Fall2005.ZipfIntro History
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In physics, Zipf's law is a special case of a power law. When n is 1 (Zipf's ideal), the phenomenon is called ''1/f'' or pink noise. When n is 0 it is called white noise. When n is 2 it is called ''1/f'''^2^' or brown(ian) noise [6]. Zipf (''1/f'', pink noise) distributions have been discovered in a wide range of human and naturally occurring phenomena, including city sizes, incomes, subroutine calls, earthquake magnitudes, thickness of sediment depositions, clouds, trees, extinctions of species, traffic jams, and visits to websites [1 through 11].
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In physics, Zipf's law is a special case of a power law. When n is 1 (Zipf's ideal), the phenomenon is called ''1/f'' or pink noise. When n is 0 it is called white noise. When n is 2 it is called ''1/f'''^2^' or brown(ian) noise [6]. Zipf (''1/f'', pink noise) distributions have been discovered in a wide range of human and naturally occurring phenomena, including music, city sizes, incomes, subroutine calls, earthquake magnitudes, thickness of sediment depositions, clouds, trees, extinctions of species, traffic jams, and visits to websites [1 through 11].
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Surprisingly, if we compare a word’s frequency of occurrence with its [[http://mathworld.wolfram.com/StatisticalRank.html  statistical rank]], we notice an inverse relationship: successive word counts are roughly proportional to 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, and so on [4]. This is captured by the formula:
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Surprisingly, if we compare a word’s frequency of occurrence with its [[http://mathworld.wolfram.com/StatisticalRank.html  statistical rank]], we notice an inverse relationship: successive word counts are roughly proportional to 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, and so on [4]. This is captured by the formula:
Changed lines 2021 from:
In physics, Zipf's law is a special case of a power law. When n is 1 (Zipf's ideal), the phenomenon is called 1/f or pink noise. When n is 0 it is called white noise. When n is 2 it is called brown noise. Zipf (1/f, pink noise) distributions have been discovered in a wide range of human and naturally occurring phenomena, including city sizes, incomes, subroutine calls, earthquake magnitudes, thickness of sediment depositions, clouds, trees, extinctions of species, traffic jams, and visits to websites [1 through 10].
to:
In physics, Zipf's law is a special case of a power law. When n is 1 (Zipf's ideal), the phenomenon is called ''1/f'' or pink noise. When n is 0 it is called white noise. When n is 2 it is called ''1/f'''^2^' or brown(ian) noise [6]. Zipf (''1/f'', pink noise) distributions have been discovered in a wide range of human and naturally occurring phenomena, including city sizes, incomes, subroutine calls, earthquake magnitudes, thickness of sediment depositions, clouds, trees, extinctions of species, traffic jams, and visits to websites [1 through 11].
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by website's [[http://mathworld.wolfram.com/StatisticalRank.html  statistical rank]] (xaxis) on log scale [8].
In general, the slope may range from 0 to ''negative infinity'', with –1.0 denoting Zipf's ideal. A slope near 0 indicates a random probability of occurrence (e.g., having yaxis values generated by @@Math.random()@@). A slope tending towards ''negative infinity'' indicates a monotonous phenomenon (i.e., one event predominates). It has been suggested that a slope near –1.0, corresponds to a balance that feels natural and even aesthetically pleasing to humans, for certain phenomena, such as music, urban structures, and landscapes [3, 6, 9].
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by website's [[http://mathworld.wolfram.com/StatisticalRank.html  statistical rank]] (xaxis) on log scale [9].
In general, the slope may range from 0 to ''negative infinity'', with –1.0 denoting Zipf's ideal. A slope near 0 indicates a random probability of occurrence (e.g., having yaxis values generated by @@Math.random()@@). A slope tending towards ''negative infinity'' indicates a monotonous phenomenon (i.e., one event predominates). It has been suggested that a slope near –1.0, corresponds to a balance that feels natural and even aesthetically pleasing to humans, for certain phenomena, such as music, urban structures, and landscapes [3, 7, 10].
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Zipf was independently wealthy; it is believed that he published his last book with his own money. Since electronic computers were unavailable at the time, he collected data by hiring human "computers" to count words in newspapers, books, and periodicals for numerous days at a time [11].
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Zipf was independently wealthy; it is believed that he published his last book with his own money. Since electronic computers were unavailable at the time, he collected data by hiring human "computers" to count words in newspapers, books, and periodicals for numerous days at a time [12].
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# Bourke, P. (1998). [[http://local.wasp.uwa.edu.au/~pbourke/fractals/noise/  "Generating noise with different power spectra laws"]], accessed October 26, 2006.


