Internal Cantor distance and entropy of multidimensional Peano-Hilbert spaces (Q2366782)

The author proposes certain algorithms for characterizing the internal structure of infinite point sets and determining a corresponding average dimension. An algorithm is proposed also for determining the average internal distance between different points of a Cantor set. The author concludes that Cantorian space-time is based on an average Cantorian distance of about 0.629 while smooth space-time is retrieved when the average Cantorian distance tends to 0.5 which is interpreted to mean that the average Cantorian distance tends towards the average distance of a continuous smooth line at vanishing resolution when space is viewed from a great distance.