Crochet Wibble Science!
Since I've started crocheting some flatworms lately, humble creatures made of delightfully wibbly hyperbolic surfaces, I figured it might be worth doing some Science(TM) to better get a sense of exactly which approaches get which levels of wibbliness in the resulting piece. Join me for my adventures in Wibble Science!
So, for each of these experiments, I started with two straight rows of single crochet, to give a straight base before introducing any increases that would thus turn into hyperbolic wibbles.
Test 1: The Linear Wibble
The way to do this is simple. Choose a number of increases for the first row, space them out evenly, and then do the same number of increases in subsequent rows - which means adding one more single crochet in between the increases than you did for the previous row. So, choosing to start off with an increase every other stitch, it goes like this:
repeat (sc, inc) repeat (2sc, inc) repeat (3sc, inc) repeat (4sc, inc)
Thus, the row expands in such a way as to introduce wibble, but the wibble is linear, expanding by the same amount each row. Adding more rows like this makes the wibble bigger, but not more wibbly. For example, here's my test piece I made, starting with rows of 12sc and then following the above pattern, thus giving it 6 increases per row:
A satisfying, polite level of wibble! This was the wibble I instinctively went for on my first wibbly flatworm, and I think it was a good pick. Nicely wibbly, but it doesn't get too overwhelming.
But what if you started with more wibble? What if you went with an increase every stitch from the beginning, and then went out linearly from there?
repeat (inc) every stitch repeat (sc, inc) repeat (2sc, inc) repeat (3sc, inc)
Well, that's a lot more chaotic! It's difficult for the wibbles to even fit in the space given to them by the base row. But even then, the wibble is still linear, not expanding beyond itself. You might see what I mean better once we see what an exponential wibble looks like.
One more for the linear wibbles - how about a lesser wibble, starting with one increase every three stitches?
repeat (2sc, inc) repeat (3sc, inc) repeat (4sc, inc) repeat (5sc, inc)
Yep, it's gentler than the first one, not going up and down quite as much!
So, to sum up linear wibbles: they will stay the same amount of wibble all along, and the amount of wibble you get depends entirely on how densely you decide to pack increases into the first row you start increasing in.
Test 2: The Exponential Wibble
But what if linear wibbles aren't enough? What if you want a wibble that gets more wibbly the bigger it gets? Good news: exponential wibbles are even easier to work out a pattern for than linear ones. Pick a density of increases for your first row (let's say, one increase every two stitches again), and then… do that every row.
repeat (sc, inc) repeat the above for every row
That's all there is to it! This will increase your stitch count exponentially - with this example, the first row multiplies the stitch count by 1.5, then the next row will multiply that count by 1.5, and so on, and so on. You will be drowning in stitches very quickly! Here's the example piece I made, which started with a base of 12sc again, but ballooned to 90 stitches in only five rows!
Look at those wibbles! They're at least as chaotic as the linear wibble made starting with twice as frequent increases, if not more so. Here it looks rather messy, but…
…if you settle it just right, it can look quite pretty! See how it increases not just in size but in amount of wibble, curving back on itself in a way the wibbliest linear wibble did not?
So, the exponential wibble: even wibblier, even prettier, but with a downside of ballooning your stitch count to a ridiculous degree very quickly. No I did not want to make another example piece showing an exponential wibble made with increases in every stitch, I value my sanity.
Test 3: The Double Linear Wibble
But here's another thing I wanted to test: what if you make a linear wibble, but then after a few rows, you shift it to a wibblier, but still linear, wibble? Like so:
repeat (sc, inc) repeat (2sc, inc) repeat (3sc, inc) repeat (4sc, inc) repeat (sc, inc) repeat (2sc, inc) repeat (3sc, inc)
This might seem at first like we aren't increasing the wibble any more when we make the shift - after all, we started off with an (sc, inc) wibble, and then we're shifting to… another (sc, inc) wibble? But that second wibble is wibblier because we already got so far expanding the first wibble. Let's say we have a base row of 12sc again; the first wibble has 6 increases per row, up to 36 stitches by the time we reach (4sc, inc). Doing (sc, inc) on that 36-stitch row now gives us… 18 increases per row! The second wibble has in fact increased in wibbliness by a factor of 3!
Aaand it looks… like this. Somewhat underwhelming compared to what I'd hoped for. It's somewhat more chaotic than the wibbliest linear wibble we made (but is that just because it's got so many more rows?). And you can kind of see where the shift to the second wibblier wibble happened - around where the red is in this variegated yarn. But it's not as elegant and pretty as the straight-up exponential wibble we made before.
Confession time: I tested this method of wibble because I was attempting to emulate a delightful kind of wibble I'd seen in a species of flatworm called the Orsak Flatworm.
(image source: https://www.inaturalist.org/observations/254485786)
Look at this glorious, ridiculous creature. Its wibbles have wibbles. I love it.
So my thinking was that the first stage of linear wibble here would give the base wibble, and then having a second stage of denser linear wibble would give it those extra wibbles on top of the first wibble. You can kind of see that beginning to happen in my test piece… but the thickness of the crocheted "fabric" just doesn't allow it to wibble that tightly.
Maybe this could be gotten to work, if I were willing to crochet at a bigger scale. Still use the same weight of yarn, but make my rows much longer (and the increases further apart to match that), so that the crocheted "fabric" becomes comparatively thinner compared to the shaping. Maybe that would wibble enough. Buuuuut I like to work in a smallish scale, so I wouldn't really want to make a flatworm that has quite that amount of ever-increasing stitches.
Given that, I was willing to throw up my hook and accept that wibbles within wibbles were probably beyond what I was able to do, at least at the scale I like to work at. But then…!
Attempting Wibbles Within Wibbles, Take 2
I got hit with an idea - a way I could try and force those tinier wibbles to still take shape as wibbles even with the thickness of my crochet piece. I just had to make the stitches exaggerate the wibbliness more.
The base wibble starts off the same:
repeat (sc, inc) repeat (2sc, inc) repeat (3sc, inc) repeat (4sc, inc)
but then…
repeat (sc, inc3)
(That's not three increases, that's an increase3, aka my preferred name for what's usually called "3sc in 1", because it's the same dang thing as an increase, just for three stitches instead of two, it should have a variant on the same name. (Usually the 3 is in subscript, but tumblr doesn't do that.) I'll grumble and use the less elegant but "Proper" Notation in actual published patterns, but for my ramblings here, you get the more sensible terms, sue me.)
Shoving that extra big increase in helps give the crochet a bit more of a distinct pointy shape. And, I discovered a way to work the inc3s which delightfully helped even more at giving it that zigzagginess:
Work the first stitch of the increase into the front loop only. Work the second stitch of the increase into the back loop only of the same stitch. Then work the third and final stitch of the increase through both loops. This shifts the stitches you work just slightly so that one wants to be more at the front, and its neighbour wants to be more at the back, thus making it more zigzaggy. Look!
This is the example piece I crocheted like this. It has the mini zigzags! It's only a start, but what a good base for wibble within wibble!
So, using this as a base, let's add one more row to really lock in that second-level wibble:
repeat (sc, inc) repeat (2sc, inc) repeat (3sc, inc) repeat (4sc, inc) repeat (sc, inc3) repeat (sc, inc)
(This is, in fact, still increasing linearly. (sc, inc3) works out to an increase of two stitches per… two stitches, equivalent to one regular increase every stitch. Then for the next row, as one does for a linear wibble, we're adding one more single crochet between each of those increases!)
Note that here, you want to make sure your increases land in the middle stitch of last row's inc3s, and the stitches that were a plain sc last row. Those were the stitches that were already starting to form the "points" of the mini zigzag, so we want to accentuate that more here.
I also did a little thing where, for increasing into the stitches on the previous row that were pointing towards me, I worked my increase in the front loop only for the first stitch (then through both loops for the second) - whereas for increasing into the stitches on the previous row that were pointing away from me, I worked the first stitch of the increase in the back loop only. Again, trying to coax the stitches to lie in the direction I wanted them to.
And the result?
Look at that! It worked! It's still a bit constrained by the thickness of the crochet, but you can see the little wibbles! The wibbles do indeed have wibbles! WIBBLES ACHIEVED.
