Avigad introduced the notion of UD–randomness based in Weyl’s 1916 definition of uniform distribution modulo one. We prove that there exists a weakly 1–random real that is neither UD–random nor weakly 1–generic. We also show that no 2–generic real can Turing compute a UD–random real.
Calvert, Wesley and Franklin, Johanna. "Genericity and UD-random reals." Journal of Logic and Analysis 7, No. 4 (Jan 2015): 1--10.