Pentagonal star infinite zoom loop
Animated GIF
Inspired by this nice #mathart by Mrs Lister on Twitter.
How to
1) Create A=(0,1)
2) A'=Rotate(A, 72°)
3) penta=Polygon(A, A', 5). This creates the regular pentagon AA'BCD
4) Draw some diagonals to get intersection points G & H in the central pentagon to form the "brokenstar" pattern : Polygon(C, A', D, B, G, H)
5) The ratio between two broken-stars is phi², so define phi=(1+sqrt(5))/2.
N.B. If you didn't know this, you could have defined the ratio of two segments in GeoGebra to have the dilation factor.
6) Create the list Lstatic=Sequence(Dilate({brokenstar}, (1 / phi)^(2k), A), k, -2, 10)
This creates a bunch of stars but it's not moving yet
7) Create a slider b from 0 to 0.99 increment of 0.01.
Tip about the 0.99 : Set the max at 1-increment to have a seamless loop.
8) Dilate(Lstatic, phi^(2b), A)
This is the only thing to show, hide everything else.
9) Animate b (increasing)
10) Export to GIF, approx 50 ms per frame