Function Repository Resource:

LogDifferences

Find logarithmic differences of elements in a list

Contributed by: Stephen Wolfram

ResourceFunction["LogDifferences"][list]

gives the logarithmic differences of elements in list.

Details and Options

ResourceFunction["LogDifferences"][list] for a list with elements of the form n^p is equivalent to ConstantArray[p,Length[list]-1].

Log differences for a length-n list of powers gives a list with n-1 copies of the exponent:

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$ResourceFunction["LogDifferences"][Table[n^3, {n, 10}]]$

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Use a symbolic list:

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Find the connectivity graph for a Sierpiński mesh:

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Find successive average graph neighborhood volumes with the resource function GraphNeighborhoodVolumes:

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Plot the log differences, which show an effective dimension around 1.58:

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