2009/10/27 by Francisco R. Villatoro, Villatoro, Francisco R.
Materials Science · Mathematics · Physics and Astronomy · #28A80 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.0910.5014
openalex publication_date 2009/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic Cantor sets is introduced by means of properly defining operators for the addition, subtraction, multiplication, and division. The new operators have the usual properties of the corresponding operations with real numbers. The combination of an infinitesimal change of fractal dimension with these arithmetic operators allows the manipulation of fractal dimension with the tools of calculus.