Fractal Property for A Novel Function generated by Generalized Approximate 3x+1 Functions
Jia Wang, Xin Li
Available Online March 2014.
- https://doi.org/10.2991/mce-14.2014.82How to use a DOI?
- fractal; generalized 3x+1 function; generalized approximate 3x+1 function; convergence; escape time algorithm
- 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).
- 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 -