Holographic basis functions

What are holographic basis functions? we've seen holograms. They can be stored in crystals, and when you smash them into bits, the original hologram will be perfectly preserved in each crystal shard. Basis functions are less obvious. They are the elements of a configuration. For example, any waveform can be decomposed and perfectly described by a set of other waveforms, referred to as basis functions. Consider holographic basis functions. What could they possibly be, and why would anyone care. For one, you get holographic basis functions whenever a configuration can be perfectly described by smaller versions of itself. Holographic basis functions have a treelike structure. A tree, in some imperfect sense, is composed of smaller versions of itself. Hmmm, maybe trees are less holographic, and are perhaps more polygraphic, composed of idiosyncratic smaller trees that are not scaled downs replicas. It is interesting to wonder whether the thin veneer of reality is also composed of polygraphic basis functions, which could be thought of as selected parts of our experiences from the past; the polygraphic set of unique memories. How much of the past can we see when we stare into the present.