> It's not obvious to me that fern branches are 'anatomically variable and non-iterating bifurcations', rather than a recursive process that bottoms out at a size boundary.

But hardly any (no?) real-life phenomena are the latter! As a mathematician, I'm as bothered by imprecise use of mathematical terminology as anyone, but, if we're going to call anything in real life a fractal, then it surely means something more like "appears to contain structure at multiple scales" than "the same structure at all scales". As @throwbadubadu points out (https://news.ycombinator.com/item?id=35903049), the classical example of a coast-line will also have different structure at small scales and at large ones, so either we throw out calling that a fractal (OK with me!), or we accept that we're using precise language imprecisely.