Morning thought

[magid]

I was working on yet another hyperbolic doodle (I've been playing with color more than form for these, just doubling each stitch as I go to make an item), and this morning on the T got to thinking about how the edge row always looks like so much of the brain coral I'm making. And I started thinking more about it, and realized that it is, in fact, the majority of the piece, if I've really been doubling the whole time. If the innermost starting circle is x stitches, then the second row is 2x stitches, the third row is 4x stitches, and so on. So the last row is 2ⁿx stitches, and all the rest of it is 2⁰x + 2¹x + 2²x + ... + 2^{n – 1}x stitches, which is always less than 2ⁿx. Which is to say, factoring out the base number of stitches x, _y=0&sum^y=n–1 2^y < 2ⁿ.

*checks to see what photos are already uploaded*

So in this photo,



since it's a 2 to 1 ratio, the outer row has more stitches than the rest of the piece together. Strangely, though, when I'm using a second color for the outer row, it feels like it goes much faster than this would imply.

Comments

Re: Cool!

[magid]

Thanks!

I have a bunch more photos of crocheted stuff that I've done in a gallery hosted on LJ (same username).