Elevener

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Elevener
x = 6, y = 6, rule = B3/S23 4b2o$3bobo$3bo$b3o$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] [[ ZOOM 42 ]]
Pattern type Strict still life
Number of cells 11
Bounding box 6 × 6
Frequency class 19.1
Discovered by Unknown
Year of discovery Unknown

Elevener (or gull[1] or intentionless[2]) is an 11-cell still life. It consists of two siamesed eater 1s that share three cells of their tails while retaining both their glider-eating and boat-bit-catching capabilities.

Construction

x = 33, y = 22, rule = B3/S23 24bo$22b2o$23b2o3$bo$2bo$3o3$27b2o$27bo$28b3o$30bo$30bobo$31b2o4$4b2o15bo$3bobo14b2o$5bo14bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 380 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 40 PAUSE 2 LOOP 41 ]]
A 4G synthesis[3]
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An elevener can be formed by applying a banana spark to the tail of an eater 1; as both the construction of the eater 1 and the conversion to the elevener can be done in two gliders, a total of four gliders suffice to construct an elevener.[3] There is also a 3-glider collision that produces a constellation of an elevener, a block and a beehive,[note 1] leading to another two-stage 4-glider synthesis for the still life.

x = 42, y = 57, rule = B3/S23 10bo$11bo$9b3o8$36b2o$36bo$18b2o17b3o$19bo19bo$19bobo17bobo$8bo11b2o 18b2o$8b2o$7bobo5$21bo$20bo$20b3o6$36b2o$36bo$18b2o17b3o$5b3o11bo19bo$ 7bo11bobo17bobo$6bo13b2o18b2o5$obo$b2o$bo7bo$7bobo$8b2o6$36b2o$36bo$ 18b2o17b3o$19bo19bo$4bo14bobo17bobo$4b2o14b2o18b2o$3bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 THEME Book ZOOM 8 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 32 PAUSE 2 LOOP 33 ]]
Three conversions from a fishhook[3]
(click above to open LifeViewer)
x = 139, y = 152, rule = B3/S23 bo$2bo$3o93$95bo$94bo$94b3o5$110b2o$110bo$111b3o$113bo$113bobo$114b2o 3$81b2o$80bobo$82bo37$137b2o$136b2o$138bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THEME Book ZOOM 8 X 15 Y 20 AUTOSTART GPS 30 T 0 PAUSE 1 T 20 PAUSE 3 T 318 PAUSE 1 T 398 PAUSE 2 LOOP 399 ]]
A two-stage 4G synthesis via an intermediate elevener+block+beehive constellation[note 1]
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Occurrence

See also: List of common still lifes, List of still lifes with 11 cells

Elevener is the forty-seventh most common still life in Achim Flammenkamp's census (the second-most common of its size, after the boat tie ship), being less common than cis-mirrored bookend but more common than block on cap.[4]

It is the 47th most common still life on Adam P. Goucher's Catagolue, being less common than cis-rotated bookend but more common than mirrored dock. It is the 2nd most common still life with 11 cells, being less common than boat tie ship but more common than trans-loaf with tail.[5]

The octohash database includes 11 collisions between a glider and a small constellation with an elevener in the ash, including 6 clean one-glider seeds.[note 2] An elevener also occurs in final patterns of 23 collisions in the octo3obj database.[note 3]

In other rules

In HighLife, the elevener is almost 60 times more common than it is in Life. In B34e/S23, it is even more common, as fleet predecessors evolve into two eleveners instead of two ship-ties.

x = 7, y = 4, rule = B36/S23 4bo$2o2b2o$2o3b2o$4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 380 THEME Book ZOOM 30 X 1 AUTOSTART GPS 5 PAUSE 2 LOOP 24 ]]
Elevener evolving from a block and a B-heptomino in HighLife
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See also

References

  1. "Gull". The Life Lexicon. Stephen Silver. Retrieved on April 24, 2009.
  2. "Intentionless". The Life Lexicon. Stephen Silver. Retrieved on June 13, 2009.
  3. 3.0 3.1 3.2 The 46 eleven-bit still-lifes at Mark D. Niemiec's Life Page (download pattern file: 11/11-38.rle)
  4. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  5. Adam P. Goucher. "Statistics". Catagolue. Retrieved on May 5, 2023.

Notes

  1. 1.0 1.1 An elevener+block+beehive constellation with a 3G synthesis: xs21_g88e13z11zy933y24aa4
  2. All 6 clean 1G seeds in the octohash database involve an eater 1 → elevener conversion by a spark from a glider hitting a common object.
  3. 10 out of 23 octo3obj collisions converge to a sequence 8b2o2b2o$8b2ob2o$13bo$2o$2o2$2o$2o7b2o$9b2o! with final population 767. Two other collisions converge to the sequence 3o5b2o$8b2o3$3b3o2bo$7b2o$7bobo! with final population oscillating between 117 and 119. The remaining 11 collisions can all be distinguished by the final population.

External links