Towards the bottom of the wikipedia article on Parametric Equations - https://en.wikipedia.org/wiki/Parametric_equation - there is a section entitled "Some sophisticated functions". The first two of these functions can be used to make coasters. Pictures of the functions are at - https://commons.wikimedia.org/wiki/File:Param_02.jpg - and at - https://commons.wikimedia.org/wiki/File:Param_03.jpg - The openSCAD code can be used to construct any of the pictured functions. Here are 9 coasters based on the two functions.

MakerBot

MakerBot Replicator (5th Generation)

Doesn't Matter

0.3 mm

OpenSCAD code is included which lists the parameters passed to the modules creating the coasters. Other interesting coasters can be made by trying different combinations of the parameters. Param3_mark5.stl, which possibly resembles a face, came from trial experiments. It is the central figure in the image above.