First, however, a little bit about technique: The magnitude of a particular data set, whatever its source, is ranked from greatest to least. Then, fractal binning is applied over a range of dimensions. The maximum dimension is D(max) = 2*n, in which the value of n produces the smallest value larger than the maximum magnitude of the data set. Each dimension is then determined by D(I) = D(maximum)/M, in which M = 2*N/M, M =1, M*. Each bin I for dimension D(I) is occupied if there is one or more values such that bin I = integer (magnitude/D(i)). Then for each dimension, the number of occupied bins is totaled.

First example: Number of performances of Broadway musicals, ranked from most to least, for the top 100 (not counting some which are still running).

The longest running musicals (Andrew Lloyd Webber's

*Cats*is the current leader among closed shows; however his*Phantom of the Opera*is still running).Note that a true fractal would display a linear trend on a log-log plot. However a simple linear trend is apparent for only the top two bins, not one extended over a longer range of scales.

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