Generalized Binet dynamics

  • Authors:

  • Chen Ning;Clifford A. Reiter

  • Affiliations:

  • Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168, China;Department of Mathematics, Lafayette College, Easton, PA 18042, USA

  • Venue:
  • Computers and Graphics
  • Year:
  • 2007

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Abstract

The Binet formula provides a mechanism for the Fibonacci numbers to be viewed as a function of a complex variable. The Binet formula may be generalized by using other bases and multiplicative parameters that also give functions of a complex variable. Thus, filled-in Julia sets that exhibit escape time may be constructed. Moreover, these functions have computable critical points and hence we can create escape time images of the critical point based upon the underlying multiplicative parameter. Like the classic Mandelbrot set, these parameter space images provide an atlas of Julia sets.