Hyperbolic Knitting (Fuzzy Math)

Inspired by the forms of the crochet coral reef but prefer sticks to hooks? Here are 2 experiments in hyperbolic knitting.

Both of these shapes are made using the same basic pattern. If you can knit in the round and work an increase, you can do this, too. Here's how to play along:

Pick a number of stitches to cast on.
Pick another number, which we'll call (X).

Using double-pointed needles, cast on to work in the round (start out as for i-cord and add more needles as you need them)

k(X), increase 1, k(X), increase 1 , k(X), increase 1...

That's it! Bind off when you feel like stopping or you run low on yarn or needle-space. Since this is an exponential form, each round will ruffle more than the last and use more and more yarn.

The smaller the number you choose for (X), the sooner and sharper your form will ruffle. The bigger (X) is, the skinnier your form will be.

In each of these models, I cast on 4 stitches. For the tall skinny one, (X) is 15. For the fat one, it's 5.

I used yarn-overs for the increases because I wanted the random-ish pattern that the increases make to be visible. Using kfb or a lifted increase will be less visible and will make the ruffling more pronounced.

Have fun with it!