I have wanted for a while to use lacy tape and knit circles to make…well, actually I was stumped on application. When I described my swatch experiments on Twitter, Naomi Parkhurst dm-med a sketch of how I could make a crescent shawl with them, and I tucked that into my mental file of things I really wanted to figure out but thought might be hard.
In the mean time, my oldest son finished his college degree, and since he has studied a whole lot more mathematics than I have, I asked him what to investigate.
Apollonian Gaskets he said. Oh. Wow.
https://www.wikihow.com/Create-an-Apollonian-Gasket
https://www.americanscientist.org/article/a-tisket-a-tasket-an-apollonian-gasket
http://www.malinc.se/math/geometry/apolloniangasketen.php
https://mathworld.wolfram.com/ApollonianGasket.html
https://www.jasondavies.com/apollonian-gasket/
So, I need to figure out, what the size of the shawl should be, and can you take an Apollonian Gasket, spread it out and put lacy tape leading between the circles, or should the whole thing be held together with smaller and smaller circles? Will I finally be designing with color (one strand at a time of course, I’m that lazy) and will it sell?