A Surprising Similarity Between Stars and Atoms

     The Space Telescope Science Institute recently released beautiful and enigmatic images of stars called Planetary Nebulae, which are ejecting their outer envelopes (N.Y. Times, 23 Dec 97, p. C1). The images show that the stellar shells can have an interesting variety of shapes and symmetries, which remain largely unexplained.

     In 1989 a fractal cosmological model predicated that Planetary Nebulae shapes would bear a strong resemblance to visual representations of electron probability densities in the atom. The latter refer to the probabilities for finding the electron at a given location with respect to the nucleus of the atom.

     Before discussing the reasons for expecting similarities between what would appear to be two radically different types of systems on vastly different scales, let's look at several comparisons.