Can anything in nature be more geometric than ferns?
At this time of year the spores are mature and the sporangia, or spore-bearing structures, are beginning to rupture and discharge their contents to start the life cycle one more time.
Each species of fern has its own way of maximising the space available for spore production. This is Lady Fern - Athyrium filix-femina - which has very delicate fronds with curved sporangia:
Scaly Male Fern - Dryopteris affinis - on the other hand, has very round sporangia in much straighter rows.