We describe the appearance of the dynamics associated to the tangent bifurcation in low dimensional nonlinear maps in descriptions of condensed matter and in complex systems. We first recall the basic features of the intermittency route to chaos via this kind of bifurcation and then we give an account of two precise equivalences between apparently different physical problems. The first one concerns the electronic transport properties obtained via the scattering matrix of a solid defined on a double Cayley tree. This strict analogy reveals in detail the nature of the mobility edge normally studied near (not at) the metal-insulator transition in electronic systems. The second relates to the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity. The analogy effortlessly, and quantitatively, reproduces the bends or tails observed in real data for small and large rank. It also suggests a possible thermodynamic structure underlying these empirical laws as a further equivalence can be established with cluster fluctuations at criticality. Finally, we comment on a discrete-time version of the replicator equation for two-strategy games for which intermittency is expected to occur.