A nested series of curvilinear stars

From the 2023 Maple Conference Art Gallery

We start with a pattern of nested stars where each star is nested in the previous one, its vertices touching
the point of contact of two successive branches of the previous star.
And we trace for each star the arcs of a circle which connect two successive vertices and whose center is
the point of contact of two successive branches.
For the vertices, we use the angle (1) of these for which the point of contact of two successive arcs of a
star touches the middle of the arc of a circle of the next nested star.
We thus obtain the drawing below having a certain resemblance to a cauliflower.
The colors are added with Paint software on Windows.

This pattern is created with my maplet found on Maple Application Center at:
https://fr.maplesoft.com/Applications/Detail.aspx?id=154588
(1) The specific angles are on my twitter account :
https://twitter.com/ElioC12/status/1543687167179984896?s=20