Macbi wrote:In fact I already figured out a bit about the positioning of the cells and the rules.
If you want a 2-cell high-period oscillator the two cells have to be one cell apart orthogonally. Then you have to have B2i, S0, B2a, S1e. You can't have B0, B1c, B1e, B2c, B3i.
So to search for 2 cell oscillators you can set LLS up with two cells one cell apart in some size of bounding box and enforce the rules I mentioned.
Then all LLS is doing is searching through all remaining rules to find an oscillator of the given period.
This is pretty much the method (and rule restrictions I followed), although I also enforced D4+ symmetry and forgot about the -c option (instead I enforced the center cell on in relevant generations). There is however an alternate set of rule restrictions: here are a few high period oscillators without S0 and with B2c in their rule specification:
p30, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aci4aintw/S1e2ai4ei5y
obo!
p32, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aci4aintw/S1e2ai4ei5y
obo!
p34, 2 cells
Code: Select all
x = 3, y = 1, rule = B2-kn3e4t5iqy6i/S12i3eqy4cerw5iy6c7e8
obo!
p36, 2 cells
Code: Select all
x = 3, y = 1, rule = B2acei4cr5e7e/S1e2cik3enr4aet
obo!
p62, 2 cells
Code: Select all
x = 3, y = 1, rule = B2-ek3n4ctw/S12i3ace5i
obo!
Here are a few more reductions down to 2 cells for even periods:
p60, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aei3q4ceinr5j6ci7e/S01e2ek3-acnq4eiknqr5aeiy7e
obo!
p64, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aik3any4eikt5eiy6e8/S01e2-an3knry4-nqtw5iky7e
obo!
p66, 2 cells
Code: Select all
x = 3, y = 1, rule = B2ai3k4cinqty5ijy7e8/S01e2eik3jry4acint5cijny6ac7e
obo!
p68, 2 cells
Code: Select all
x = 3, y = 1, rule = B2ai3aen4ajnrt5eikny6ce7e8/S01e2ei3acery4aceirwy5ceky6c
obo!
Edit: (I couldn't resist)
p70, 2 cells
Code: Select all
x = 3, y = 1, rule = B2ain3acr4eijnwy5-jkny6-cn7e/S01e2-ai3-in4jknty5-qr6-in7e8
obo!
p72, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aei3cjqy4-aet5-q6ace7e8/S01e2ei3aijkr4ackw5acer6ack
obo!
p74, 2 cells
Code: Select all
x = 3, y = 1, rule = B2-ck3aeky4eir5jy8/S01e2eik3en4acnqt5ciny6cek7e
obo!
p76, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aei3enq4eijkq5ceny6ci7e/S01e2eik3cinr4enrt5-jkr6ei
obo!
p78, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aei3aenq4aiktw5ae6cei8/S01e2ein3-ain4aijkn5ry6ci
obo!
Most of those searches only took a few minutes. For some reason p80 is taking much longer.
[/edit]
Edit 2:
p80, 2 cells (30 mins in lls)
Code: Select all
x = 3, y = 1, rule = B2aei3acen4aciy5einy6i/S01e2in3aejy4acejn5ij6ac7e
obo!
p82, 2 cells (20 mins in lls)
Code: Select all
x = 3, y = 1, rule = B2aei3ekqry4jnr5cej6ci7e8/S01e2eik3ejnr4cirt5jy6ce7e8
obo!
If anyone is curious, this is the method I've been using to find these (example for p78, 2 minutes search time):
Code: Select all
$ python make_lls_grid.py -p 39 -m 90 -f 3 3 5 7 > osc.txt
$ python lls osc.txt -r pB2ai3-i45678/S012345678 --force_at_most 2 -s "D4+" -m -c 0 2 -c 0 6
[/edit]
Edit 3:
p84, 2 cells
Code: Select all
x = 3, y = 1, rule = B2ai3acejq4eky5eijy6ae7e8/S01e2cei3-ciny4-ejqrz5-cejr7e8
obo!
p86, 2 cells
Code: Select all
x = 3, y = 1, rule = B2aei3cekqy4-acrt5-aeij6-n7e8/S01e2ekn3einr4nqrtwy5-eqr6ack7e
obo!
[/edit]
Macbi wrote:77topaz wrote:I wonder, what is that maximum period? Is that even calculable with current technology?
More possible to answer would be "What's the minimum period not achievable?".
Even that might be problematic, because there's no easy way to define a limit on what the bounding box of the oscillator is or what its maximum population is. There's probably a way, but I can't see how you rule out an extremely high period oscillator which grows and grows and then suddenly collapses back down to 2 cells. I suspect though that any upper bound would be astronomically larger than the true value.