Upper limit for oscillator period with N cells in envelope box

[vilc]

Since you ask about 2xN ...
I did some exhaustive searches using EPE. Here are the results:
3x3
maximum : p72 (already known, but double-checked)

Code: Select all

x = 3, y = 3, rule = B2ei3er4aijkn5inq/S012ak3ajnr4i5ijn6ak
3o2$o!

2x4
maximum : p44 (already known, but double-checked)

Code: Select all

x = 4, y = 2, rule = B2ek3ejr4ai/S012ai3aeijr4a
bobo$o!

2x5
maximum : p64

Code: Select all

x = 5, y = 2, rule = B2ik3ar4ar/S012aci3ajn4ir5i
bo$o2b2o!

2x6
maximum : p134

Code: Select all

x = 6, y = 2, rule = B2ek3ajnr4i/S01e2ac3aijr4ir5i
o$bobobo!

2x7
maximum : p184

Code: Select all

x = 7, y = 2, rule = B2ek3aejn4ai/S01e2aik3aijnr4r5i
bo$obobobo!

The 3x4 search has been running for a couple of days, but I don't know if I can complete it.

Edit :
New record for 3x4 : p250 (previously p248)

Code: Select all

x = 4, y = 3, rule = B2ek3acjy4ainyz5ciknr6-an/S012ce3aeqr4airyz5-ckr6-ik7c
bobo2$o!

Found after nearly 200 billions EPE iterations on this 3-cell pattern.

Edit 2:
p252 in 3x4 bounding-box (same search, 382 billions of iterations done).

Code: Select all

x = 4, y = 3, rule = B2ek3acjk4-ejnqr5einr6-en/S012e3aeqr4-entwyz5-aey6ck
bobo2$o!

Edit 3:
Still better : a 3x4 p262.

Code: Select all

x = 4, y = 3, rule = B2ek3acjk4acikty5-knqy6-ai7c/S012ce3aer4acijkr5-ijy6aei7e
bobo2$o!

Edit 4: (11/05/25)
p268, search still running.

Code: Select all

x = 4, y = 3, rule = B2ek3acjk4-jrtw5cinry6ikn7/S012ce3aery4acqrwz5-air6cin7
bobo2$o!