Fractal sets, by definition, are non-differentiable, however their dimensioncan be continuous, differentiable, and arithmetically manipulable as functionof their construction parameters. A new arithmetic for fractal dimension ofpolyadic Cantor sets is introduced by means of properly defining operators forthe addition, subtraction, multiplication, and division. The new operators havethe usual properties of the corresponding operations with real numbers. Thecombination of an infinitesimal change of fractal dimension with thesearithmetic operators allows the manipulation of fractal dimension with thetools of calculus.
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