Multidimensional scaling and visualization of patterns in prime numbers

This paper explores the prime numbers (PN) in the perspective of complex systems (CS) using computational and information visualization resources. The PN are interpreted as features that characterize the outputs of a CS. Four distinct metrics are adopted to assess the differences between such objects, namely the Canberra, Euclidean, Jaccard and Lorentzian distances, and the information is treated with a multidimensional scaling (MDS) algorithm. The MDS produces loci, organized according with the objects' features, that are analyzed under the light of the emerging patterns. Additionally, these patterns are explored in the Fourier domain under the point of view of fractional calculus. The representations constitute a new philosophy for tackling the challenging topic of PN using advanced scientific visualization. (C) 2019 Elsevier B.V. All rights reserved.