Stable patterns which are not glider-constructible

[400spartans]

Population 321 unsynthesizable p2 oscillator:

Code: Select all

x = 32, y = 27, rule = B3/S23
5b2o4b2o4b2o4b2o$4bo2bo2bo2bo2bo2bo2bo2bo$4b3o2bo2bo2bo2bo2bo2bo2b2o$
2b2o6b2o4b2o4b2o4bo$3bo2b2ob2ob2ob2ob2ob2ob2obo$3bobob2o4b2o4b2o4b2ob
3o$2b2obo2bo2bo2bo2bo2bo2bo2bobo2bo$5b2o2b4o2b4o2b4o5b2o$4b2o2bo2bo2bo
2bo2bo2bo2b2o$b2obo2b2o4b2o4b2o4b2obo$obobob2ob2ob2ob2ob2ob2ob2o2bo$bo
3bo4b2o4b2o4b2o3bo$7bo2bo2bo2bo2bo2bo2bo2b3o$6b4o2b4o2b4o2b4o3bo$7bo2b
o2bo2bo2bo2bo2bo2b3o$bo3bo4b2o4b2o4b2o3bo$obobob2ob2ob2ob2ob2ob2ob2o2b
o$b2obo2b2o4b2o4b2o4b2obo$4b2o2bo2bo2bo2bo2bo2bo2b2o$5b2o2b4o2b4o2b4o
5b2o$2b2obo2bo2bo2bo2bo2bo2bo2bobo2bo$3bobob2o4b2o4b2o4b2ob3o$3bo2b2ob
2ob2ob2ob2ob2ob2obo$2b2o6b2o4b2o4b2o4bo$4b3o2bo2bo2bo2bo2bo2bo2b2o$4bo
2bo2bo2bo2bo2bo2bo2bo$5b2o4b2o4b2o4b2o!

and a LifeHistory view of a 275-cell self-forcing patch for this oscillator (in phase-1):

Code: Select all

x = 32, y = 27, rule = LifeHistory
5.2A4.2A4.2A4.2A$4.A2.A2.A2.A2.A2.A2.A2.A$4.3A2.A2.A2.A2.A2.A2.A2.2A$
2.2A3.2A4.2A4.2A4.2A.A$3.A2.2A.2A.2A.2A.2A.2A.2A.A$3.A.A4.2A4.2A4.2A
4.3A$2.2A.A2.A2DC2DC2DC2DC2DCD.A.A2.A$3.A2.2A2C2D4C2D4C2DC2A3.2A$3.2A
.2DC2DC2DC2DC2DC2DCD.2A$.2A.A.4D2C4D2C4D2CD3.A$A.A.A.2CD2CD2CD2CD2CD
2CDCA2.A$.A3.AD2C4D2C4D2C4D3A$6.DC2DC2DC2DC2DC2DC2DA2.3A$6.C2D4C2D4C
2D4C2.A3.A$6.DC2DC2DC2DC2DC2DC2DA2.3A$.A3.AD2C4D2C4D2C4D3A$A.A.A.2CD
2CD2CD2CD2CD2CDCA2.A$.2A.A.4D2C4D2C4D2CD3.A$3.2A.2DC2DC2DC2DC2DC2DCD.
2A$3.A2.2A2C2D4C2D4C2DC2A3.2A$2.2A.A2.A2DC2DC2DC2DC2DCD.A.A2.A$3.A.A
4.2A4.2A4.2A4.3A$3.A2.2A.2A.2A.2A.2A.2A.2A.A$2.2A3.2A4.2A4.2A4.2A.A$
4.3A2.A2.A2.A2.A2.A2.A2.2A$4.A2.A2.A2.A2.A2.A2.A2.A$5.2A4.2A4.2A4.2A!

The patch forces a copy of itself two generations back.

[400spartans]

The following patch of a p2 agar forces a copy of itself 8 generations back, and a copy of itself 8 generations back and translated 6 cells to the left. It was found using a copy of gol-agars modified to let forced preimages grow beyond the bounds of the original pattern.

Code: Select all

x = 29, y = 17, rule = LifeHistory
8.2A2DAD2A2DAD2A2DAD2AD$4.3DADA3DADA3DADA3DADAD$.2ADA2D2ADA2D2ADA2D2A
DA2D2ADA$.A2D2ADA2D2ADA2D2ADA2D2ADA2DA$.3DADA3DADA3DADA3DADA3DA$.2DAD
2A2DAD2A2DAD2A2DAD2A2DAD$.2ADA2D2ADA2D2ADA2D2ADA2D2ADA$.ADA3DADA3DADA
3DADA3DADAD$2.2A2DAD2A2DAD2A2DAD2A2DAD2AD$2.2D2ADA2D2ADA2D2ADA2D2ADA
2DA$.3DADA3DADA3DADA3DADA3DA$2.2D2ADA2D2ADA2D2ADA2D2ADA2DA$2.2A2DAD2A
2DAD2A2DAD2A2DAD2AD$DADA3DADA3DADA3DADA3DADAD$2.ADA2D2ADA2D2ADA2D2ADA
2D2ADA$3.D2ADA2D2ADA2D2ADA2D2ADA2DA$7.3DADA3DADA3DADA3DA!

In some sense, this means the preimages of this pattern grow at a speed of 3c/4.

This is the first known pattern to force a copy of itself translated by a non-zero amount in a previous generation. While it cannot be stabilized into a self-forcing spaceship, it does suggest that self-forcing spaceships should be possible.

If this pattern (or a pattern containing this pattern) can be shown to not be an nth generation orphan (i.e. if there exists an infinite sequence of generations that evolve into the pattern), then this will also yield fixed-population solutions to the generalized grandfather problem (at least for n = 8a+b for some fixed b).