We study wave packet systems WP(ψ,M); that is, countable collections of dilations, translations, and modulations of a single function ψ ∈ L2(R). The parameters of these unitary actions form a discrete subset M ⊂ R+ × R × R. We introduce analogues of the notion of Beurling density, adapted to the geometry of discrete subsets of R+ × R × R, and notions of lower and upper dimensions associated wit...