Chen Ning and Clifford A. Reiter, Generalized Binet Dynamics, Computers & Graphics, 31 (2007) 301-307.

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 give a type of atlas into the Julia sets.

See also: · Some Images and animations related to the paper [Auxiliary Materials for Generalized Binet Dynamics] [Preprint] · A related paper: Escape Time Zooms of the Fibonacci Numbers [Abstract] [Auxiliary Materials]