@simontatham
Hmm, don't know about the dots.
Maybe you could personalize them by putting faces on them.

One inspiration I got from Bosman's book is "generalized Yin Yang". You can subdivide the circle into parts that have both equal area and equal circumference. The lines defining the subdivisions are all circle segments with integer relative diameters.
The Yin Yang is a powerful symbol. The rainbow is also often used these days to symbolize diversity. I was quite pleased with the possibility of combining these 2 symbols.