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Many archaeological patterns are fractal. Fractal analysis, therefore, has much to contribute to archaeology. This article offers an introduction to fractal analysis for archaeologists. This article explains what fractals are, describes the essential methods of fractal analysis, and presents archaeological examples. Some examples have been published previously, while others are presented in this article appear for the first time. The authors 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 efforts to understand nonlinearities in past cultural dynamics.