Escape Time Zooms of the Fibonacci Numbers The Fibonacci numbers are usually defined via a recursion: Fn+2= Fn+1 Fn, F0=0, and F1=1. The sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,.... These numbers may also be computed via a closed form known as the Binet formula.

It is:

where

and

.

That function can be vieed as a function of a complex variable and we consider here some zooms near two of the fixed points.

fib0.mov

fib5.mov

A J script which can generate such an image is: fib_v_fig3.html

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See also:

1. C. A. Reiter, Views of Fibonacci Dynamics, Computers & Graphics 28 2 (2004) 297-300. Preprint [1.7M], [Abstract]
   
2. The Fibonacci Association, http://www.mscs.dal.ca/Fibonacci/