Yeah it's sort of overkill for the sundial, and doesn't necessarily explain how you construct such a fractal, only that it exists (although the proof may be constructive, but it isn't given).

I appreciated the math, as someone with measure theory and analysis experience, and the result is very cool, but it's a bit funny how it's just thrown in there.

That said, assuming the reader knows the requisite math it's a very concise explanation of the necessary theory. I tried to explain the math somewhere else in the comments but I'm afraid I didn't do a great job.