Unsynthesizable oscillator 1

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Unsynthesizable oscillator 1
x = 60, y = 53, rule = B3/S23 27b2ob2o$27bo3bo$28b3o$16bobo5b2o7b2o5bobo$14bo3bobo3b2o7b2o3bobo3bo$ 12bo2bo4bobo2bo2b3o2bo2bobo4bo2bo$10bo2bobo4bo2b3obobobob3o2bo4bobo2bo $11bob2o4b2obobo3bobo3bobob2o4b2obo$8bob2o10bo5b3o5bo10b2obo$7bob2o6b 5ob5o3b5ob5o6b2obo$8b2obob2obobo3bo2bobo3bobo2bo3bobob2obob2o$11b3o3bo b2obo2b3o3b3o2bob2obo3b3o$6b3o5bo2b3o2b3o3b3o3b3o2b3o2bo5b3o$6bo2bo3bo b2o5bobo3bobo3bobo5b2obo3bo3bo$8b2o3b2obo2bo2b3o2bobobo2b3o2bo2bob2o4b 2obo$10b2obob2obob2o3b2obobob2o3b2obob2obobo4bo$10bo2bobo3bobo3bobo3bo bo3bobo3bobob5o$8b2o2b2o5b2obobob2o3b2obobob2o5bo6b3o$7bo6b5o2bobobo2b 3o2bobobo2b5ob5o4bo$4b2o2b3ob2o2bobo3bobo3bobo3bobo3bobo2bo3bo3bobo$3b o2b2o2b2obo2b3o3b2obo2b3o3b2obo2b3o2bob2ob2obob2o$3b3o2b4o2b2o3b3o2bob 2o3b3o2bob2o3b3o2b4obo$6bobo4bobo3bobo3bobo3bobo3bobo3bobo7bo$5b2obo3b 4o3b3o2bobobo2b3o2bobobo2b3o2bo4bob2o$6b2o2b2o4b3o3b2obobob2o3b2obobob 2o3b2obo2b2ob2o$7bo3b2o3bobo3bobo3bobo3bobo3bobo3bob2o2bo$5bobob2ob2ob obobobobobobobobobobobobobobobobobob2o$4bob2obo4bobobobobobobobobobobo bobobobobobobo2bob2o$4bo5bob2obo3bobo3bobo3bobo3bobo3bobo7bobo$2b2ob3o b2o2b3o3b2obobob2o3b2obobob2o3b2obob4o4bo$3bobo2bobo5b3o2bobobo2b3o2bo bobo2b3o2bobo4b5o2bo$2bo2b2ob3o2bo2bobo3bobo3bobo3bobo3bobo3bob2obo5b 3o$2b2obobo3b2obob3o3b2obo2b3o3b2obo2b3o3b3o2b2ob3o$2o5bo3bobo5b3o2bob 2o3b3o2bob2o3b3o5bobo2bob2o$o2b3obo2bobobobo2bobo3bobo3bobo3bobo3bobo 2bo2b3ob2o2bo$b2o2b2ob2obobobobob3o2bobobo2b3o2bob2o3b3obob2o3bobo$3bo bo2bobo3bobo5b2obobob2o3b2obo2b3o5bobo3bo3bo$3bobo2b2obobobobobo2bobo 3bobo3bobo3bobo2bobobobo2bobo$2b2o2bo2bobo2bobobobob2obobobobobobobo2b 3obobobobob2ob2o2bo$4b2o5bo5bobo3bobo2bobobobobob2o5bobo3bobo2bob2o$4b ob4ob4obob2o5bo5bobo3bobo2bobobobobob2ob3o$5b2o3bo4bobo2b4ob4obobobobo b2obobobobo2bobo5b2o$8bo2bob2obo3bobo4bobob3o2bobo3bobo5bo5bobo$5b2ob 2obo2b3o3b2o2b2o2b2o6bo5b2obob4obob3o2bo$6bo4bo5b3o2bobo3b2o2b3obob4o 2bobo5b2o3b2o$6bob3o3bobo2bo2bobo6bobo3bobobo3bob2ob2o3b2o$7bo3b2ob4ob 3obo3bobob2ob2obo2b2o3b3o3bo4bo$8b2o3bo5bob2o3bob2o2bob2obobo2b3o5bo4b o$10b3ob3o9bo3b2o5bobobo3bobo2bobobo$10bo2bobo2bo2b2o4b3o7bob4ob4ob2ob 2o$13bo3b2obo2bo5bo5b2obo8bo3bo$14b3o3bobo12bo2bobo2bo2bob2obo$16bo3b 2o15b2ob2o3b2obobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 GPS 2 ZOOM 8 ]]
Pattern type Oscillator
Number of cells 1077
Bounding box 60 × 53
Period 2 (mod: 2)
Heat 717
Volatility 0.50 | 0.50
Kinetic symmetry n
Discovered by Oscar Cunningham
Ilkka Törmä
Ville Salo
Year of discovery 2022

Unsynthesizable oscillator 1 is an oscillator that is provably impossible to synthesize. It is the first such oscillator where the proof of impossibility does not involve the still life patch in the solution for unique father problem.

The first example was constructed on April 27, 2022 by Oscar Cunningham based on a "self-forcing" finite patch of period-2 agar found by Ilkka Törmä and Ville Salo.[1] A reduced form by wwei23 is shown in the infobox.[2]

References

  1. Oscar Cunningham (April 27, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  2. Dave Greene (May 2, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums

External links