08-PowerLaws

08-PowerLaws - 3/25/2008 Stubborness: Depth Frequency...

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3/25/2008 1 Stubborness: Depth Frequency Relationships in Snow Avalanches 1 2 3 4 ± Power law distributions show scale invariance. ± A shape which resembles itself at all scales is called fractal. ± Fractal , a term invented by Benoit Mandelbrot. From latin adj. fractus : broken into irregular pieces. ± Fractals are scale invariant . 5 From: The Fractal Geometry of Nature Image from: ht p:/ upload.wikimedia.org/wikipedia/commons/2/20/Britain-fractal-coastline-combined.jpg 6
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3/25/2008 2 ± Mandelbrot (1982) says that a power law distribution has a geometric equivalent. He uses a lexiconographic tree as an example of a book’s word frequency distribution. ± Therefore power law distributions are intimately linked with fractal shapes . From: The Fractal Geometry of Nature 7 Rosenthal, W., and K. Elder (2003), Evidence of chaos in slab avalanching, Cold Reg. Sci. Tech. , 37 , 243-253. 8 Frequency 9 Clauset, A., and Cosma Rohil a Shalizi, and M. E. J. Newman (2007), Power-law distributions in empirical data, edited. ± (m) Population of cities in the United States.
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This note was uploaded on 08/06/2008 for the course ESM 236 taught by Professor Dozier during the Spring '08 term at UCSB.

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08-PowerLaws - 3/25/2008 Stubborness: Depth Frequency...

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