On Sinkholes and Galaxies: An Example of Fractal Universality

The universality of fractals implies that very different physical processes can give rise to similar complex spatial patterns. Sinkholes (dolines) and galaxies provide a striking example of this universality. If each sinkhole in a karst massif is represented by a point, and each galaxy in a given zone of the sky is represented by a point, and these point sets are projected onto planes, the resulting two-dimensional point fields are indistinguishable. Spatial statistics have been used to compare sinkhole fields from four karst massifs in Spain with the projected maps of galaxies and to quantify the similarity of their spatial patterns. The spatial patterns of sinkholes are largely determined by the intersections of geological fractures, whereas astrophysicists and cosmologists hypothesise that galaxy clusters form at the intersections of filaments of dark matter. These are very different physical controls that result in similar spatial patterns.