Fractals are not really new. I met them back in the early 90’s while trying to find answers to peculiarities of data series for a chapter of my PhD thesis. It was just before the release of the movie about the announced doom of (any) Jurassic Park, which popularized the scientific awareness that natural (non linear) systems are unpredictable, what is known as the deterministic chaos.
Fractals are, lets say, the geometry by which chaotic systems express themselves, both in space or time. They are characterized by having a fractionated number as dimension. The name fractal comes from this, the fact that its dimension is not an integer number as Euclidian space objects. Being a fractal means that it reveals the property of self-similarity, i.e. have the same pattern repeating itself at different space or time scales, like Russian dolls harboring inside smaller and smaller replicas of themselves.
Following a wide range of applications of the fractal concept, geometry and dimensionality to natural objects (e.g. trees, lungs, circulatory system, irregular surface relieves) and processes (e.g. ecological succession; well this one, derived from my own research, still needs to be independently proven), applications of fractals to Paleontology are known from, for instance, the shape analysis of Ammonite suture lines or the branching organization of the Ediacaran rangeomorph fronds.
The novelty of this new paper is that attention is now focussed on the spatial distribution of the fossiliferous outcrops themselves. Fossils occur at the surface as the end product of a long and complex interplay of natural processes, ranging from the paleobiogeographic conditions of the producer of the fossil precursor (we call it the subfossil) itself, to a variety of fossildiagenetic processes, that may include tectonic deformation and even low grade regional metamorphism. In the end, antropogenic actions (such as constructions, road or rail cutting or dam excavations) also have to be considered as determinant for the discovery of an orictocoenoses, the scientific term for an assemblage of fossils inside its geological context, the rocks.
Image credit: click for source
Title: “Recurrent hierarchical patterns and the fractal distribution of fossil localities”
Author: Roy E. Plotnick
Read it online: full-text available here
“Understanding the spatial structure of fossil localities is critical for interpreting Earth system processes based on their geographic distribution. Coordinates of marine and terrestrial sites in the conterminous United States for 17 time bins were analyzed using point pattern statistics. Lacunarity analysis shows that the spatial distributions of sites are fractal for almost every studied interval, indicating that clumping of localities occurs at multiple scales. Random hierarchical multiplicative processes provide a theoretical null model for the distribution of collecting sites, consistent with their occurrence being a complex product of numerous biological, geological, and anthropogenic processes acting at many spatial and temporal scales. Mechanistic models for the formation, preservation, and exposure of fossil localities and other geologic entities can be tested using point pattern and related spatial statistics.”
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