The internet contains all sorts of things you never would have thought there was a need for (and a few that make you wonder how much spare time people have on their hands...) One thing I stumbled upon a few days ago is the inspiration for this post. A few crafty crochet-ers decided to create (and I am not making this up -- REALLY) a reef....as in the coral variety. It is totally made out of yarn and the shapes are pretty close to some growing out in the Caribbean right now. Turns out, this was also a mathmatical experiment of sorts. The wavy, fluted edges of the corals were mimicked in crochet by strategic increases in stitches. Really cool!
Also, there are a number of patterns based on the Fibonacci sequence (0,1,1,2,3,5,8,13,etc...). I found a scarf pattern that was pretty interesting. You pick a variety of colors for your scarf and then begin knitting. As long as the number of rows per color equals a number in the Fibonacci sequence, the overall color combination is pleasing and balanced. Very interesting, as this allows the artist to create several different looks from the same group of colors. It is also a great stash reducer -- very important as you can only hide so much yarn under the bed after your husband begins to notice the random skeins running about the place...but I digress....
Another nifty numerical pattern was featured on knitty.com a few issues ago. (Go visit them here!) "Numbers" is a bag that can be knitted in whatever gauge you feel like and felted (or not). It incorporates a given number (that you choose) as a multiple that you use to increase and decrease the shape of the bag. The size of the needles, the number you choose and the number of rows you choose to knit all affect the end result. As you can see from the pictures, you can get some really interesting accessories! The neatest thing about this is that the designer made a conscious decision to play with the pattern's math with stylish results.
It gives you a lot to think about. For me, these are the first patterns in the "pending project" basket that use this concept. I look forward to trying them, if for no other reason than to see what comes out.