# Stack Diagram for 1D Box-Counting Steps

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The box-counting dimension [1–4] can be defined as

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Contributed by: Ki-Jung Moon (December 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Box counting is a method of gathering data for analyzing complex patterns by breaking a dataset, object, image, etc. into smaller and smaller pieces, typically "box" shaped, and analyzing the pieces at each smaller scale [1].

References

[1] Wikipedia. "Box Counting." (Feb 1, 2013) en.wikipedia.org/wiki/Box_counting.

[2] B. Mandelbrot, *The Fractal Geometry of Nature*, San Francisco: W. H. Freeman, 1982.

[3] H.-O. Peitgen, H. Jürgens, and D. Saupe, *Chaos and Fractals: New Frontiers of Science*, 2nd ed., New York: Springer, 2004.

[4] S. Wolfram, *A New Kind of Science*, Champaign, IL: Wolfram Media, 2002.

[5] R. May, "Simple Mathematical Models with Very Complicated Dynamics," *Nature*, 261(5560), 1976 pp. 459–467.

[6] M. J. Feigenbaum, "Quantitative Universality for a Class of Non-Linear Transformations," *Journal of Statistical Physics*, 19, 1978 pp. 25–52.

[7] M. J. Feigenbaum, "The Universal Metric Properties of Nonlinear Transformations," *Journal of Statistical Physics*, 21, 1979 pp. 669–706.

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