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A Clustering Perspective of the Collatz Conjecture

Author

Listed:
  • José A. Tenreiro Machado

    (Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
    These authors contributed equally to this work.)

  • Alexandra Galhano

    (Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • José A. Tenreiro Machado & Alexandra Galhano & Daniel Cao Labora, 2021. "A Clustering Perspective of the Collatz Conjecture," Mathematics, MDPI, vol. 9(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:314-:d:493818
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    References listed on IDEAS

    as
    1. Frank Emmert-Streib, 2013. "Structural Properties and Complexity of a New Network Class: Collatz Step Graphs," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-14, February.
    2. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    3. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    4. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
    5. de Leeuw, Jan & Mair, Patrick, 2009. "Multidimensional Scaling Using Majorization: SMACOF in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i03).
    Full references (including those not matched with items on IDEAS)

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