Fractal Torus, Fractal Flowers

 It's been awhile since I shared with you a fractal flower. I am always struck by the toroidal nature of these flowers when I see them on my dog walks. I snapped this picture on my iPhone; sorry about the poor resolution.

In the group of flowers above, you can see both toruses and fractals at various stages of manifestation. Let's look closer.

 

When the flower begins to emerge, it unfurls from a torus shape.

As the bud begins to open, you can see the torus walls and center. You can also see that its walls are composed of the fractals that will make up the bud cluster.

The more the bud opens, the less it looks like a torus as it begins to flatten out.

At last the torus is replaced by the fractal flowers. You can see that this one toroidal bud has produced a fractal pattern of smaller buds that look like the mother bud. And inside of those smaller buds are another iteration of the flower bud pattern. If we look even closer, we would discover that the smallest flower heads are themselves also made of smaller flower heads.

So what we have here, in this simple plant, is a fractal pattern of at least four iterations.  It reminds me of this fractal formula: