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: