Proceedings of the 2014 International Conference on Mechatronics, Control and Electronic Engineering

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

Authors
Jia Wang, Xin Li
Corresponding Author
Jia Wang
Available Online March 2014.
DOI
https://doi.org/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).
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Proceedings
2014 International Conference on Mechatronics, Control and Electronic Engineering (MCE-14)
Part of series
Advances in Intelligent Systems Research
Publication Date
March 2014
ISBN
978-94-62520-31-8
ISSN
1951-6851
DOI
https://doi.org/10.2991/mce-14.2014.82How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

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  - 2014 International Conference on Mechatronics, Control and Electronic Engineering (MCE-14)
PB  - Atlantis Press
SP  - 369
EP  - 372
SN  - 1951-6851
UR  - https://doi.org/10.2991/mce-14.2014.82
DO  - https://doi.org/10.2991/mce-14.2014.82
ID  - Wang2014/03
ER  -