Johanna Franklin

Associate Professor of Mathematics
Hofstra University
Hempstead, New York, USA

As a theoretical mathematician, I find it immensely satisfying to create tangible objects, both decorative and practical. Unfortunately, it is difficult to represent ideas from my research specialization, computability theory, or even mathematical logic more generally via textile arts. It is a particular joy to have found a way to represent a very abstract concept, a sequence of steps in a computation of a universal Turing machine, in a physical way by interpreting such a machine as a cellular automaton simulating it.

53 x 32 cm
fingering-weight wool yarn

This piece illustrates 186 iterations of two cellular automata (CAs). Each blue stitch represents a 1 and each gray stitch a 0, and the color of stitch n in a row is determined by the colors of stitches n-1, n, and n+1 in the row immediately above it. The blue-bordered side illustrates the Rule 110 CA, and the gray-bordered side illustrates Rule 193, its mirrored complement. Both are Turing complete.

We can see a stripe of dots and a stripe of larger triangles coming down from the top, their interaction in the middle, and then both stripes proceeding onwards in their original directions until the stripe of dots disappears into a corner at the bottom.

Many thanks to my colleague Eric Rowland for generating these iterations for me!