Sterling Roth writes:
Inspired by the dense, uniform packing of mirror tiles on a disco ball, I attempted to recreate the effect in Blender's geometry nodes.
The main challenge was finding the spiral path the tiles are placed on around the ball. Some research led me to the formula for a spherical helix.
Now all I had to do was convert the formula to math nodes:
While it may look scary, the trick is to just go piece by piece, and remember your order of operations! The mnemonic I always remember is: Please Excuse My Dear Aunt Sally - Parenthesis, Exponents, Multiply, Divide, Add, Subtract.
Once the math for the spiral was worked out, I used that to set the positions of vertices in a mesh line primitive, which was converted to curve and resampled to get the even spacing. Check out the Blender artists post for more information, and a free, CC0 download of the .blend file.