Example: S_{5}, spiral with 5 arms.

The centre of the Mandelbrot set is a cardioid; it is surrounded by
circles (a circle number n corresponds to a set of fixed points of the
function f^{n} (=f o f o...o f) where f(z)=z^{2}+c).

More Theory about this series of circles

(comparison with figure 34 on page 61 of '**Beauty of Fractals**')

In order to get spirals with 5 arms, we zoom in a circle number 5:

The circle 'ends' with a star (a degenerated spiral!) with 5 arms; on
both sides of the star there are spirals with 5 arms:

* the directions of rotation are opposite on both sides

* farer from the centre the arms are more twisted.

Here is a zoom of one such spiral:

Created: 1996-08 ; Last update: 1997-03-31

Homepage http://www2.vo.lu/homepages/phahn