  We study four (families of) sets of algebraic integers of degree less than or
equal to three. Apart from being simply defined, we show that they share two
distinctive characteristics: almost uniformity and arithmetical independence.
Here, ``almost uniformity'' means that the elements of a finite set are
distributed almost equidistantly in the unit interval, while ``arithmetical
independence'' means that the number fields generated by the elements of a set
do not have a mutual inclusion relation each other. Furthermore, we reveal to
what extent the algebraic number fields generated by the elements of the four
sets can cover quadratic or cubic fields.
