The built world offers all sorts of stark geometric compositions to explore. The natural world offers often softer organic compositions. Yin and yang, hard and soft, different photographic worlds, isn’t it?
Oh, hell, no. Nature can produce powerfully geometric structures. The built world can flow organically. Let’s see some of your photos that illustrate this. I’ll go first: Deadwood geometry dancing against the sky:
Especially on the microscopic scale there are plenty of examples. Lots of regular tesselations and geometric forms, fibonacci spirals and almost-fibonacci dpirals, and so forth.
But you’re not looking for strict periodic structures. So I offer hexagonal basaltic columns, such as Giant’s Causeway and a host of other, less well-known structures. They’re hexagonal, like a beehive, but nowhere near as regular. It finally occurred to me that these must be frozen Benard Cells made when the molten basalt was cooling. That explains the almost-regular shape.
This is not so strongly geometric as I’d like, but I just took it a couple of weeks ago and I like it.
Perhaps more familiar to Americans, or at least more local, is Devil’s Tower, WY.
For a different sort of geometry, how about romanesco?
Launaea arborescens, commonly known as Mol-albina or Wire Netting Bush is a plant that is common around the Mediterranean and is composed of a dense network of branched spines - the geometric nature is difficult to photograph - when seen IRL, it looks just like a hexagonal mesh.
Hard to believe this plant is closely related to lettuce!