For a hyperbolic knot or link K the volume density is a ratio of hyperbolic volume to crossing number, and the determinant density is the ratio of 2\pi\log(det(K)) to the crossing number. We explore limit points of both densities for families of links approaching semi-regular biperiodic alternating links. We explicitly realize and relate the limits for both using techniques from geometry, topology, graph theory, dimer models, and Mahler measure of two-variable polynomials. This is joint work with Ilya Kofman and Jessica Purcell. Speaker(s): Abhijit Champanerkar (CUNY)