Quick edit of the diamonds coaster design ( https://www.thingiverse.com/thing:2772489 ) with circles instead of diamonds.

This visually pleasing circles design is based on the number Phi, "the golden ratio," and can be edited in the OpenSCAD file included. There are only two variables to change, the size of the circles, and the width of the lines. The coaster itself is 10cm in diameter, which should be large enough for almost any cup you can throw on it.

I've included .stl for 10mm size circles with 2mm width lines. If you'd like any other sizes uploaded in .stl form let me know, but the OpenSCAD file can help you there. Just edit 2 vars, render, export, slice, print, and enjoy!

I plan to make a few more geometric 'designs' for this same type coaster 'base' as well as a coaster holder for them soon, too.