Due to popular demand (well one person suggested it), I decided to revisit the improvised hat and see if I could write directions for what I did. As I didn't take notes the first time around, I decided to re-knit it while the memory is still somewhat fresh.
As I mentioned before, I worked from the top down, which meant using a center start. There are more sophisticated ways of doing this than what I chose (Emily Ocker's Cast On), Judy's Magic Cast On); but this is what I did.
I used worsted weight yarn and a size needle that generally gives me 5 sts per inch in stockinette. I used bits of several colors which I will call W (white), B (brown), R (red) and O (orange). The white isn't exactly white in either hat, and in the first version the red is more of a deep rust, but these names will do.
Using the plain old long tail method, I cast on four stitches on one needle. Then I turned the work (as if I were working in rows). With one dpn I knit into the front and the back of the first stitch; with a second dpn I knit into the front and the back of the second stitch; with a third dpn I knit into the front and the back of the third stitch; with a fourth needle knit front and back of fourth st. Then I arranged the needles in a square so that I could proceed in rounds from there.
The last stitch is hiding under the needle on the left. I really have a total of eight stitches.
From here, I worked in rounds. The very first round I knit into the front and back of every stitch for a total of 16.
Then I started alternating 1 round even in knit with one increase round. The increase rounds went like this:
*k2, M1*; rep from *
*k3, M1*; rep from *
*k4, M1*; rep from*
and so on.
After a few rounds I hung a safety pin on the first stitch to mark the beginning. When I had enough stitches to fit, I changed to a 16" circular needle.
I kept going until I had 16 stitches less than my desired final number. Then I worked an increase round followed by two plain rounds, two times.
With that, the crown of the hat was done. This post is more than long enough. I'll continue it later.