A Clustering Perspective of the Collatz Conjecture
José A. Tenreiro Machado,
Alexandra Galhano,
Daniel Cao Labora
Affiliations
José A. Tenreiro Machado
Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Alexandra Galhano
Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Daniel Cao Labora
Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, Institute of Mathematics (IMAT), Universidade de Santiago de Compostela (USC), Rúa Lope Gómez de Marzoa s/n, 15782 Santiago de Compostela, Spain
This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of why is it hard from the mathematical point of view. The second part is dedicated to the visualization of behaviors of the Collatz iteration function and the analysis of the results.
