 ticks. This is because gliders travel at c/4, and when the path length is increased, the glider has to travel one full diagonal cell farther on both the outward trip and the return trip. If one of the 90-degree reflectors is colour-changing and one is colour-preserving, it is possible to achieve a 4-tick change in timing by swapping the two reflectors: the total distance that the glider travels is then changed by just one half diagonal.

A complete toolkit for adjusting glider timings therefore requires eight different combinations of reflectors for each color of output. Timing changes that are multiples of 8 (often called "mod 8" adjustments) can be made just by moving reflectors. But adjusting a glider's timing by 1, 2, 3, 4, 5, 6, or 7 ticks requires replacing one or more reflectors with new mechanisms that have the appropriate timing. The period-doubler toolkit[1] is a recent example of this kind of universal substitution mechanism.

When using reflectors in period x:

PeriodCP1CP2CC
3 Snark p3 bumper Unknown
4 Snark p4 bumper p4 CC cenark p4 bouncer
5 Snark p5 bumper p5 bouncer
6 Snark p6 bumper p6 bouncer
7 Snark p7 bumper p7 bouncer
8 Snark p8 bumper p8 bouncer
9 Snark p9 bumper p9 bouncer
10 Snark p5 bumper p5 bouncer
11 Snark p11 bumper Unknown
12 Snark p6 bumper p6 bouncer
13 Snark Unknown Unknown
14 Snark p7 bumper 34P14 shuttle as reflector
15 Snark p15 bumper p15 bouncer
CP1 is the Snark.

CP2 is a CP reflector that is not the Snark (e.g. Bumper).

CC is a CC reflector (e.g. Bouncer).

By using 3 reflectors, it can basically lead a glider from one place and time to any other place and time. The Snark is used as the CP reflector, and the bouncer is used as a CC reflector. By putting one more reflector that is CP but a different timing compared to the Snark, tne glider stream will be easy to rephase in steps of 1-7.

References

  1. ↑ Chris Cain (January 13, 2018). Re: Construction practice (discussion thread) at the ConwayLife.com forums

External links

Retrieved from "https://conwaylife.com/w/index.php?title=Reflector&oldid=69716"