As humans, our brains are wired to look for patterns. We see recognizable shapes in clouds, we marvel at all kinds of "coincidences," and we generally try to make sense of the sometimes chaotic world around us. And because we're so hard-wired for patternicity, it's actually hard to try to be completely random. If you try, for example, to come up with a random set of numbers, you might find yourself starting out fine with "3,1,2,2,1" but then maybe your brain kicks in and thinks that looks too much like a pattern, so then it comes up with "9"--not because it's truly random but specifically because it's different. That's the type of thing that made people think that iPod's "shuffle" feature was not really random when it first came out. They'd have a huge library of songs, and they'd think something was up because 3 out of the last 5 songs were all from the same album. It's said that iPods had to be reprogrammed to avoid clustering and repeating. This made them less mathematically random in order to seem more random to listeners.
I wanted to make a spring dress for my daughter and was inspired by cherry blossoms because that's one of my favorite trees. I love how the cherry blossoms gradually get darker and then rain down when it's time for the leaves to come in. I had admired Twinkle's Incredible Skirt and wanted to do that sort of color transition to simulate the white blossoms transitioning into pink and falling down. When I got to the colorwork, though, I found it hard to be random about which stitches were white and which were pink. I just couldn't make it look right. My wonderful (and nerdy) husband offered to do a quick Mathematica program to generate some random numbers for me. This was sweet, but besides the fact that it was hard to read (I'd have to keep track of my stitch count so that I'd know to make stitch #156 and #212 pink), I ran into the same kind of clustering problem that iPod users encountered. On some rows, it just so happened that there would be lots of one color all in a pile, making it look less random.
So what I decided to do was to make it pseudo-random. I decided, for example, that I wanted 1 stitch in the next 12 to be pink and the rest white. So I used the random number generator to pick a number from 1 to 12 for me. Whichever number came up would be the stitch that I'd make pink. Then I'd have the generator pick a new number for me and make that stitch the pink one in the next cluster of 12. The next row would have a pink stitch in each cluster of 11, then 10, etc. After a couple of rows of having an even number of white and pink stitches, the process was reversed.
If you've stuck it out this far in the post, then I really should show you some pics :-)
More pics and details on the rest of the construction are on Ravelry and in the gallery.