Visualizing generalized \(3x+1\) function dynamics based on fractal

DOI10.1016/j.amc.2006.07.168zbMath1116.37034OpenAlexW2003073348MaRDI QIDQ2371424

Xuejing Yu, Xing-Yuan Wang

Publication date: 4 July 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.07.168

zbMATH Keywords

dynamicsstopping timeescape timefractaltotal stopping timegeneralized \(3x+1\) function

Mathematics Subject Classification ID

Recurrences (11B37) Fractals (28A80) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems involving maps of the interval (37E05)

Cites Work

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• Number theory in science and communication. With applications in cryptography, physics, digital information, computing, and self-similarity.
• The dynamical system generated by the \(3n+1\) function
• The autoconjugacy of the \(3x+1\) function.
• A linear algebra approach to the conjecture of Collatz
• The 3x+ 1 Conjugacy Map
• The 3x + 1 Problem and Its Generalizations
• A stopping time problem on the positive integers
• A Non-Iterative 2-Adic Statement of the 3N + 1 Conjecture
• The set of rational cycles for the 3x+1 problem
• On a generalization of the \(3x+1\) problem

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