The Broken Past: Fractals in Archaeology

Abstract

Many archaeological patterns are fractal. Fractal analysis, therefore, has much to contribute to archaeology. This article offers an introduction to fractal analysis for archaeologists. We explain what fractals are, describe the essential methods of fractal analysis, and present archaeological examples. Some examples have been published previously, while others are presented here for the first time.We also explain the connection between fractal geometry and nonlinear dynamical systems. Fractals are the geometry of complex nonlinear systems. Therefore, fractal analysis is an indispensable method in our efforts to understand nonlinearities in past cultural dynamics.

Islands of Inquiry: Colonisation, seafaring and the archaeology of maritime landscapes (TA29) : Colonisation, seafaring and the archaeology of maritime landscapes

“…They characterise certain uneven patterns of diffusion. To paraphrase Brown et al (2005Brown et al ( , 2007; also Ravilious 2006), they are a form of random walk. In Brownian motion, the best-known kind of random walk, the sizes of the steps are normally distributed ( In contrast, Lévy flights exhibit step lengths with distributions characterised by 'power-law tails' (Figure 1).…”

Fractal Worlds: An Archaeology of Nested Spatial Scales

“…Perhaps surprisingly, they exist throughout nature, for example, in the form of a fern with branching pinnas that are in turn composed of branching pinnules, the overall structure of the plant replicated at each scalar involution. Self-similarity is not always a characteristic of archaeologically interesting patterns (though it sometimes is, as in the repetitive branchings of roads, trails, and paths, or the distribution of debitage size classes; Brown et al, 2005), but interesting patterning of some form certainly exists at ever-increasing and everdecreasing remove. Not only archaeologists attend to such changes in scale: the past people we study did so too, manipulating these changes for aesthetic effect, or to illuminate other kinds of meaningful structure.…”

“…By centering and unifying the phenomenological universe, the human body-the subject par excellence of discursive miniaturization-serves to anchor this scalar slipperiness, and so provides a valuable analytic key for exploring the way that people in the past conceptualized their worlds. Following Zubrow's (2007) pioneering application of fractal analysis to architecture and tool types, archaeologists have taken it up for the analysis of lithic reduction sequences, ceramic fragmentation and decoration, settlement structure and growth, and colonization processes, among other things (Brown, 2001;Brown et al, 2005;Lilley, 2008;Diachenko, 2013). Fractional ("fractal") dimensions can be derived for a wide range of commonly quantified archaeological phenomena, such as the frequency of debitage of diminishing size classes (Brown et al, 2005:47 -52) or the distribution of sites across a range of settlement size classes (Diachenko, 2013), employing the sorts of procedures mathematically illustrated by Mandelbrot.…”

Fractal analysis of canopy architectures of Acacia angustissima, Gliricidia sepium, and Leucaena collinsii for estimation of aboveground biomass in a short rotation forest in eastern Zambia

“…The fractal theory is based on the existence, within an object, of self similarity arising from repeated iteration of a structural unit which forms a nested replica of the object at multiple scales and the same rules govern branching at each subsequent level (van Noordiwjk and Mulia 2002;Richardson and zu Dohna 2003;Koziowski et al 2004;Brown et al 2005;Price and Enquist 2007;Allen et al 2008). In plants, canopy branching has a fractal pattern if the rules governing branching are independent of scale (Gisiger 2001;Camarero et al 2003;Halley et al 2004;Brown et al 2005;Makela and Valentine 2006).…”

“…In plants, canopy branching has a fractal pattern if the rules governing branching are independent of scale (Gisiger 2001;Camarero et al 2003;Halley et al 2004;Brown et al 2005;Makela and Valentine 2006). The fundamental physical and biological principles as well as features of architecture, biomechanics, and hydrodynamics of vascular plants determine branching pattern in trees (West et al 1999;Enquist 2002).…”