I am trying to create a circular fractal in which each circle is composed by a given number $n$ of smaller circles.
It would look something like this for $n = 8$:
However, I don't know how to calculate the radius of the smaller circles.
Of course I know that the distance from the centre of the bigger circle to the centres of the smaller circles is $r_1 – r_2$, where $r_1$ is the radius of the bigger circle and $r_2$ is the radius of the smaller ones, and that their radius is $\frac{d}{2}$ where $d$ is the distance between two adjacent circles' s centres.
$d$ is for sure related to $n$ but I don't know how to calculate it.
Best Answer
Consider the triangle formed by the centers of two adjacent small circles and by the center of the outer circle; if the inner circles touch, then one has: $$ (r_1-r_2)\sin{\pi\over n}=r_2. $$ From that you can compute $r_2$: $$ r_2=r_1{\sin(\pi/n)\over1+\sin(\pi/n)}. $$