Further thoughts on the pretty picture. While I was stitching it, I was wondering if there were any other permutation matrices that would produce Fibonacci snowflakes. There are indeed — after I finished it, I turned it over and there was the order 3 snowflake in the centre. (The photo below is less clear than the front view because of the knots where I had to join thread, but hopefully it’s clear enough.) This corresponds to taking our original permutation matrix “backwards”, i.e. [17, 18, 20, 21, 14, 11, 24, 10, etc].
I like this because it’s a result that’s trivial to see once you’ve stitched it but is not at all obvious from any other way of rendering it (e.g. drawing it on paper or digitally).
