Uniform Syncopation

Daina Taimina's pattern for hyperbolic crochet or knitting seems deceptively regular: for a chosen counting number n, make an increase every nth stitch. In other words, in every nth stitch on the current row, you form two stitches, transforming each n-stitch block into an (n+1)-stitch block in the following row. While the resulting fabric approximates a surface of uniform curvature, this n to n+1 shift makes the distribution of increases highly irregular. Each surface in Uniform Syncopation was knitted by hand in two-color brioche stitch on 1.5 mm needles and mounted on copper wire. In two-color brioche, each increase forms a branching of the main color (red on some surfaces, yellow on the others), making the configuration of increases visible. The lower hanging surfaces show the first five possible n values, with n = 1 for the smallest and n = 5 for the largest. In the top surface, n = 6. The only surface in which the resulting main-color tree is geometrically regular is the smallest, on which the yellow stitch lines fork at every possible branching point.

The prior artwork Hyperbolic Constellation used bead crochet in the round to explore similar themes.