Really cool and in-depth, thank you!

I believe that there is a typo in the pattern formula (right after "Looking closely you might pick up on the pattern"): it should read

  5**(n/2) instead of 5**n
  5**((n-1)/2) instead of 5**(n-1)

Also, regarding Knuth's mistake: Youtube comments point out that his fractal is in fact correct; he just mistook the beginning point with the end point. Loosely speaking, the fractal is symmetrical about its middle turn, which is precisely the one Knuth believed to be incorrect. All in all, he still made a fractal-related mistake, so the conclusion holds.

Good catch, corrected the formula!