Small digitwise perturbations of a number make it normal to unrelated bases
(Lobachevskii Journal of Mathematics, Volume XI)
Let r, g ≥ 2 be integers such that logg/logr is irrational. We show that under r-digitwise random perturbations of an expanded to base r real number x, which are small enough to preserve r-digit asymptotic frequency spectrum of x, the g-adic digits of x tend to have the most chaotic behaviour.