A universe of projections: may Plato be right?

A deterministic geometric procedure, yielding a multitude of interesting patterns as projections of simple multifractal measures supported by the graphs of fractal interpolating functions, is reviewed. It is shown, via a variety of examples, that such patterns encompass the intricate data sets gathered in a host of geophysical applications over one, two, and three dimensions, including both irregular and crystal-like sets. This suggests that a compact framework for complexity may one day be unraveled via these ideas and their extensions, in consonance with Plato’s notions in his famous allegory of the cave.