high density predecessors of the full board

[Timelord Missionary]

Here is an extensible line agar that, at its peak, has a density of 3/4, no matter what period it is:

Code: Select all

x = 3, y = 17, rule = B3/S23:T8,17
b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o!

Code: Select all

x = 16, y = 17, rule = B3/S23:T16,17
3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o
2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3o
b3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$3ob3o2b3ob3o$
3ob3o2b3ob3o!

Code: Select all

x = 3, y = 17, rule = B3/S23:T32,17
b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o$b2o!

It has a period (2^n)-2, for n>2.

[HartmutHolzwart]

While this is a very interesting patterns, it’s not p2. I changed direction and wanted to see what can actually be realized as density pairs.


Another one with density quotient 4/3

Code: Select all

#N 15x5_Skew3_Gen0_Final
x = 15, y = 5, rule = B3/S23:T15,5
o5b3o4b2o$b3o5b3o$4b3o5b3o$3o4b3o$3b3o4b3o!

Code: Select all

#N 20x5_ChickenWire_Gen0_Final
x = 20, y = 5, rule = B3/S23:T20,5
4o3b3o4b3o3b$o3b4o3b3o4b2o$2b3o3b4o3b3o2b$2o4b3o3b4o3bo$3b3o4b3o3b4o!