In 2013, Avigad introduced a notion of randomness based on Weyl's 1916 work on uniform distribution modulo one: a real $x$ is said to be UD- random if the sequence $\langle a_i x angle$ is uniformly distributed on the unit interval for any computable sequence of distinct integers $\langle a_i angle$. I will review Avigad's work and then present some new results on the relationship between the UD-random reals and other classes of random and generic reals.

This work is joint with Wesley Calvert.