Fractal Property for A Novel Function generated by Generalized Approximate 3x+1 Functions

DOI

10.2991/mce-14.2014.82How to use a DOI?

Keywords

fractal; generalized 3x+1 function; generalized approximate 3x+1 function; convergence; escape time algorithm

Abstract

Today, study of generalized 3x+1 function becomes a highlight in fractal area. In this paper, since fractal property of generalized 3x+1 functions T(z) and C(z) is difficult to study, we study two approximate generalized 3x+1 functions B(z) and D(z), which are produced by T(z) and C(z), in the real axis. First, we provide a novel function A(z) from two functions B(z) and D(z), which are extended by T(z) and C(z). Then, we analyze fractal property of A(z), and point out that the fractal properties of A(z) contains the information of B(z) and D(z). Finally, we draw the fractal figures of A(z) by escape time algorithm. These fractal figures validate our conclusion of A(z).

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jia Wang
AU  - Xin Li
PY  - 2014/03
DA  - 2014/03
TI  - Fractal Property for A Novel Function generated by Generalized Approximate 3x+1 Functions
BT  - Proceedings of the 2014 International Conference on Mechatronics, Control and Electronic Engineering
PB  - Atlantis Press
SP  - 369
EP  - 372
SN  - 1951-6851
UR  - https://doi.org/10.2991/mce-14.2014.82
DO  - 10.2991/mce-14.2014.82
ID  - Wang2014/03
ER  -