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Formulae for cycles in the Maldelbrot set III

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  • Stephenson, John

Abstract

The analytical solutions to the parts of the boundary of the Mandelbrot set associated with cycles of order 7 and 8 are obtained by an arithmetic method in the form of polynomials. The “inverse orbit” method of calculating the values of cycle centres is extended to complex cases, and applied to cycles up to order 10. Some geometrical aspects of the various cardioids and bubbles are explored.

Suggested Citation

  • Stephenson, John, 1992. "Formulae for cycles in the Maldelbrot set III," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 190(1), pages 117-129.
    • Handle: RePEc:eee:phsmap:v:190:y:1992:i:1:p:117-129
    DOI: 10.1016/0378-4371(92)90081-Z
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    1. Stephenson, John & Ridgway, Douglas T., 1992. "Formulae for cycles in the Mandelbrot set II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 190(1), pages 104-116.
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