Twin bees shuttle

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Twin bees shuttle
x = 29, y = 11, rule = B3/S23 17b2o$2o15bobo7b2o$2o17bo7b2o$17b3o4$17b3o$2o17bo$2o15bobo$17b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ GPS 10 THUMBSIZE 2 ZOOM 14 ]]
Pattern type Oscillator
Oscillator type Shuttle
Number of cells 28
Bounding box 32×13
Frequency class 38.2
Period 46
Mod 46
Heat 32.5
Volatility 0.98
Strict volatility 0.94
Discovered by Bill Gosper
Year of discovery 1971

The twin bees shuttle (or B-heptomino shuttle[1]) can refer to one of four very closely related period-46 shuttle oscillators in which two B-heptominos travel back and forth between stabilising blocks. The four variants are shown as follows, with the 3-block variant shown in the infobox to the right due to having the lowest minimum population:

Image Name Min. population Info Kinetic symmetry apgcode Cost in gliders
Cistwinbeesshuttle.png Cis-twin bees shuttle 43 Blocks are "on the same side" n-f xp46_330279cx1aad3y833zx4e93x855bc 7
Transtwinbeesshuttle.png Trans-twin bees shuttle 43 Blocks are "on different sides" n.f xp46_330279cx1aad3zx4e93x855bcy8cc 7
3blocktwinbeesshuttle.png 3-block twin bees shuttle 28 3 blocks are used n xp46_033y133zzzckgsxsgkczz0cc 8
4blocktwinbeesshuttle.png 4-block twin bees shuttle 32 4 blocks are used -f+f xp46_033y133zzzckgsxsgkczz0ccy1cc 10

The twin bees shuttle was found by Bill Gosper in 1971.[2][3] Before the Snark was discovered, it and its variants were the basis of all known period-46 oscillators (the version at right being the smallest based on its minimum population of 28 cells), and until the discovery of Tanner's p46, the basis of all known true period 46 guns including the second known basic gun, new gun 1. The simplest such gun is the bi-gun, in which two twin bees shuttles collide with each other head-on (much like the collision of two queen bees in the Gosper glider gun).

Alternative stabilizations

There are numerous other ways to stabilize the ends other than the four detailed above.

Sides stabilised by only a single block (as can be seen in three of the above variants) result in the creation of a very large spark, referred to as the twin bees shuttle spark, which is useful in a number of ways (see #Reactions).

The image below shows David Bell's double block reaction (on the left), which results in a shorter but wider shuttle than usual, as well as Heinrich Koenig's hat stabilization (on the right).

x = 81, y = 69, rule = B3/S23 50bo25bo$49bobo23bobo$49bobo23bobo$2o27b2o16b3ob2o21b2ob3o$bo27bo16bo 33bo$bobo23bobo17b3ob2o21b2ob3o$2b2o8bo14b2o20bob2o7bo13b2obo$11b2o46b 2o$10b2o46b2o$11b2o2b2o42b2o2b2o4$11b2o2b2o42b2o2b2o$10b2o46b2o$11b2o 46b2o$2b2o8bo14b2o31bo$bobo23bobo$bo27bo18b2o27b2o$2o27b2o18bo27bo$46b 3o29b3o$46bo33bo6$52b2o19b2o$52b2o19b2o2$12bo47bo$11b2o38b2o6b2o13b2o$ 10b2o39b2o5b2o14b2o$4bo6b2o2b2o9bo32b2o2b2o$2b3o21b3o$bo27bo$2b3o21b3o $4bo6b2o2b2o9bo32b2o2b2o$10b2o39b2o5b2o14b2o$11b2o38b2o6b2o13b2o$12bo 47bo2$52b2o19b2o$52b2o19b2o7$7b2o13b2o31b2o13b2o$6bobo13bobo29bobo13bo bo$7bo15bo31bo15bo2$12bo47bo$4b2o5b2o12b2o25b2o5b2o12b2o$4b2o4b2o13b2o 25b2o4b2o13b2o$11b2o2b2o42b2o2b2o4$11b2o2b2o42b2o2b2o$4b2o4b2o13b2o21b 2o8b2o17b2o$4b2o5b2o12b2o21b2o9b2o16b2o$12bo47bo2$7bo15bo28bo21bo$6bob o13bobo26bobo19bobo$7b2o13b2o28b2o19b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 23 LOOP 46 ZOOM 4 ]]
Some additional ways to stabilize the twin bees shuttle;
the top-left variant is used in centinal
(click above to open LifeViewer)
RLE: here Plaintext: here

Some of the stabilizations are SKOPs, like the following:

x = 41, y = 9, rule = B3/S23 2o14b2o$2o15b2o$13b5o17b3o$13b4o18b3o$35b3o$13b4o21b3o$13b5o20b3o$2o15b2o8b2o 9b3o$2o14b2o9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 23 LOOP 46 ZOOM 8 ]]
SKOP 184: with figure eight
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 11, y = 40, rule = B3/S23 b2o5b2o$b2o5b2o16$2obo3bob2o$o2bo3bo2bo$b3o3b3o8$8b2o$8b2o6$3b2o$b2o2b2o$bo4b o$2bo2bo$obo2bobo$2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 23 LOOP 46 ZOOM 7 ]]
SKOP 230: with fumarole
(click above to open LifeViewer)
RLE: here Plaintext: here

Reactions

The twin bees shuttle is capable of several interesting reactions, mostly due to the twin bees shuttle spark, many of which are detailed below.

With blocks

The twin bees shuttle spark is capable of being partially eaten by a correctly-positioned block, yielding further possible variants of the shuttle, many of which have occurred naturally. Since the spark is odd-symmetric whereas the block is even-symmetric, there are two ways in which each block can be positioned to yield a valid oscillator.

A block is said to be in "cis" position if closer to the shuttle, such that the spark interacts with it at its farther side, and in "trans" position if farther from the shuttle, such that the spark interacts with it at its closer side.

A table of all possibilities can be found as follows:

Base shuttle Block count Image Min. population Block positions apgcode Cost in gliders
cis 1 Cistwinbeesshuttlecis.png 47 cis xp46_330279cx1aad3y833zx4e93x855bcyd66 9
Cistwinbeesshuttletrans.png 47 trans xp46_330279cx1aad3y833zx4e93x855bcydcc 9
2 Cistwinbeesshuttleciscis.png 51 cis cis xp46_66y2279cx1aad3yd66zy1cc04e93x855bcy8cc 11
Cistwinbeesshuttlecistrans.png 51 cis trans xp46_33y2279cx1aad3yd66zy1cc04e93x855bcy8cc 11
Cistwinbeesshuttletranstrans.png 51 trans trans xp46_33y2279cx1aad3yd33zy1cc04e93x855bcy8cc 11
trans 1 Transtwinbeesshuttlecis.png 47 cis xp46_330279cx1aad3yd66zx4e93x855bcy8cc 8
Transtwinbeesshuttletrans.png 47 trans xp46_330279cx1aad3yd33zx4e93x855bcy8cc 9
2 Transtwinbeesshuttleciscis.png 51 cis cis xp46_66y2279cx1aad3y833zy1cc04e93x855bcyd66 11
Transtwinbeesshuttlecistrans.png 51 cis trans xp46_33y2279cx1aad3y833zy1cc04e93x855bcyd66 11
Transtwinbeesshuttletranstrans.png 51 trans trans xp46_33y2279cx1aad3y833zy1cc04e93x855bcydcc 11
3-block 1 3blocktwinbeesshuttlecis.png 32 cis xp46_66ybb9ey366zooybk4sy8cczyd11 10
3blocktwinbeesshuttletrans.png 32 trans xp46_66ybb9ey366zooybk4sy8oozyd11 10

Glider conversions and reflections

Interactions based on the twin bees shuttle are numerous and can have many applications. Some notable reactions are period 46 oscillators that can directly reflect gliders, lightweight spaceships, and middleweight spaceships, as well as convert gliders to lightweight spaceships and lightweight spaceships to middleweight spaceships. The large spark's ability to convert gliders into lightweight spaceships is made use of by double X.

The stop and go reaction, where a glider is converted to a block and then reflected 180 degrees, was found by by Dean Hickerson in January 1992.[4] The reaction can be used to construct higher-period oscillators such as this p184.

The period-92 do-see-do reaction was found by David Bell in 1996.[5] It is a 90-degree glider reflection reaction in which the gliders appear to circle around each other.

x = 42, y = 11, rule = B3/S23 40bo$39bo$2o14b2o9b2o10b3o$2o15b2o8b2o$13b5o$13b4o2$13b4o$13b5o$2o15b 2o$2o14b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 23 LOOP 184 ]]
The stop and go reaction
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 55, y = 38, rule = b3/s23 54bo$52b2ob$53b2o17$48b2o5b$48bo6b$46bobo6b$46b2o7b$31bo23b$29b2o24b$ 30b2o23b$24bo30b$10b2o9b2o3bo28b$2o7bobo9b2obob2o27b$2o7bo10bo6b2o26b$ 9b3o9b2obob2o27b$21b2o3bo28b$24bo30b2$9b3o43b$2o7bo17b2o26b$2o7bobo15b 2o26b$10b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 7 ]]
The do-see-do reaction
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 192, y = 109, rule = B3/S23 156b2o5b2o$11b2o143b2o5b2o$b2o7bobo$b2o6b2obo$10b2o26b2o68b2o$11bo26bo bo7b2o58b2o$40bo7b2o4b3o$11bo26b3o13bo2bo$10b2o42bo33b2o$b2o6b2obo41bo 3bo29b2o$b2o7bobo41bo26b2o$11b2o7bobo15b3o14bobo22b5o$20b2o18bo7b2o14b 2o14bo4bo3b2o$21bo16bobo7b2o14b2o14b3o2bo3b2o17b3o3b3o$38b2o41bo2b2o 21bo2bo3bo2bo$82b2o23b2obo3bob2o2$b2o39bo2bo19b2o15b2o71b2obo3bob2o$b 2o17b4o22bo18b2o14bo2b2o69bo2bo3bo2bo$19bo3bo18bo3bo13b3o17b3o2bo3b2o 65b3o3b3o$23bo19b4o13bo2bo16bo4bo3b2o$19bo2bo36bo4bo15b5o42b2o$61bobo 17b2o44bobo$59b4o25b2o37bo$60bo27b2o$b3o3b3o$bo2bobo2bo$o3bobo3bo$4o3b 4o$bo7bo$148b3o3b3o12b3o$108b2o5b2o30bo2bo3bo2bo11bo$108b2o5b2o30b2obo 3bob2o12bo$138b3o$138bo$59b3o5b3o69bo$59b3o5b3o$60b2o5b2o$62bo3bo$60bo 2bobo2bo$59bo3bobo3bo$60bo2bobo2bo112b2o$60b3o3b3o112bobo$181bo$b2o5b 2o46b2o13b2o$b2o5b2o46b2o2b2o5b2o2b2o$60b2o5b2o2$148b2o5b2o$148b2o5b2o 19$114b4o$114bo3bo$88b2o24bo26b2o$88b2o25bo2bo22b2o2$148b2o$140b2o5bob o15b2o$140b2o5bo17b2o$147b3o2$189bo$89bo5bo68b2o21bo3bo$88b3o3b3o50b3o 14b2o20bo$87b2obo3bob2o42b2o5bo38bo4bo$140b2o5bobo19bo16b5o$148b2o18b 3o$90bo3bo73bo$90bo3bo46b2o26bo2bo$141b2o27bobo3$169bo$170b2o4$84b2o 13b2o$84b2o2b2o5b2o2b2o$88b2o5b2o2$162bo7bo$161b4o3b4o$161bo3bobo3bo$ 162bo2bobo2bo$162b3o3b3o4$158b2o13b2o$158b2o2b2o5b2o2b2o$162b2o5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 3.4 HEIGHT 600 WIDTH 800 ]]
Several other interactions
(click above to open LifeViewer)
RLE: here Plaintext: here

Commonness

On Catagolue, it is the most common period 46 oscillator, with all natural oscillators of that period featuring it in some form.[6]

A four-fold version of this oscillator first appeared semi-naturally in December 2014 in a soup found by Richard Schank.[7] A monomerized version, specifically the cis isomer, later appeared in an asymmetric soup found by Brett Berger on April 16, 2015.[8] The trans version first appeared on May 7 in a soup also found by Berger,[9] and the three-block version first appeared on October 15 in a soup found by Tomas Rokicki.[10] Other three-block versions, with one of the blocks placed further away, were found by Adam P. Goucher in July and September 2016.[11][12] After numerous appearances in symmetric soups, the bilaterally symmetric four-block twin bees shuttle first appeared in the C1 symmetry on April 1, 2022, in a soup found by Charity Engine.[13]

The cis isomer is about 15.1% more common than the trans isomer.

Glider synthesis

There is a 5-glider component that turns any one-sided stabilization of the twin bees, such as a block, into a twin bees shuttle variant by adding the two B-heptominoes and a stabilizing block. This yields 7-glider syntheses for two-block variants, and 8-glider syntheses for some 3-block variants.

x = 62, y = 38, rule = B3/S23 59bobo$59b2o$60bo10$17b2o$17b2o3$28b2o$27bobo4bo$29bo3b2o$33bobo2$28b o$28b2o$27bobo12$bo$b2o$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The 5-glider component mentioned above, being applied to a block
(click above to open LifeViewer)

Gallery

x = 37, y = 15, rule = B3/S23 24b2o$24b2o$36bo$10b2o22b3o$2o7bobo13b2o6bo$2o7bo15b2o6b2o$9b3o4$9b3o 21b3o$2o7bo20b2o$2o7bobo13bo4b2o$10b2o11bobo4bobo$24b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The current smallest period-46 glider gun,
using the three quarters traffic light catalyst
(click above to open LifeViewer)
RLE: here Plaintext: here

See also

References

  1. "B-heptomino shuttle". The Life Lexicon. Stephen Silver.
  2. Robert Wainwright (September 1971). Lifeline, vol 3, page 4.
  3. Dean Hickerson's oscillator stamp collection.
  4. "Stop and go". The Life Lexicon. Stephen Silver.
  5. "Do-see-do". The Life Lexicon. Stephen Silver.
  6. Adam P. Goucher. "Statistics". Catagolue. Retrieved on October 27, 2018.
  7. Richard Schank (December 19, 2014). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  8. Matthias Merzenich (April 16, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. gameoflifeboy (May 7, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  10. gameoflifeboy (October 15, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  11. Apple Bottom (July 16, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  12. Apple Bottom (September 26, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  13. catglue (April 1, 2022). Message in #cgol on the Conwaylife Lounge Discord server

External links

  • 32P46.1 at Heinrich Koenig's Game of Life Object Catalogs