Partial Pile of Embedded Torus Links
Designer and Artist: sarah-marie belcastro
Material and Method: Knit wool yarn
Year of Creation: 2022
My research in topological graph theory has primarily concerned low-genus surfaces, and especially the torus. I have in the past knitted embeddings of graphs and knots on copies of the torus, and was inspired to make a rainbow of tori with a slightly shifted rainbow of embedded torus links. Every embedded torus link is straightforward to visualize as straight line segments on an arrowed rectangle, and appears as a sort of candy striping on a knitted torus. However, some links look more like vertical striping and some more like diagonal striping. I chose a sequence of torus links of semi-increasing complexity so that both the number of components and the style of appearance would vary over the sequence. Here are shown a completed (3,1) torus link together with knitted, but neither stuffed nor grafted, (0,2), (4,2), (3,3), and (6,2) links embedded on tori of increasing size. Link components differ in color from each other and have colors that reflect adjacent tori in the stack. Eventually these tori will all be stuffed, and will be accompanied by three additional tori so that the rainbow is complete. The biggest design challenge in creating this piece was choosing and sourcing harmonious colors of Dream in Color Classy, as several of these colorways have not been produced in many years.