Bobbin lace patterns look like they could be the output of some finite state automata:
[Obligatory disclaimer: I am not a lacemaker, but my very geeky SO is (and a knitter and weaver and so on and so forth) and often delivers discourses on the subject and several of my friends have been similarly inclined math geeks who knit & such.]
To a first approximation a lot of them are - simple geometric/topological rules applied in a loop, a small number of branches, occasionally recursion. There's a huge amount of technique and no small amount of technical knowledge in making them work with a relatively high friction material with variable tensile strength & stretch. Execution on this stuff often involves keeping more mental state than most of the programming I do so clearly it's not always as simple an automata as it might seem, but there's a kinship.
But knitting is not the only programming language for string-based objects. There’s weaving, crochet, lace, macramé, and more—ostensibly you could make all the same things with these techniques as you can with knitting, but you will go about many things differently, and different languages are suited to different kinds of problems.
But this shouldn’t be surprising: programming is a craft, and all crafts have parallels.