David Hilbert

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David Hilbert
x = 33, y = 26, rule = B3/S23 7b2o15b2o$8bo15bo$6bo19bo$6b5o11b5o$10bo11bo$4b4o17b4o$4bo2bo17bo2bo$ 21bo$21bo$9bo4b2ob2o2bob2o$8b3o3b2obo6b2o$7bo2b2o6bo$7b3o12bo$22bobo$ 3b2o11b2o4bo2bo2b2o$3bo12b2o5b2o4bo$2obo12b2o11bob2o$ob2ob2o19b2ob2obo $5bo21bo$5bobo17bobo$6b2o17b2o$10bo11bo$6b5o11b5o$6bo19bo$8bo15bo$7b2o 15b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ GPS 11.5 THUMBSIZE 2 ZOOM 10 ]]
Pattern type Oscillator
Number of cells 122
Bounding box 33 × 26
Period 23 (mod: 23)
Heat 34.6
Volatility 0.71 | 0.71
Kinetic symmetry n
Discovered by Luka Okanishi
praosylen
Year of discovery 2019

David Hilbert[1][note 1] was the first period-23 oscillator to be discovered. It was found by Luka Okanishi on November 24, 2019[2] based on a partial result by praosylen.[1] It consists of two copies of an engine, itself consisting of a B-heptomino being hassled by two unusual catalysts and a block, supported by a known period-agnostic beehive shuttle mechanism (seen in, for example, an extension of the carnival shuttle). There are several isomers known (including trans- versions and different phase offsets), with the one pictured having minimum population and bounding box. A 101-glider synthesis for one of these variants was posted by Goldtiger997 on December 29.[3]

Other p23 oscillators can be constructed that combine and monomerise David Hilbert with the p23 honey farm hassler.[4]

David Hilbert was voted Pattern of the Year for 2019 on the ConwayLife.com forums.[5]

Gallery

x = 34, y = 26, rule = B3/S23 25b2o$25bo$27bo$23b5o$23bo$8b2o16b4o$2bob2obobo4bo11bo2bo$2b2obobo4b3o $6b2o3bo$11b2o5b2o4bo$2o16b2o3b3o$bo20b2o2bo$bobo20b3o$2b2o3bo2bo$9b2o 5b2o11b2o$16b2o12bo$8b2o6b2o12bob2o$2b2o4bo2bo15b2ob2obo$bobo24bo$bo24b obo$2o24b2o$6b2o15bo$7bo3b2o2b2o6b5o$4b3o4bobo2bo10bo$4bo4bobob2o10bo $9b2o14b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL HEIGHT 500 WIDTH 600 GPS 23 ZOOM 16 THEME Book STARTFROM 23 ]]
Monomerised David Hilbert with p23 honey farm hassler. Many other phase shifts also work.
(click above to open LifeViewer)
Catagoluehere
x = 191, y = 75, rule = B3/S23 16b2o30b2o30b2o30b2o30b2o30b2o$16bo31bo31bo31bo31bo31bo$17bo31bo31bo 31bo31bo31bo$14b4o28b4o28b4o28b4o28b4o28b4o$5b2o7bo22b2o7bo22b2o7bo22b 2o7bo22b2o7bo22b2o7bo$5bo11b3o17bobo9b3o17bo11b3o17bo11b3o17bo11b3o17b o11b3o$2b2obo11bo2bob2o10b2obo11bo2bob2o10b2obob2o8bo2bob2o10b2obo11bo 2bob2o10b2obo11bo2bob2o10b2obo11bo2bob2o$o2bob2o7bo2bob2obo2bo6bo2bobo 4bo4b2o2b2obo2bo6bo2bob6o8b2obo2bo6bo2bob5o9b2obo2bo6bo2bob2o2bo9b2obo 2bo6bo2bob2o2b2o8b2obo2bo$2obo5bobo2bo2bo4bob2o6b2obobo5bo2b3o5bob2o6b 2obobo2b3o3b3o5bob2o6b2obo6b2o2b2o6bob2o6b2obo3b2obo3b2o6bob2o6b2obo4b o5b2o6bob2o$3bo6bo2bo3bo4bo12bo5b2o2bo3bo4bo12bo7bobo2bo5bo12bo2bo8b2o 5bo12bo3b2ob2o3bo6bo12bo4bo2bobobo6bo$3b2o9b3o4b2o12b2o9b3o4b2o12b2o9b 3o4b2o12b2o2bo4bob2o5b2o12b2o2bo2b2o3bo5b2o12b2o3b3ob3o6b2o$14b3o30bo 57b2o29bobobobo25b2o3b2o3$9b2o30b2o30b2o30b2o30b2o30b2o$9b2o4bo25b2o4b o25b2o4bo25b2o4bo25b2o4bo25b2o4bo$14bobo29bobo29bobo29bobo29bobo29bobo $9b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob 2o$9b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b 2ob2o4$3b2o6b2o3bobo2b2o12b2o6b2o3bobo2b2o12b2o6b2o3bobo2b2o12b2o6b2o 3bobo2b2o12b2o6b2o3bobo2b2o12b2o6b2o3bobo2b2o$3bo6b2o5b2o3bo12bo6b2o5b 2o3bo12bo6b2o5b2o3bo12bo6b2o5b2o3bo12bo6b2o5b2o3bo12bo6b2o5b2o3bo$2obo 7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o6b2obo7b2o5b2o2b ob2o6b2obo7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o$o2bob2o5bo6b2obo2bo6bo2bo b2o5bo6b2obo2bo6bo2bob2o5bo6b2obo2bo6bo2bob2o5bo6b2obo2bo6bo2bob2o5bo 6b2obo2bo6bo2bob2o5bo6b2obo2bo$2b2obo11bo2bob2o10b2obo11bo2bob2o10b2ob o11bo2bob2o10b2obo11bo2bob2o10b2obo11bo2bob2o10b2obo11bo2bob2o$5bo11b 3o17bo11b3o17bo11b3o17bo11b3o17bo11b3o17bo11b3o$5b2o7bo22b2o7bo22b2o7b o22b2o7bo22b2o7bo22b2o7bo$14b4o28b4o28b4o28b4o28b4o28b4o$17bo31bo31bo 31bo31bo31bo$16bo31bo31bo31bo31bo31bo$16b2o30b2o30b2o30b2o30b2o30b2o 10$13b2o30b2o30b2o30b2o30b2o30b2o$14bo31bo31bo31bo31bo31bo$13bo31bo31b o31bo31bo31bo$13b4o28b4o28b4o28b4o28b4o28b4o$16bo7b2o22bo7b2o22bo7b2o 22bo7b2o22bo7b2o22bo7b2o$11b3o11bo17b3o9bobo17b3o11bo17b3o11bo17b3o11b o17b3o11bo$7b2obo2bo11bob2o10b2obo2bo11bob2o10b2obo2bo8b2obob2o10b2obo 2bo11bob2o10b2obo2bo11bob2o10b2obo2bo11bob2o$5bo2bob2obo2bo7b2obo2bo6b o2bob2o2b2o4bo4bobo2bo6bo2bob2o8b6obo2bo6bo2bob2o9b5obo2bo6bo2bob2o9bo 2b2obo2bo6bo2bob2o8b2o2b2obo2bo$5b2obo4bo2bo2bobo5bob2o6b2obo5b3o2bo5b obob2o6b2obo5b3o3b3o2bobob2o6b2obo6b2o2b2o6bob2o6b2obo6b2o3bob2o3bob2o 6b2obo6b2o5bo4bob2o$8bo4bo3bo2bo6bo12bo4bo3bo2b2o5bo12bo5bo2bobo7bo12b o5b2o8bo2bo12bo6bo3b2ob2o3bo12bo6bobobo2bo4bo$8b2o4b3o9b2o12b2o4b3o9b 2o12b2o4b3o9b2o12b2o5b2obo4bo2b2o12b2o5bo3b2o2bo2b2o12b2o6b3ob3o3b2o$ 14b3o30bo68b2o26bobobobo25b2o3b2o3$20b2o30b2o30b2o30b2o30b2o30b2o$15bo 4b2o25bo4b2o25bo4b2o25bo4b2o25bo4b2o25bo4b2o$14bobo29bobo29bobo29bobo 29bobo29bobo$9b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob 2o23b2o2b2ob2o$9b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b2ob2o23b2o2b 2ob2o23b2o2b2ob2o4$3b2o6b2o3bobo2b2o12b2o6b2o3bobo2b2o12b2o6b2o3bobo2b 2o12b2o6b2o3bobo2b2o12b2o6b2o3bobo2b2o12b2o6b2o3bobo2b2o$3bo6b2o5b2o3b o12bo6b2o5b2o3bo12bo6b2o5b2o3bo12bo6b2o5b2o3bo12bo6b2o5b2o3bo12bo6b2o 5b2o3bo$2obo7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o6b2o bo7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o6b2obo7b2o5b2o2bob2o$o2bob2o5bo6b 2obo2bo6bo2bob2o5bo6b2obo2bo6bo2bob2o5bo6b2obo2bo6bo2bob2o5bo6b2obo2bo 6bo2bob2o5bo6b2obo2bo6bo2bob2o5bo6b2obo2bo$2b2obo11bo2bob2o10b2obo11bo 2bob2o10b2obo11bo2bob2o10b2obo11bo2bob2o10b2obo11bo2bob2o10b2obo11bo2b ob2o$5bo11b3o17bo11b3o17bo11b3o17bo11b3o17bo11b3o17bo11b3o$5b2o7bo22b 2o7bo22b2o7bo22b2o7bo22b2o7bo22b2o7bo$14b4o28b4o28b4o28b4o28b4o28b4o$ 17bo31bo31bo31bo31bo31bo$16bo31bo31bo31bo31bo31bo$16b2o30b2o30b2o30b2o 30b2o30b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 HEIGHT 640 WIDTH 1200 ZOOM 6 GPS 23 ]]
Twelve variants of David Hilbert. The variants on the top are cis-isomers, while the bottom variants are trans-isomers.
From left to right, each one has a different phase shift. From left to right: 6 to 11 ticks phase difference.
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See also

Notes

  1. Named after German mathematician David Hilbert in reference to his 23 problems.

References

  1. 1.0 1.1 Luka Okanishi (November 25, 2019). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  2. Luka Okanishi (November 24, 2019). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. Goldtiger997 (December 29, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  4. James Pascua (February 16, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  5. Dave Greene (March 16, 2020). Re: POTY 2019 Voting (discussion thread) at the ConwayLife.com forums

External links