Consider a life pattern that consists of the cell (0,1), plus the straight
n-omino (0..n-1,0). This is an L-shaped pattern with one arm of length 2
and the other of length n (counting the corner as belonging to both arms).
What is its settle-time as a function of n? Of course, defining the settle
time rigorously is philosophically fraught, but all the cases I have looked
at resolve eventually, into a simple structure of oscillators and
spaceships, so the difficult questions haven't arisen yet.
The nth L in this family has n+1 cells. Starting from n = 0, I get the
following settle times:
1, 1, 1, 3, 9, 40, 13,122, 30, 786, 342, 186, 2062, 268, 89, 1180, 307,
3526, 49, 79, 875
The last number is the settle time for the case n=20.
This sequence is very reminiscent of A152389, which gives the settle time
for simple straight n-ominoes.
Can anyone confirm the values I've given here, and provide a few more? I'd
like to submit the sequence to OEIS.
