The Fractal Dimensions of Lithic Reduction

The Broken Past: Fractals in Archaeology

“…Many chert and obsidian debitage size-frequency distributions are fractal (Brown, 1999;Brown, 2001). That is, the number of pieces of debitage of different sizes constitutes a fractal frequency distribution.…”

“…Many, although not all, datasets from experimental reduction of stone tools exhibit power-law frequency distributions. Their fractal dimensions range from 1.2 to 3.3 (Brown, 2001, Table II). Archaeological assemblages of debitage also exhibit fractal size-frequency distributions (Brown, 1999;Brown, 2001).…”

“…Their fractal dimensions range from 1.2 to 3.3 (Brown, 2001, Table II). Archaeological assemblages of debitage also exhibit fractal size-frequency distributions (Brown, 1999;Brown, 2001). For such fractal datasets, the fractal method is, by far, the simplest and the mathematically most correct way of evaluating the frequencies of various sizes of debitage.…”

“…The fractal dimension of an assemblage of debitage is a measure of stage of reduction (Brown, 2001). This makes sense because the fractal dimension quantifies the proportion of small to large flakes, and the proportion of small flakes normally increases with stage of reduction, so it is logical that the fractal dimension should correlate with stage of reduction.…”

Fractal Worlds: An Archaeology of Nested Spatial Scales

“…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.…”