That may be true but there were lifeforms with more fractal structures like the precambrian Charnia (https://en.wikipedia.org/wiki/Charnia ) and other Rangeomorphs ( https://en.wikipedia.org/wiki/Rangeomorph ).

The main difference the author is getting at (I suspect, I'm not a biologist) is that these earlier life forms display a multilevel fractal self-similarity within their fronds, basically fronds of fronds of fronds of fronds, instead of modern plants where the fronds have structural differences like leaves/buds that keep the pattern from replicating past a certain point.

The weird thing is that as far as body plans go, a fractal shape would maximize surface area while minimizing body volume which would seem advantageous for a filter feeding organism. It's not clear why such a simple design went extinct so quickly.