14-, 15-, and 16-bit still life syntheses

A week or so ago, a better recipe was found for the last still life on Mark Niemiec's list of expensive 14-bit syntheses. Now all 14-bit still lifes can be constructed with less than 14 gliders -- less than 1 glider per bit, as the old saying goes.

Catagolue results continue to be very useful in finding new recipes.

Code: Select all

#C 12-glider synthesis for the last 14-bit still life,
#C snake bridge snake / 12.105, which had previously cost at least
#C one glider per bit.
#C Goldtiger997, 6 October 2016, optimized by Mark Niemiec on 7 October.
x = 79, y = 71, rule = LifeHistory
7.A$.A6.A$2.A3.3A$3A2$16.A$14.A.A$15.2A6$36.A$34.A.A$35.2A8$30.3A$32.
A$31.A4$31.3A$33.A11.2D.D$32.A12.D.2D$43.2D$39.2D.D$39.D.2D6$52.A$51.
2A$20.2A5.3A21.A.A$21.2A6.A$20.A7.A22$3.3A$5.A70.2A$4.A4.2A65.A.A$10.
2A64.A$9.A!
#C [[ AUTOFIT AUTOSTART GPS 25 LOOP 150 ]]

UPDATE: The next challenge along these lines was to similarly reduce 15-bit still life costs to below 1 glider per bit. The process started later in the same forum thread, and was completed on November 19, 2016, with the following 14-glider synthesis:

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#C 14-glider synthesis for the last 15-bit still life
#C which had previously cost at least one glider per bit.
#C Extrementhusiast, 19 November 2016
x = 48, y = 38, rule = B3/S23
17bobo$17b2o$18bo$4bobo$5b2o$5bo$18bo$18bobo$18b2o2$obo$b2o39b2o$bo40b
o3b2o$20b3o21bo2bo$20bo22b2obo$21bo6bo16bo$8b2o18bobo14bobo$7bobo18b2o
16b2o$9bo2$5b2o$4bobo$6bo9b2o$10b2o3bobo$11b2o4bo$10bo4$8b3o$7bo2bo$
10bo$6bo3bo$10bo$7bobo$32b3o$32bo$33bo!
#C [[ AUTOFIT AUTOSTART GPS 25 LOOP 150 ]]

UPDATE 2: The next project involved a similar reduction for 16-bit still life recipes. The official project kickoff was on December 16, 2016, when 443 of the 3,286 16-bit still lifes had no synthesis in less than 16 gliders in Chris Cain's database. It concluded successfully on May 24, 2017.

UPDATE 3: As of 12 July 2019, every 15-bit still life has a recipe with at most 13 gliders. Other upper limits include a maximum of 12 gliders needed for 14-bit still lifes, and a maximum of only (N-4) gliders needed for 8-bit through 13-bit still lifes.