This week’s Geek Craft is Hyperbolic Crochet. And here is a nice article on Hyperbolic Crochet (you only really need to worry about section 2 if you don’t care about the actual math).

Hyperbolic crochet, despite being useful for some pretty complex math, is rather easy to do. It requires only one kind of stitch, and is based on a simple concept. To make a hyperbolic plane you simply start with a small chain, say 6 stitches. You turn your work and then work across the row adding an extra stitch every N stitches. The smaller N is, the sharper the hyperbolic plane will curve and the more wavy the end result will be. Once you hit the end of the row, you turn over and continue back the other way, once again adding an extra stitch every N stitches. For aesthetic purposes N should be under 5 or so, as anything above 5 will grow too slowly and be very floppy.

For example, lets say you wanted to create a modestly floppy hyperbolic plane, so you pick N to be 4. You start with a chain of 6, turn your work and then single crochet into the first 3 loops. In the forth loop you put two single crochets (called an increase for those familiar with the terminology). Then you do one single crochet in each chain loop to the end of the row (2 Single Crochet). You turn the work over and do a single chain to bring yourself up to the next row (counts as 1 single crochet). Since you’re at 3 single crochet stitches (The two from the previous row, and the chain that counts as a single crochet), you skip the first loop on the next row (because of the chain) and do a two single crochet increase in the second loop. Again, the N value is maintained even as you move to the next row, so you’re adding an additional stitch every fourth stitch. You continue doing that until it’s as big as you want it to be, continually following the pattern of three single crochet then two single crochet in the same stitch.

Gradually, as you add row after row that are always slightly longer than the row before, the plane will bunch up and start to curve and get floppy. By the time you have a few dozen rows, the plane will be very annular (that is to say the plane curves and forms rings).

I personally utilized this technique when making the cactus flowers for my cactus project I crocheted earlier this year.

The flowers for this cactus were both produced using a variation of hyperbolic planes.

The Institute for Figuring also draws heavily upon hyperbolic planes for their Crochet Coral Reef program. If you’re interested in learning about crocheting coral reefs, there is a basic brochure on how to do it here. Otherwise the institute for figuring has a book for sale ($20) on crocheting coral and they run programs in various areas where you can attend small classes on coral crochet.

-Confusion is a state of mind, or is it?