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Chaotic behavior of the transcendental mapping (Z→cosh (Z)+μ)

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Abstract

This note presents graphically interesting behavior in chaotic systems defined by iterates of the transcendental function (z→cosh (z)+μ).

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References

  1. Fisher A (1985) Chaos: the ultimate asymmetry. Mosaic 16:24–30

    Google Scholar 

  2. Peterson I (1986) Toying with a touch of chaos. Science News 129:277–278

    Google Scholar 

  3. Devaney R, Krych M (1984) Dynamics of exp(z). Ergodic Theory Dyn Syst 4:35–52

    Google Scholar 

  4. Peitgen H, Richter P (1986) The beauty of fractals. Springer, Berlin Heidelberg New York

    Google Scholar 

  5. Mandelbrot B (1982) The fractal geometry of nature. Freeman, San Francisco

    Google Scholar 

  6. Pickover C (1989) Computers, pattern, chaos and beauty. Springer, Berlin Heidelberg New York (in press)

    Google Scholar 

  7. Pickover C (1989) How to design using recursive composite functions. Leonardo 22(2) (in press)

  8. Pickover C (1988) Overrelaxation and chaos. Phys Lett A 30(3):125–128

    Google Scholar 

  9. Pickover C (1988) A note on rendering chaotic “repeller distance-towers”. Comput Phys 2(3):75–76

    Google Scholar 

  10. Pickover C (1988) From noise comes beauty: textures remniscent of rug weavings and wood grains spring from simple formulas (mathematics and beauty X). Comput Graph World 11(3):115–116

    Google Scholar 

  11. Pickover C (1988) Mathematics and beauty XI: a sampling of spirals and “strange” spirals in nature, science, and art Leonardo 21 (2):173–181

    Google Scholar 

  12. Pickover C (1988) A note on rendering 3-D strange-attractors. Comput Graph 12(2):263–267

    Google Scholar 

  13. Pickover C (1987) Blooming integers: an elegantly simple algorithm generates complex patterns (mathematics and beauty III) Comput Graph World 10(3):54–57

    Google Scholar 

  14. Pickover C (1988) Pattern formation and chaos in networks. Commun ACM 31(2):136–151

    Google Scholar 

  15. Pickover C (1987) Biomorphs: computer displays of biological forms generated from mathematical leed back loops. Comput Graph Forum 5(4):313–316

    Google Scholar 

  16. Peterson I (1987) Portraits of Equations. Science News 132(12):184–186 (and cover picture).

    Google Scholar 

Download references

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, NY, USA

    Clifford A. Pickover

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  1. Clifford A. Pickover
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Pickover, C.A. Chaotic behavior of the transcendental mapping (Z→cosh (Z)+μ). The Visual Computer 4, 243–246 (1988). https://doi.org/10.1007/BF01901279

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  • DOI: https://doi.org/10.1007/BF01901279

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