In my recent post all the structures that had an odd number of arms had no minibrot and the ones with an even number of arms did (except a spiral). I am not sure if that is a general conclusion for the whole Mandelbrot set of just the tiny area I looked at.
I have explored some more since the post and I found a few more interesting tidbits. When zooming in on one of the even armed structures I noticed that it caused a new feature to get inserted between some familiar structures that I had seen before. At the start of the zoom it caused the whole repeating feature set to get reset to the beginning. One result of the reset to the beginning was that I passed the original structure that I zoomed in on again. If you took the "detour" a second time it added a second feature exactly like the first right after the first. Seeing the pattern, I could add as many features of this type to the fractal as I wanted by taking the same detour over and over as I zoomed in. You can also pick to add one feature type then a different feature type by picking the detours as you zoom in. It seems possible to customize the fractal by adding the shapes you want after finding out what each kind of detour does.