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Attraction in Positive Direction of Real Axis of Two Generalized 3x + 1 Functions

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Green Communications and Networks

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 113))

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Abstract

To study attractive character of two generalized 3x + 1 functions T(z) and C(z) at positive direction of real axis, at first, we define attractive domain and series. Secondly, we analyze attractive domain and series of T(z) and C(z) and point out the structure of attractive domains surrounding the same attractive series that are similar to each other. Finally, we draw the fractal figures of the two functions by escape time algorithm and validate the structure rule of the attractive domain and series of T(z) and C(z) from the figures.

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Author information

Authors and Affiliations

  1. Software College, Changchun Institute of Technology, Room 205, The 9th Teaching Building, No. 2494, Hongqi Street, Changchun, 130012, China

    Liu Shuai & Fu Weina

  2. College of Computer Science and Technology, Jilin University, B234, The Computer Building, No. 2699, Qianjin Street, Changchun, 130021, China

    Liu Shuai, Ke Hongchang & Wang Xin

Authors
  1. Liu Shuai
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  2. Fu Weina
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  3. Ke Hongchang
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  4. Wang Xin
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Corresponding author

Correspondence to Liu Shuai .

Editor information

Editors and Affiliations

  1. , Department of Electronic Engineering, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai, 200240, China, People's Republic

    Yuhang Yang

  2. , Electrical & Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore

    Maode Ma

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© 2012 Springer Science+Business Media B.V.

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Shuai, L., Weina, F., Hongchang, K., Xin, W. (2012). Attraction in Positive Direction of Real Axis of Two Generalized 3x + 1 Functions. In: Yang, Y., Ma, M. (eds) Green Communications and Networks. Lecture Notes in Electrical Engineering, vol 113. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2169-2_81

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  • DOI: https://doi.org/10.1007/978-94-007-2169-2_81

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-2168-5

  • Online ISBN: 978-94-007-2169-2

  • eBook Packages: EngineeringEngineering (R0)

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