User blog comment:LittlePeng9/ITTM galore/@comment-5529393-20140318225602

For more low-hanging fruit:

0 _ _ r 0 0 1 _ r 0 0 2 _ r 0 1 _ 1 l 0 1 1 2 l 0 1 2 _ l 1 L _ _ r 1 L 1 _ r 1 L 2 _ r halt

The second cell flashes 1 each w steps, so starts at 1 and flashes to 2 each w^2 steps; the second cell starts at 2, and so the first cell flashes to 1 each w^3 steps; the first cell starts at 1 and flashes to 2 each w^4 steps; and at w^5 steps, it starts at 2 and halts.

Similarly, we can write a 2 state, n symbol program that halts in w^(2n-1) steps.