@janellecshane I was going through your #Skyknit pattern collection and I realized that ditherbing makes a shape with hyperbolic #geometry
like potato chips, or like this http://crochetcoralreef.org/ (though these are #crochet and not #knitting because it's easier to deal with that many stitches in crochet)
this is a mathematical shape that was thought to be impossible to represent irl at arbitrarily large sizes before somebody crocheted it
#fiberarts
@janellecshane here's what ditherbing looks like after 14 rows. I'll do it again later with a needle size that doesn't hurt my hands, but the knots look better than I expected, and in the side view you can already see the crinkling that comes with being a hyperbolic surface. #knitting #skyknit #geometry
@janellecshane that's exactly what I expect, though you have to make it pretty big to really start to see it crinkle. I'll try it again this week with yarn and needles that don't set off my arthritis as much. Maybe I'll end up with a useful dish scrubby.
@DialMforMara With apparently a different gauge, it turns out BarbS0201 on Ravelry saw crinkles after 12 rows.
https://www.ravelry.com/discuss/lazy-stupid-and-godless/3718985/801-825#815
@janellecshane awesome. That's a hyperbolic surface, all right.
@janellecshane The difference is probably that Barb cast on more stitches to start, so there were more places to curve. I tried to start from the smallest/flattest point (my choice of words is not at all mathematically rigorous), so I'm seeing less curve early on.
@DialMforMara Someone noticed "fishcock" starting to curve as well, and is wondering if it is also hyperbolic.
https://www.ravelry.com/discuss/lazy-stupid-and-godless/3718985/501-525#521
@janellecshane Hmm, it might be. The tipoff is that each section increases the number of stitches by the same ratio. For example, in ditherbing, every fourth row the stitch count is multiplied by roughly 4/3 (the *k2 kfb* row turns every 3 stitches into 4).
@janellecshane In contrast, spherical geometry increases or decreases the stitch count by the same *number*, not the same ratio. It's common to knit a circle by adding eight stitches every other row, or a sphere by adding 6 every other row.
I think that's generalizable? Maybe adding too many stitches in a spherical pattern makes a hyperbolic pattern? I need to do more swatching.
@DialMforMara That makes sense! Sort of like a geometric vs arithmetic series. The hyperbolic patterns would have some kind of recursion that keeps ballooning the shape. I can't read knitspeak well enough to tell if any particular pattern does this, but at least now I know what that property is.
@DialMforMara Wait I just read that again and WHAT!? One of SkyKnit's patterns is a hyperbolic surface? This is beyond cool. Reading up on hyperbolic surfaces now... you expect the shape to balloon out in magnificent crinkles?