This was modeled with a small OpenSCAD file--less than 30 lines in all. If you choose to edit and compile the OpenSCAD file yourself, be patient. On my PC it took nearly an hour to compile. The Thingiverse community probably doesn't need Yet One More Coaster Model, but it seemed a practical use for the concept.

The spiral pattern of spheres uses the Golden Ratio in much the same way as the arrangement of tiny flowers in a sunflower head.