To play around with these ideas, I wrote a script in p5js that allows you to vary that angle:
So, you can create some beautiful patterns, and with the laser cutter, you could cut out the circles. But I was also interested in the idea of the dots representing the center of cells. Enter the Voronoi diagram. Given a set of points, it finds cells containing those points, with the property that any border that separates two points is equidistant from the points.
We think this evokes the idea of biological cells, and led to our abstract Cellular Clock: