Trick 1: How to find spirals with n arms.

Example: S5, 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 fn (=f o f o...o f) where f(z)=z2+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
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